This is a separate document.
This document is intended especially to convert Anglo-Saxon
measures into metric (=European-continental) measures. It
consists of separate tables for linear, cubic, etc. measures.
Biblical, monetary and some important physical numbers have
also been enlisted in this document, in separate tables. The
document consists of three parts:
This chapter is the manual about how to read the tables. The second chapter shows the important differences between the Metric and the Anglo-Saxon measure system. The third chapter shows some conversion factors between the different Anglo-Saxon measure systems of the same class (e.g. between AVDP and Troy). This chapter is also a helpful introduction to the separate document of Part 4. The following five chapters together form the second part of the document. They contain the tables with the conversion of the measures. The last five chapters together form the third part of the document. They contain other conversion factors, even monetary ones. At the end of every section a text line can be clicked to return to the contents list.
The document is made such that it is useful for the scientists, the engineers, the merchants and the 'ordinary people'. Consequently some of the comments to the tables (especially those in the chapter about the earth sciences) may be too difficult for the non-scientists. They should not worry about this and simply skip those comments and look directly at the tables. The only consequence of this skip is that the accuracy of the figures in the tables can be interpreted wrongly and thus is lessened. Since even then enough accuracy is left for the ordinary daily life this decrease does not harm at all.
Great care has been taken to make the textes and tables in this document comprehensive and reliable. Still errors and flaws may have slipped in.
Copying this document or parts of it for commercial sale of these copies is prohibited. Useage of the document is free of license.
DISCLAIMER
The author of the document can never be held
responsible for damages and injuries that might have
resulted from erroneous or inaccurate data in this document.
He is also not responsible for misinterpretations by the
reader and their consequences.
!!This section is very important and should not be skipped!!
In this document all quantitative values are displayed with the numbers consisting of the well-known ten digits (0 to 9) and the few punctuation marks. Everyone uses this notation system daily. But nearly nobody knows that this system has its roots in the ancient Hinduistic India. One may call it the 'extended Indian number-system'.
In this document sometimes numbers are written with spaces between groups of digits. These spaces are for readability and don't have any meaning. Thus 123 45 equals 12345. In imitation of the Americans the period is used to separate the fraction from the integral part. This period is called "decimal point". The comma is not used at all.
The symbol @ in a number means exponent notation with power
of ten. In fact it shifts the decimal point over the number of
positions given by the exponent value. The shifting is done to
the right when the exponent is positive, and to the left when
the exponent is negative. Examples:
3.1 @ 2 = 310
547.8 @ -3 = 0.5478
4.1378 @ 5 = 413.78 @ 3 = 41378 @ 1
= 413780
41378 @ -5 = 413.78 @ -3 = 4.1378 @ -1
= 0.41378
The useage of the metric prefixes
is given by example:
0.8 mg = 0.8 milligram = 0.8 * 1000 microgram = 800 ug
5.7 hm = 5.7 hectometer = 5.7 @ 2 meter = 570 m
This useage is also shown in the section about the
basic metric units
Square and cubic measures are written in two ways: with
the abbreviation of 'square' or 'cubic' before it or with
the digit 2 or 3 behind its abbreviation. Example:
Area: 1 sq.inch = 1 sq.in = 1 in2
5.3 sq.meter = 5.3 sq.m = 5.3 m2
Volume: 1 cu.inch = 1 cu.in = 1 in3
5.3 cu.meter = 5.3 cu.m = 5.3 m3
When a metric prefix is used the reading of square and cubic
measures must be done as shown by the examples:
1 dm3 is not 1 d(m3), but it is 1 (dm)3.
1 dm3 = 1 (dm)3 equals 1 liter. 1 d(m3) would equal 100 liters.
1 hm2 is not 1 h(m2), but it is 1 (hm)2.
1 hm2 = 1 (hm)2 equals 100 x 100 = 10000 m2 = 1 hectare.
1 h(m2) would equal 100 m2 = 0.01 hectare = 1 are.
See also the section about metric pitfalls.
This document has two classes of numbers, the exact and the
approximating ones.
A number written with a decimal point in the series of digits
is always an approximating number, except when explicitly it
is stated as being exact.
Exact are all numbers without decimal point and the numbers
marked with the embracketed asterisk [*]. Generally they are
exact because of being defined so. A number without decimal
point (= integral number) is never meant to be non-exact.
An exact number is a number in which the fractional part extends at the right side with zeros only. This zero-extension is infinitely long. An approximating number has non-zero digits at the right of its fractional part, which have been omitted for the sake of readability. Then rounding off is applied.
Examples:
50 = exact 50
50. = approx. 50, i.e. somewhere between 49.5 and 50.5
50.0 = approx 50.0, i.e. somewhere between 49.95 and 50.05
50.48 = approx. 50.48, i.e. between 50.475 and 50.485
50.48[*] = exact 50.48 = 50.4800000.....000.....
1234.5@-3 = (shift point to the left over three digits) = 1.2345
12.345@+2 = (shift point to the right over two digits) = 1234.5
123.45@-6[*] = exact 0.00012345
In the actual tables the marking with the asterisk can be applied in either one of the three ways:
The grid symbol # means 'number of' or 'amount of'. This
symbol is often used on top of a table column. Example:
# meters = amount in meters.
This instruction holds for the following chapters:
The way of reading the conversion tables is given by an example. For this extractions of the linear surveyor+chain tables are shown. At first the interrelations amongst the non-metric measures are shown, and after this the relations with the metric measures.
name consists of # yards
---- ----------- -------
chain 11 fathom 22
fathom 2 yard 2
yard 3 foot 1
foot 12 inch 1/3
inch 1/36
chain 4 rod 22
rod (= pole = perch) 25 link 5.5
link 7.92 inch [*] 0.22 [*]
This example shows that a chain consists of 11 fathoms. A fathom on its turn consists of two yards, a yard consists of three feet, and a foot consists of 12 inches. But a chain can also be handled as a set of four rods. A rod (which is also named pole or perch) on its turn consists of 25 links. Each link contains a non-integral number of inches: 7.92 . The bracketed asterisk shows this value is exact.
From these numbers one can calculate that a chain consists of 11 * 2 = 22 yards, or of 11 * 2 * 3 = 66 feet, or of 4 * 25 = 100 links, and that a fathom consists of 2 * 3 * 12 = 72 inches, and so on. A chain consists of 11 * 2 * 3 * 12 = 792 inches, but it also consists of 4 * 25 * 7.92 = again 792 inches. This method of multiplication in cascade allows everyone to calculate how many inches fit in a yard or how many feet in a rod, and so on.
Also forwards-backwards calculations can be performed.
Example: How many links fit into one yard ? Four answers
are possible.
abbrev. # meters [*] name inverse
------ ------------ ---- -------
ch 20.1168 chain 49.7097 / km
rd 5.0292 rod (= pole = perch) 198.84 / km
fath 1.8288 fathom 0.54681 / m
yd 0.9144 yard 1.0936 / m
ft 0.3048 foot 3.2808 / m
li 0.201168 link 4.9710 / m
in 0.0254 inch 39.370 / m
This table shows that the length of a chain is a little bit more than 20 meters. A little bit less than 50 chains fit into one kilometer. A foot has a length of 30.48 centimeters. Three feet plus a little bit more than a quarter foot fit into one meter. One inch has the length of 2.54 centimeters. More than 39 of them fit into one meter.
Note that in this example all the values in the left column (# meters) are exact, and those in the right column (inverse) are not. This is accidentally and not common in other tables. The values in their right column may be exact, and those in the left column may not be exact. Or in one column some values are exact and others are not.
This table can also be used for calculating the non-metric
interrelations. But as the numeric values are not so accurate
generally, try not to use this method.
Example: How many links fit into one yard ? Four answers
are possible:
The Anglo-Saxon measure system is a collection of factly independent measure systems. Sometimes such a self-sufficient system has an own name. Well-known are the names of the weight systems. The name 'Avoirdupois' is derived from the old French 'Avoir de pois' which means 'goods of (i.e. sold by) weight and not by volume or pieces'. The name 'Troy' references to a weight used at a fair in the central-French city of Troyes.
In the course of time a lot of measure units have been added to the set of existing units. And new units are still added. Consequently the tables cannot exhaustively mention all units.
In the whole document synonyms and abbreviations are used
for some measure units. They are used intermixedly. The most
important synonyms are:
British = Imperial = UK = United Kingdom
US = USA = United States of America
Fluid = Liquid
Meter = Metre
Liter = Litre
A few decades ago the metric system was also called Giorgi-system.
The singular unit name or the officially forbidden plural name of a unit are also used intermixedly, but not in the abbreviations. Example: 5 kilograms = 5 kilogram = 5 kg, but 5 kgs is not used.
Square metric measure units are used when the sizes of areas are measured. They are displayed in two ways: with the digit 2 behind the metric unit, or with the 'word' SQ (=square) before it. Thus: m2 = sq.m, dm2 = sq.dm, cm2 = sq.cm .
Cubic metric measure units are used when the sizes of volumes are measured. They are displayed in two ways: with the digit 3 behind the metric unit, or with the 'word' CU (=cubic) before it. Thus: m3 = cu.m, dm3 = cu.dm, cm3 = cu.cm . (cu.cm is often abbreviated to: cc) .
This instruction holds for the following chapters:
The chapter about the metric measure system is the
finalization of the list of conversions between the metric
and Anglo-Saxon system. It shows the complete(!) set of
names to be used in daily practice.
At first it gives a list of all metric prefixes with their
extended names. It shows that the everyday American people
use other names for them than the Europeans use, which
sometimes can be quite confusing.
Secondly it shows the four basic measure units and the method
of how to combine a prefix with a basic unit to construct the
desired measure unit.
At third it gives some old European names whose values fit
easily in the metric system.
At last it gives a proposal for new names to ease the use
of the metric system for people accustomed to the Anglo-Saxon
system.
A lot of systems have been invented to measure pressures of gases and liquids. All had their own definitions and units of measure. This fact results in a table of eight by eight cells with the factors for conversion between these units. The chapter itself explains how to read this table and gives some additional medical information.
The chapter with the physical constants shows the values of
a lot of generally applicable constants gained by laboratory
experiments in chemistry, physics and mechanics. It also contains
the rules for conversion between the five temperature scales and
a list of important mathematical constants.
The constants concerning pressures have their own chapter about
pressures.
The tables about the measures and money types used in Biblical times show the Biblical name of every item, the number of another item it consists of, the estimated number of a present-day item, the English name given to it in translations, and the location in the Bible of one sentence (='verse') wherein it is used.
The chapter about the European currency exchange rates shows
the official rates between the Euro-coin and the national coins
and some easy ways to approximate these rates quickly in the head
and without calculator.
For those people who also use the anglosaxon-metric tables: The
table with the official rates looks like the tables for the
relations with metrics. It is not, as the the second and fourth
column have been interchanged. So the column '1 Euro equals' is
similar to the 'inverse' column in the metrics-relation tables.
Every human society feels the need to quantify properties like time, length and mass for engineering and trade. In response to this need in early days every country or even every region had its own measure system. At present two systems are used globally: the American and the European system. Generally a country chooses to use only one of both. In reality this choice shows a greater difference in 'technics-culture' between both groups of countries than only the measure system, like the table shows:
TECHNICS CULTURE
subject American European
------- -------- --------
Electrical mains 110 volt, 60 Hz 230 volt, 50 Hz
Television (4:3) EIA-525-60-NTSC CCIR-625-50-Pal/Secam
Measures system Anglo-Saxon Napoleonic (=metric)
Weight,Mass Stone, Pound, Ounce (Kilo-)Gram
Length, Distance Mile, Yard, Foot, Inch (Kilo-,Centi-)Meter
Volume,Capacity Barrel, Gallon Liter, Cubic meter
Car-engine-power SAE-HP DIN-HP/PS
Cylinder-capacity c.inch cc
Gas-/Airpressure psi, psf bar, Pascal
Temperature Fahrenheit Celsius
Number (example) 6,789,012,345.67 6.789.012.345,67
Calendar-date- Month + Day + Year Day + Month + Year,
-notation Year + Month + Day
Hour of the day 12 hours + AM or PM 24 hours
AM = morning
PM = afternoon
The indicators AM and PM are derived from the Latin language:
AM = ante meridiem = in the morning,
PM = post meridiem = in the afternoon.
The number example shows the use of the punctuation marks. Both
number figures represent the same value. That is elucidated in
the next table:
NUMERIC FIGURES NOTATION
Punctuation marks in numbers America Europe
---------------------------- ------- ------
Subdivision of the digits in groups of three: comma period
Separation between integer and fractional part: period comma
Example: 12,345.67 = 12.345,67
In this conversion document the American punctuation is used.
Scientists like to use the punctuation and measures system of Europe.
The vocal pronouncement of the numbers above one million is also
different between both cultures. That pronouncement is shown in
the prefixes of the metric system.
The first table shows some weird symbol sequences for the transmission of television pictures. I do not explain the meaning of these sequences, but one can see that they are not the same in both columns. In fact they tell that the two television systems are incompatible! Consequently a videotape recorded in an 'American-type' country can not be played in an apparatus made for use in a 'European-type' country. American VHS differs from European VHS. Only the empty tapes are equal! When a TV-network wants to broadcast pictures taken in the other system, it first has to transform them into the own system, otherwise everyone's TV-set would become confused.
Until twenty years ago the USA, Europe and the Soviet-Union were the leading countries in the world, in economical, political and military power. Consequently the other countries felt obliged to copy one of their technical cultures. This choice was highly influenced by political and colonial relations. Consequently the global map has become a random patchwork of the two cultures, like the example shows:
COUNTRY WITH ... SYSTEM
American European
-------- --------
United States of America continental Europe
Japan, South Korea former Soviet-Union states
Taiwan Peoples Republic of China
continent South America Republic of South Africa
air-forces Europe (Nato!) air-force Russia
Some countries have a 'mixed culture', like Great Britain.
The Soviet Union applied the European culture.
The road side for the driving of motorcars is NOT related to the technics culture, as the following table shows:
TRAFFIC DRIVING SIDE
Left driving Right driving
------------ -------------
Great-Britain continental Europe
Cyprus Turkey, Greece
Australia Canada
Japan, South-Korea United States of America
Hong-Kong, Taiwan Peoples Republic of China
India, Pakistan 'Arabic' states: Maroc to Iran
Rep. South Africa Israel, Palestina
Philippines continent South + Meso America
Indonesia former Soviet-Union states
Sweden until 1963 Sweden after 1963
Roughly one third of the countries in the world has left driving traffic, and two third has right driving traffic.
The German and the English people pronounce several numeric values below one million in a different way. The differences are for the values between 20 and 100 and for the values between 1000 and 100,000. The table shows them with examples. Herein E means English and G means German (translated into English).
NUMBER VOCALISATION
value pronouncement
----- -------------
15 E=G: fifteen
36 E: thirty six
G: six and thirty
115 E=G: hundred fifteen
436 E: four hundred thirty six
G: four hundred six and thirty
1500 E: fifteen hundred
G: thousand five hundred
3600 E: thirty six hundred
G: three thousand six hundred
11500 E=G: eleven thousand five hundred
43600 E: fourty three thousand six hundred
G: three and fourty thousand six hundred
In the Netherlands a mixture of both systems is used. France
uses a third system.
The numbers above one million are vocalized differently by Europe
and America. That is shown by the every-day-name column in the
prefixes of the metric system.
In this document the USA-word Meter and the UK-word Metre denoting the same quantity are used intermixedly. Similar holds for the USA-word Liter and the UK-word Litre.
The ordinary daily words are written in the British version. Examples: Neighbour = neighbor, Behaviour = behavior, Useage = usage.
Sportsmen and sportswomen, especially those who perform endurance sports, like marathon runners, often use a heart-rate monitor in their training. Such monitor often consists of a chest belt and a wrist watch. Before the sports(wo)man can use his/her monitor (s)he has to be enter several values about the body e.g. length, weight and gender, into the wrist watch of the monitor. Also the monitor must be synchronized to the actual date and time.
A well-known brand of monitors is the Finnish company Polar. The manuals of several of these monitors have a snag: They do not tell about the hughe importance the selection of the technics culture has for a good operation of the monitor.
Before entering the present date and time and the 'fixed' body values into the Polar heart-rate monitor, the user must tell it which technics culture (s)he wants to apply. (S)he must select one of the two and cannot select a mixture of both. Alas, several Polar manuals suggest that this selection is of minor importance, as they do not state clearly its many consequences. In some monitors themselves this setting is quite cumbersome and prone to errors or even hidden deeply away in the midst of a sequence of other settings. So the user should first try to find out where in the monitor's setting system the culture is set, and perform this before all other settings. Examples of possible setting indicators are 12--24 HOURS and LB/IN--KG/CM.
The Metric measure system has many hughe advantages above the Anglo-Saxon system. The most important advantage is that the metric system has no difficult conversion factors between the denominations of a measure type. So, once one gets accustomed to it, life becomes much easier and a little bit cheaper. Therefore nearly all scientists like to use this system even when they live and work in a country that uses the Anglo-Saxon system, e.g. the USA.
In my view life is very difficult for the factories of shoes and clothes, as they use their own measure systems that are incomprehensible to the ordinary people (who are the customers!) and even differ from country to country. Very vague are the non-numeric indicators like XXL, M, ES and so on. The apparel systems are even worse than the Anglo-Saxon system! It is unbelievable that these factories do not switch to the metric system, but stubbornly stay at their own archaic ones. In case they would switch to the metric system, the consumers can measure their body simply at home and much easier select the right piece of clothing in the shop. This would give a boost to the mail-order and internet shops since less pieces of apparel would not fit and be returned. It also would give a boost to the ordinary shops as they can serve more customers on the same (expensive!) floor space. Also clothes can be given as a birthday present which will give an additional boost to the sales. At present nearly everyone is afraid of buying clothes for a friend or relative since "they will fit never".
History has shown that the economy and wealth increase when life is made easier for the ordinary consumers. Look at the motorcar, the tape-recorder and above all the computer: as soon as they became easier to operate their sales increased. This increase lowered the prices and enabled the manufacturers to improve the easiness of the operation, thus increasing the sales again. Difficult systems may give to the consumer the idea of skilfull craftsmanship, but in reality they create an elitarian and thus repulsing distance between the consumer and the manufacturer.
Many companies like to globalize their production and sales in order to lower the prices. So, let them first globalize the measure system. This globalization cannot trigger ethical objections except that the increase of sales may damage the natural environment more quickly. But mankind should damage the nature never at any time by any means!
We have already an example showing that globalisation of a measure system increases the wealth of most people in the world. It is the globalisation of the time measure: the creation of a standard time (Greenwich Mean Time) and the related time zones at the end of the nineteenth century. Before this moment every state and sometimes even every city or village had its own clock settings. Generally the lengthes of the time intervals like hours, minutes and seconds equalled for most locations, but the o'clock moments differed. Often these differences were only a few minutes. In the American East-coast many train passengers passed through seven local time zones, although in in general they did not travel as far away as we do. This patchwork was a waste of nerves, money and time.
Some people who like to go back in time (e.g. artisans and traditionalists) suggest that the unification of the measures may destroy the identities of the local dwellers. But the time unification shows that this is not true. The modern means of transport like bikes, trains and motorcars were already enabling people to look beyond the boundaries of their own village. So they started the deterioration of the feeling of belonging to the own small community. The unification of time made the feeling of belonging to a larger region like a state or a nation stronger as this geographical area seemed to be less fractioned.
It is easy to be romanticly nostalgic as long as one can rely on the scientific, technical and medical attainments of the modern days in case of illness, injury or emergency. The old days were often more fierceful and frightening than the present days. Only a modern war is worse than an old war. But people should be warriors never at any age! And why should the identity of a person or community be expressed by the numeric value of a measure unit? It is expressed by the appearance of the clothes (s)he wears, the kind of the music (s)he makes and the house (s)he dwells in! And the construction of these things should not be hampered by such numb things like unwieldy measure units! The human mind should be freed from them to perform its real expression.
Difficult measure systems only consume the person's identity. So let us all go metric! This chapter will show the ease of that metric system, and the whole document is intended to help the people in switching to this transparent system.
The method of naming the measure units in the metric system is quite different from that in the Anglo-Saxon system. In the metric system such a name is created by selecting a basic name from a very small set of names and combining it with a prefix which indicates a multiplication with an exponent-power of ten. This prefix can be empty; then its value equals 1.@0 = 1. In total less than 40 names and prefixes are required to give a name to every measure unit that is used in daily life. The Anglo-Saxon system requires much more than 40 names. Nevertheless this system has a smaller range of values in every property than the metric system has.
The same prefixes are used for all classes of measure types.
Classes and their basic units are: length -- Meter,
weight -- Gram, time -- Second; electricity --
Volt, and so on. All prefixes can be used with all classes. The
size of the resulting measure of a prefix with a class name is
always a power-of-ten times the size of a measure made by
another prefix and the same class name. Mathematicians call this
universal property "Orthogonality". Examples:
1 mV = 1 millivolt = 0.001 V, 1 kV = 1 kilovolt = 1000 V,
1 mg = 1 milligram = 0.001 g, 1 kg = 1 kilogram = 1000 g,
1 mm = 1 millimetre = 0.001 m, 1 km = 1 kilometre = 1000 m,
1 mA = 1 milliampere = 0.001 A, 1 kA = 1 kiloampere = 1000 A.
The universal prefixes are listed in the sub-chapter
Metric prefixes.
This sub-chapter also shows the language differences between
the American and continental-European people, even when both
speak the same language: English. In daily life both peoples use
different names for the units above the million. Example:
10@9 = one milliard in Europe
= one billion in America.
Luckily both peoples use the same scientific names.
Beside the prefixes the adjectives 'square' (= sq.) and 'cubic'
(= cu.) are in ubiquitous use in the metric system since they are
the only official way to indicate areas and volumes. They are
often notated by the suffixes 2 and 3 behind the length unit.
Thus, for example:
(m1 =) m = linear meter (for length or distance)
m2 = sq.m = square meter (for area or surface)
m3 = cu.m = cubic meter (for volume or contents size)
In the Anglo-Saxon system these adjectives exist too, but they
are used less often as surfaces and volumes often have their
own names.
Another feature of the metric system is that it does not make a difference between the useage fields of the measure. For example: All cubic measures and volumes are expressed with the same measure units. There is no distinction between Liquids, Dry materials, Solid materials, Apothecary use and so on. The rough workers in the forest and in the harbour use the same basic units as the scientists in the laboratory do. And the shopmen join them when they sell their meat or gasoline. Even the pilots of USA's former ennemies, the Sovjets, use them in their fighting planes! Only the prefixes may differ. But a prefix has always the same meaning, irrespective who uses it. The transparent and universal orthogonality is complete! In continental Europe the slogan by the creators of the metric system in 1795 has come to reality: "It is for all people, for all time".
Example of use: Let us take the measure-class Length with
its basic unit Meter. A small unit of length can be created
by adding the prefix Milli before the basic-unit name, thus
giving Millimeter. This unit of length is exactly 1/1000-th of
the length of the original meter.
A very small unit can be made by using the dwarf prefix Nano.
Thus 1 Nanometer is 1-milliardth of a meter. A large unit is
made by adding a blow-up prefix, e.g. Hecto or Kilo. Thus
1 Hectometer is 100 meters and 1 Kilometer is 1000 meters.
They equal to 1.@+11 and 1.@+12 nanometers respectively.
This construction is shown in more detail in the chapter of
the basic units.
Alas, a few anomalies make some tiny cracks in the bastion of the metric's universal orthogonality. Some of them are man-made and others arose by the physics. Some of them are shown here.
At first: Physicists made a big snag, as if they like to be terrible people. The basic unit of mass in their science of physics is not gram, but it is kilogram (1 kg = 1000 g). More about this inconsequency and its consequences is written in the chapter about the basic metric units. In daily life this snag does not give any problem.
At second: In Europe some ancient names are still in use. They are not many, and the values they stand for fit quite well in the metric system. These names are listed in the tables of the outsider units. In this document even new names for ordinary use are proposed!
Despite the smaller amount of names in the metric system, the ratio between its smallest and its largest measure unit is much greater than in the Anglo-Saxon system. The ratio between the smallest and the largest prefix is 1.@48. In any Anglo-Saxon measure class the maximum range between the smallest-valued name and the largest-valued name is less than 1.@15 . Most classes have a much smaller range. Of course this is a disadvantage, but soon it will appear to be minor when compared to the one of the next section.
The above-mentioned anomalies in the metric measure system are outdwarfed by those in the Anglo-Saxon measure system which in fact is a big collection of anomalies. It has the handicap of total lack of orthogonality and universality!
The main cause of this lack is the biological basis of many of the measure units, especially our human body. This body seems to be a nice toolcase for defining measure units, especially the length units. The size of a bridge, a house, or a kitchen-table is expressed as a number of lengths of a medium-sized body part like an arm or a foot or even a foot-step. To measure small-sized objects like a dish or a candle we use a small body part like a finger. We always carry this toolkit with these coarse length units with us everywhere we go to, and we can never forget it. But this easy toolkit has one great disadvantage: Some people are tall and others are small, some people are thick and others are thin, and so are their limbs. Therefore righteous trade and commerce require standardized (= idealized) body sizes. This standardization has to be adapted when units not based on the human body must be included in the measure system.
Consequently in the early medieval times every region like a nation, township or city and every branch of industry, trade and merchandise performed the standardization in its own way, thus developing its own measure system. In later times the systems of several regions and branches were brought together. To make them 'cooperate together' several of these systems were adapted slightly. This means: the units in them were stretched or shrunk slightly. Thus the multiplication factors between the units of consecutive sizes were kept integral and not too awkward. All these processes make the history of the origination of the resulting measure system fairly muddled, and the system itself too. The Anglo-Saxon measure system is such an accumulated bunch of units.
The origins of the composing systems and their units
manifest in several ways:
- selection of basic units,
- the time in history,
- by region or township,
- kind of stuff to be measured.
These four causes will be shown with examples.
First cause: Selection of basic units.
The base of the definition of the nautical mile is
the length of one-sixtieth of one degree on the earth
equator. A unit of around this length is useful to
measure the distance of a long journey or sea voyage.
The determination of that unit needs fairly complex
apparatuses, although it can be done very accurately.
It is based on astronomy. Only a few professionals can
handle this apparatuses. In order too give their
results sense to the ordinary people the idealized
body must be designed such that the body based units
are in concert with the earth-globe based units. Here
more than one type of standard body is possible.
Second cause: Time in history.
If a new king stands up and wants to immortalize himself,
he may dictate the basic measure units to be redefined to
his body measures. Of course these are different from
those of the previous king. Thus the same country gets
another measure system.
Third cause: Dependency on region.
In past times regions like countries, counties and townships
were more self-sufficient than they are now. So there was
less trade between them. Consequently it was fairly easy
for every region to define its own measure units. A rich
region uses horses to pull the plow, but a poor region uses
oxes or donkeys. These animals work slower, and so the size
of the piece of land that can be plowed in one day is lower.
Thus the "day's-plow-unit" differs between both regions.
Fourth cause: The kind of stuff to be measured.
This factor depends typically on the kind of trade and
merchandizing. For weighing beans one cannot use a very
small bucket as the inaccuracy due to the empty spaces
near the wall would increase. Producers of beverages refer
their volumes to the size of a typically drink glass. And
coal deliverers refer to the sack they can hold firmly in
their hands or on their back. A sack of wood chips cannot
be much bigger, even when it is much lighter, otherwise it
is too big to be grasped easily. Thus every branche of trade
invents its own units of mass and weights. Another example:
One branch defines the pound as the weight of one can
filled with water, and the other branch defines the pound
as the weight of the same can filled with oil. Of course
when the latter branch uses a slightly bigger can, then
the two pounds approach each other gruesome closely, which
may be confusing as they are not exactly equal.
Note that the day's-plow area and the big-but-not-too-big coal-sack are also values with a biological base: muscle strength. Time keeping is a hybrid value. A coarse time unit is inside our body: the heart rate when we are in rest. Another time unit needs fairly difficult instruments for its definition, but it is much more accurate: the hour that is based on astronomy. Here we see the same as in the case of lengths: The moderate and small unit values can be based on biological properties everyone can perceive easily, but the large units are based on complex science and physics and need apparatuses to be measured. And both have to be brought into concert, i.e. the factor between the standardized heart-beat interval and the astronomy-hour must be integral and not too awkward.
The enforcement to the unit-cooperation causes the creation of different multiplication factors between the units of the same type that are consecutive in size. Not always these differences can be washed away by introducing new units and thus making new factors, similar to the addition of the unit tenhalf and the accompanying factor 10.5 by the author. The persistent existence of these differences between multiplication factors is the undesired and cumbersome un-orthogonality of the Anglo-Saxon measure system. Example: A yard consists of two cubits, but a cubit consists of 1.5 feet and not of two feet.
Some multiplicative factors are even quite ugly. The factors 2, 3, 4 and 5 are quite nice, but 7, 11 and even 19 are awkward. In fact nearly all numbers between 1 and 20 are used as a factor. Consequently a 'difficult' conversion factor may be needed to translate one unit into another that is not in the same so-called "multiplication chain", e.g. 1 Ramden-chain = 1.515151515.... Gunter-link. Of course the difference and sometimes-ugliness of the multiplication factors hampered the construction of a mechanical adding or subtracting machine. Only the modern electronic computers can handle them well.
Another important reason for the steady proliferation of units and names is the absence of prefixes. So for every unit of measure another name must be invented, even when that unit belongs to the same class, e.g. yard and cubit in stead of half-fathom and quarter-fathom. Therefore the system must enable everyone to easily and seamlessly add new units or new names for existing units that fit better to his job. It even invites to do so.
And the people respond! They add nearly every new contraption to the units table wherein it fits at best, of course after it has been christened with an exotic or popular name. Not surprisingly, many branches of industry and trade have often (ab)used this facility and still do. The creativity and the will to invent new and "better fitting" unit sizes appear to be endless. E.g. the name Ramden-link has been invented for the already existing and widely used foot, and a span (= linear quarter) is a kind of a small foot. This liberty for units leads to an uncontrollable proliferation of unit names. The chapter Masses: Avoirdupois - Trade+Industry is a clear result of it.
To make things worse, the newly invented Anglo-Saxon units also need not to be easily compatible with the existing ones. Consequently the 'multiplicative distances' between the units of the same class will never become equal. All these irregularities force people to invent new measure units and multiplicative factors that are more handy, thus making the problem even worse. And so the proliferation of new units and names will continue for ever. As a consequence, no document can ever display the total set of all unit names.
And still the Anglo-Saxon complexity seems not to be enough: Different application environments use different sets of names, like Troy, Avoirdupois, British-Imperial, USA-Nautical, and so on. The altitude of a tower is expressed in a naming system different from that for the altitude of a plane. Low and behold, the different naming systems often use the same set of unit names. Thus confusion may arise about the actual meaning and size of an unit. Example: A pound is 5760 grain or 7000 grain, depending on which weight measure system is used. Two different gallons and a countless number of quarts circulate in the USA. Thus the effort to save names only enhances the mess.
During the thousands of years of civilization innumerous meetings and assemblies have been held to define and redefine the basic measure units in order to keep them fit for the job and not mutually contradictory, and to avoid the quarrels about them. And these conferences are still going on.
Alltogether these points force some people to call the entire Anglo-Saxon measurement system a WOMBAT = Way Of Measuring Badly in America Today = Waste Of Money, Brains And Time.
But it can be much easier: the Metric System, also called Systeme International (= S.I.) or Giorgi system. This system is not based on values determined by biology, history, trade and commerce, but only on a very few physical values determined by modern scientists. These basic units are carefully watched by the French Bureau de Poids et des Measures (= Office for Weights and Measures) at Sèvres near Paris.
Conferences are needed only to enhance the accuracy of these units as technology progresses, but not to change them significantly. There are no slightly contradictory units that are forced to 'cooperate together'. This fact enabled the metric-system designers to prohibit all multiplicative factors except one, and favorize that single one. This makes the system total orthogonal and universal. The choosen factor is a nice one: 10 = 2 * 5. Thus a kilometer consists of 1000 meters, and a meter consists of 1000 millimeter and not of e.g. 800 millimeters.
This rigidity in the metric system makes its use easy, eases the construction of mechanical adding and subtracting machines, and enables the protection from the infinite proliferation of unit names and multiplicative factors. It firmly discourages personal creativity in the making of a new unit. It forces everyone to combine a prefix and a basic unit name to make a unit that fits better to the job. Both the prefix (like milli and kilo) and the basic name (like meter and gram) must be taken from predefined sets. These sets are fairly small, so they can be listed all together on two sheets of paper. In fact the chapter about the metric system covers the whole part of the system for daily use.
Has the metric system advantages only? Alas not!
Unnecessarily and perhaps unwittingly the designers have built
in one great (and in my eyes) quite severe disadvantage. It has
a tricky pitfall in the notation of a square or cubic measure.
An examples shows this.
dm3 does not mean d(m3) = 1/10-th of a cubic meter,
but it means (dm)3 = 1/1000-th of a cubic meter.
Similar holds for the square measure: dm2 equals 1/100-th
of a square meter and not 1/10-th.
This notation makes the range of values between two consecutive prefixes rather large, as the multiplication factor between the two prefixes becomes very large. For example: Between the consecutive prefixes Kilo and Mega this factor is one million (= 1.@6) for square measures and one milliard (= 1.@9) for cubic measures. The latter value is approximates fairly the total range of any Anglo-Saxon system.
Here the Anglo-Saxon notation system has great advantage. The average of the multiplication factors between two names with consecutive unit values is roughly the same for linear, square and cubic measures. For example, a fathom is two yards and a peck is two gallons. Perhaps this advantage has motivated the American and some British people to stick to their measure system.
So it seems reasonable that in the daily talks of the ordinary British everyman who has to get accustomed to the metric system, names will be given to intermediately sized values which fit well inside this metric system. Therefore the people may create new names, but also borrow existing ones from the continental-European and the Anglo-Saxon system. In the latter case the name may be given a metric value in the neighbourhood of its original Anglo-Saxon value. Perhaps the proposed set of names may emerge. It is not surprising that in this set the number of volumes is high. It is to split up the hughe range of one 'official' volume step.
The old Imperial (now UK) measure system was originally defined by three standard measures which were held in London: the yard, the pound and the gallon. For example, the gallon was the volume of ten AVDP-pounds of water at 62 degrees Fahrenheit and a pressure of 30 inch mercury. The USA had their own system that also was defined originally by physical standard measures: the yard, the pound, the gallon and the bushel. Similarily herein the gallon was roughly the volume of ten Troy-pounds of water.
At present all these basic standard measures are redefined by referencing them to the standard measures of the S-I-system that have been developed in 1795, introduced by Napoleone Buonaparte in his empire, and are nowadays widely used in continental Europe: the metre, the kilogram and the litre. These equivalence figures are exact. Hence the bracketed asterisk [*] on top of the values column.
Anglo-Saxon Metric Where used
name value [*] type USA UK
----------- -------------------------- ----------
yard 0.9144 metre USA + UK
pound (avdp) 0.453 592 37 kilogram USA + UK
gallon 4.546 09 litre UK
gallon (fluid) 3.785 411 784 litre USA
bushel (dry) 35.239 070 166 88 litre USA
[*] = All values in this column are defined as being exact.
Note particularly that the UK gallon is a different size to the US-fluid gallon so that NO liquid measures of the same name are the same size in the UK and US systems. The US-fluid gallon equals 231 cubic inches.
The table also means that the accuracy of the Anglo-Saxon measures depends on the accuracy of the underlying measures in the Napoleonic system. The Anglo-Saxon measure system is not autarkic ('self-sufficient') anymore.
The defined pound is the Avoirdupois-pound. The pound of the Troy+Apothecary system is derived from this pound by the formula:
pound(tr/ap) = pound(avdp) * 5760 / 7000
= pound(avdp) * 144 / 175
= pound(avdp) * 0.822857142857....
= 0.3732417216[*] kilogram
Its reverse is:
pound(avdp) = pound(tr/ap) * 7000 / 5760
= pound(tr/ap) * 175 / 144
= pound(tr/ap) * 1.215277777777....
= 0.45359237[*] kilogram
The following table shows the conversion factors between
the three sizes of gallons. Herein: dry-gallon =
dry-bushel / 8. This table should be read as follows:
One unit written alongside the vertical axis ('row name')
equals one unit written alongside the horizontal
axis ('column name') times the numeric value in
the table cell.
Example: 1 Imperial-gallon = 1.20095 * 1 USA-fluid-gallon
GALLON | USA-fluid | USA-dry | Imperial |
------------+---------------+----------------+----------------+
USA-fluid | 1 | 0.8593670074 | 0.8326741846 |
------------+---------------+----------------+----------------+
USA-dry | 1.163647186 | 1 | 0.9689389719 |
------------+---------------+----------------+----------------+
Imperial | 1.200949926 | 1.032056743 | 1 |
------------+---------------+----------------+----------------+
From the actual volume tables it can be derived that 1 UK-gill
= 5 UK-ounce, and that 1 US-fluid-gill = 4 US-fluid-ounce.
When some inaccuracy is allowed, the following approximations can
be applied:
approximation accuracy better than
------------- --------------------
6 USA-fluid gill = 5 Imperial gill 0.08 percent
7 USA-fluid gill = 6 USA-dry gill 0.26 percent
1 Imperial gill = 1 USA-dry gill 3.3 percent
1 USA-fluid ounce = 1 Imperial ounce 4.1 percent
This approximation table holds for the three gills and most of the equally named units 'above' them (e.g. gallon, kilderkin, bushel). And it holds for the two ounces and most of the equally named units 'below' them (e.g. dram, minim).
The the number of gallons in the following units have been
defined such that the units differ less than 0.08 percent in
actual size:
USA-tierce = 84 gallon and
Imperial-puncheon = 70 gallon
USA-hogshead = 63 gallon and
Imperial-wine-hogshead = 52.5 gallon
In fact a fourth measure system for volumes exists, having its own size of the gallon. It is the old British-beer system. It is is described in the section below this one.
The volume systems used in the USA are based on old British
systems that are nearly out of use and unknown to most people.
Units in these old systems that are out of use, are nevertheless
added to the American systems in this document. If such unit has
the same name as an USA-unit but has a different size, then the
unit is marked with "OB" = Old-British. The USA-unit does not
get a mark. Example with unit name 'Tierce' in the USA-fluid
system:
Tierce = 84 gallon (used in USA)
OB-Tierce = 42 gallon (Old-British,
out of use)
The old British-beer system is a fourth measure system for fluid volumes. It has its own size of the gallon. At present this system is put aside as being 'unofficial'. So it is not used much anymore and even unknown at all to most people. For the sake of completeness its volume tables are listed also in this document. The following table shows the old British base of all four volume systems.
Present-day volumes Old-British base
------------------- ----------------
USA-Fluid Wine (by Queen-Anne)
USA-Dry Dry before 1824
Imperial Dry+Fluid since 1824
old-British beer old-British beer+ale+porter
The following table lists the number of cubic inches in a gallon for each system. In two systems this size has been changed slightly during the history. The size of the gallon in the old British-Dry-before-1824 system was 268.75 cubic inches. Nowadays it is 268.8025 cubic inches in the USA-Dry system. Similarly the size of the old British wine-gallon has once been 231.18 cu.inch = 3.7884 liters, whilst it is now exact 231 cu.inches in the USA-liquid system. The size of the Imperial gallon has only been made more accurate as the measurement apparatuses have become more accurate.
In this document the latter is assumed also for the old British-beer system. For its conversion-to-metrics table the size of the cubic present-day-inch is taken and not that of of an cubic old-inch.
Volume system # cubic inches / gallon
------------- -----------------------
USA-Fluid 231 (was 231.18)
USA-Dry 268.8025 (was 268.75)
Imperial 277.42
old-British beer 282
The actual tables of the old British-beer system show the simplicity the other three volume systems also had in early days. In the run of the last two centuries the latter have increased in size nearly uncontrollably. Thus the beer-system confirms the disadvantages of the Anglo-Saxon system.
During the same period the small Napoleonic system did increase nearly not at all. Only a few prefixes and a few complete new types of units were added. These types were unknown at the time this system was created, e.g. Ampère for electric current. The Anglo-Saxon system never adopted these new types.
The unit Tenhalf (= ten and a half gallons) means ten gallons plus five percent to compensate spillage. It accidentally happens to be equal to 1.5 * 7. It is a virtual unit as it is introduced by the author to make a better fit for other units. These units are:
name # tenhalf # gallon[*]
---- --------- -----------
wine-tun 24 252
butt 12 126
wine-puncheon 8 84
hogshead 6 63
wine-hogshead 5 52.5
(old) tierce 4 42
wine-barrel 3 31.5
tenhalf 1 10.5
Anglo-Saxon r e l a t e s t o
measure Anglo-Saxon Metrics
unit [*] [*]
Length # inch # decimeter
------ ------ -----------
inch 1 0.254
foot 12 3.048
yard 36 9.144
Surface # sq.inch # sq.decimeter
------- --------- --------------
sq.inch 1 0.064 516
sq.foot 144 9.290 304
sq.yard 1296 83.612 736
Volume # cu.inch # cu.decimeter
------ --------- --------------
cu.inch 1 0.016 387 064
cu.foot 1728 28.316 846 592
cu.yard 46656 764.554 857 984
Gallon:
USA-dry 268.8025 4.404 883 770 86
USA-fluid 231 3.785 411 784
Brit.Imp. 277.4194327916[~] 4.54 609
Old.Brit.Beer 282 4.621 152 048
Weight # grain # g r a m
------ ------- ----------
grain 1 0.064 798 91
Troy-pound 5760 373.241 7216
AVDP-pound 7000 453.592 37
In this table all values are exact,
except the one indicated by [~].
sq. means square; cu. means cubic
For the sake of clarity the length units of yarn and textiles are not presented here, but they are in a separate chapter about the measures for Yarn and Textiles.
name consists of [*] # feet [*]
---- --------------- ----------
++++++++ British nautical ++++++++
+++ geograph. league 291840 inch 24320 +++
geograph. league 4 nautical mile 24320
+++ marine league 218880 inch 18240 +++
marine league 3 admiralty mile 18240
admiralty mile 1 nautical mile 6080
(nautical) mile 10 old-cable-length 6080
old-cable-length 32 * 19 foot 608
+++ radar-data-mile 72000 inch 6000 +++
radar-data-mile 1 sea-mile 6000
sea-mile 1000 fathom 6000
++++++++ Ordinary standard +++++++
+++ (land) league 190080 inch 15840 +++
>> (land) league 3 statute mile 15840
old land-league 1.5 statute mile 7420
(statute, land) mile 4 quarter 5280
quarter 2 furlong 1320
furlong 10 (Gunter-)chain 660
(Gunter-) chain 66
>> old-Brit.land-mile 50 Ramden-chain 5000
USA-cable-length 6 Ramden-chain 600
Ramden-chain 100 foot 100
+++ Gunter and Ram(s)den ... - +++
Gunter-chain 100 Gunter-link 66
Gunter-link 7.92 inch 0.66
Ramsden-chain 100 Ramsden-link 100
Ramsden-link 12 inch 1
engineer's-chain 100 engineer's-link 100
engineer's-link 12 inch 1
+++ chain 11 * 9 * 8 = 792 inch 66 +++
Gunter-chain 1 chain 66
>> CHAIN 11 fathom 66
fathom 2 yard = verge 6
yard = verge 3 foot 3
foot 12 inch 1
>> CHAIN 4 pole (perch,lug) 66
pole (= perch = lug) 1 rod 16.5
rod 11 cubit 16.5
cubit 18 inch 1.5
>> CHAIN 4 rod 66
rod (pole,perch,lug) 25 (Gunther-)link 16.5
link = Gunther-link 7.92 inch 0.66
+++ human run/walk/length ... - +++
MARATHON-distance 26 mile + 385 yard 138435
USA-football-field 120 or 100 yard 360 or 300
with end-zone 1 (cotton-)skein 360
without end-zone 3 Ramden-chain 300
USA-military-step 30 or 36 inch 2.5[*] or 3
moderate speed 1 step 2.5[*]
quick speed 1 yard 3
CRICKET-pitch 1 Gunter-chain 66
smoot 5 feet + 7 inch 5.58333[~]
UK-rail.gauge 4 feet + 8.5[*] inch 4.70833[~]
+++ navy-cable-length 8640 inch 720 +++
navy-cable-length 1 (new)cable-length 720
(new) cable-length 2 (cotton-) skein 720
(cotton-) skein 4 shackle, shot 360
shackle = shot 7.5 mark-twain 90
mark-twain 2 fathom 12
fathom 2 yard, verge 6
yard = verge 2 cubit 3
old-cable-length 32 * 19 foot 608
USA-cable-length 100 fathom 600
+++ diverses ... rope - +++
(cotton) skein 18 rope 360
(wool) wrap 12 rope 240
+++ Ramden-chain 1200 inch 100 +++
Ramden-chain 1 engineer's chain 100
engineer's chain 5 rope 100
rope 2 US-electric-stick 20
US-electric-stick 2 stride 10
stride 1 geometrical pace 5
geometrical pace 1 (great) pace 5
(great) pace 2 step 5
step 2.5 Ramden-link 2.5
Ramden-link 1 engineer's link 1
engineer's link 1 foot 1
+++ fall 270 inch 22.5 +++
FALL 6 (English) ell 22.5
ell = English ell 5 span 3.75
FALL 5 goad 22.5
goad 2 Flemish ell 4.5
Flemish ell 3 span 2.25
+++ cubit 18 inch = 2 span = 1.5 foot 1.5 +++
yard 2 cubit 3
yard 3 foot 3
yard 36 inch 3
cubit 1.5 foot 1.5
cubit 2 span 1.5
cubit 18 inch 1.5
foot 12 inch 1
# inch [*]
++++++++ Small lengths ++++++++ ----------
+++ diverses ... hand - +++
great-lug = long-rod 7 yard = 21 foot 252
great-lug = long-rod 9 arm's-length 252
arm's length 7 hand 28
billet 5 small palm-length 40
small palm-length 2 hand 8
hand 4 inch 4
+++ diverses ... foot - +++
yard = verge 3 foot 36
step 2.5 foot 30
home-el.equip.stand.U 1.75 foot 21
diamond-mark unit 1.6 foot 19.2
cubit 1.5 foot 18
Ram(s)den-link 1 foot 12
engineer's link 1 foot 12
+++ electronic equipment ... inch - +++
home-standard U 21 inch 21
laboratory CAMA 19 inch 19
+++ span 360 button-line 9 +++
linear-quarter 1 span 9
palm-length 1 span 9
>> SPAN 2 finger-length 9
finger-length 2 nail 4.5
nail 3 finger-width 2.25
finger-width 1 digit 0.75
digit 30 button-line 0.75
button-line 0.025
>> SPAN 3 palm, ounce 9
palm = ounce 4 digit 3
digit 30 button-line 0.75
button-line 0.025
finger breadth 35 button line 7/8=0.875
>> SPAN 3 palm, ounce 9
palm = ounce 3 thumb-width 3
thumb-width 1 inch 1
inch 40 button-line 1
button-line 0.025
+++ foot 12 inch 12 +++
Ram(s)den-link 1 foot 12
engineer's link 1 foot 12
>> FOOT 2 shaftment 12
shaftment 2 palm, ounce 6
palm = ounce 3 inch 3
inch 1
>> FOOT 3 hand, fist 12
hand = fist 4 inch 4
inch 1
+++ inch ... diverses 1 +++
thumb-width 1 inch 1
>> INCH 40 button-line 1
button-line 2.5 calibre 1/40
calibre 1 centinch 1/100
centinch 10 mil, millinch 0.01
mil = millinch 1 thou, point 0.001
thou = point 4 silversmithpoint 1/1000
silversmithpoint 1/4000
>> INCH 14 print.agate-line 1
printing-agate-line 1/14
>> INCH 3 barley-corn-len. 1
barley-corn-length 4 line 1/3
line 1/12
>> INCH 16 pin-length 1
pin-length 4 shoe-ounce 1/16
shoe-ounce 1/64
+++ line 1440 twip 1/12
poppy-seed 1 line 1/12
second 1 line 1/12
>> LINE 4 shoe-iron 1/12
shoe-iron 3 hair breadth 1/48
hair-breadth 10 twip 1/144
twip 1/1440
>> LINE 6 Adobe-point 1/12
Adobe-point 2 hair-breadth 1/72
hair-breadth 10 twip 1/144
twip 1/1440
>> LINE 10 gry 1/12
gry 12 twip 1/120
twip 1/1440
[*] All numeric values in this table are exact !,
except those indicated with [~].
The table can be seen as a set of sub-tables which are
interconnected by some of the measure names. These names
are seen in two or more sub-tables. The beginning of each
sub-table is indicated by the line with the +++ symbols.
abbrev. # meters [*] name inverse
------ ------------ ---- -------
42194.988 marathon-distance 0.02369950 / km
7412.736 geographical league 0.1349030 / km
5559.552 nautical league 0.1798706 / km
4828.032 (land) league 0.2071237 / km
2414.016 old land-league 0.4142475 / km
mi 1853.184 nautical mile 0.5396118 / km
1828.8 radar-data-mile 0.5468066 / km
mi 1609.344 (statute) mile 0.6213712 / km
1524 old-British-land-mile 0.6561680 / km
Q,qtr 402.336 quarter 2.4854848 / km
219.456 (new, navy-)cable-length 4.5567221 / km
fur 201.168 furlong 4.9709695 / km
185.3184 (old, sea) cable-length 5.3961182 / km
182.88 USA-cable-length 5.4680665 / km
109.728 skein (cotton) 9.1134442 / km
109.728 US-football-f.-plus-ends 9.1134442 / km
91.44 US-football-f.-no-ends 10.936133 / km
ch 30.48 Ramden/engineer-chain 32.808399 / km
27.432 shackle = shot 36.453777 / km
ch 20.1168 chain (of Gunter) 49.709695 / km
20.1168 cricket-pitch 49.709695 / km
6.858 fall 145.81511 / km
6.4008 long-rod = great-lug 156.23047 / km
6.096 rope 164.04199 / km
5.0292 pole = perch = lug 198.83878 / km
rd 5.0292 rod 198.83878 / km
3.6576 mark-twain 273.40332 / km
3.048 USA-electric-stick 328.08399 / km
fath/fth 1.8288 fathom 546.80665 / km
1.7018 smoot (of MIT-Boston) 587.61312 / km
1.524 stride 656.16798 / km
1.524 geometrical-pace 656.16798 / km
1.524 (great) pace 656.16798 / km
1.4351 UK+EUR railway-gauge 696.81555 / km
1.3716 goad 729.07553 / km
Eng.e 1.143 (English) ell 874.89064 / km
1.016 billet 984.25197 / km
yd 0.9144 yard 1.093613 / m
0.9144 verge 1.093613 / m
0.9144 US-milit.quick pace 1.093613 / m
0.762 US-milit.modest pace 1.312336 / m
0.762 step 1.312336 / m
0.7112 arm's length 1.406074 / m
0.6858 Flemish ell 1.458151 / m
0.5334 home-elec.-standard-U 1.874766 / m
0.4826 laborat.-elec.-CAMAC 2.072109 / m
0.48768 diamond-mark unit 2.050525 / m
0.4572 cubit 2.187227 / m
0.3048 Ramden/engineer-link 3.280840 / m
ft 0.3048 foot 3.280840 / m
0.2286 span = palm-length 4.374453 / m
Q,qr 0.2286 linear-quarter 4.374453 / m
0.2032 small palm-length 4.921260 / m
li 0.201168 link (of Gunter) 4.970970 / m
0.1524 shaftment 6.461680 / m
0.1143 finger-length 8.748906 / m
0.1016 hand = fist 9.842520 / m
0.0762 ounce 13.12336 / m
0.0762 palm (-width) 13.12336 / m
nl 0.05715 nail 17.49781 / m
0.0254 thumb-width 39.37008 / m
in 0.0254 inch 39.37008 / m
0.022225 finger breadth 44.99438 / m
0.01905 finger-width = digit 52.49344 / m
abbrev. #millimeters name inverse
------ ------------ ---- -------
8.46666667 barley-corn-length 1.181102 / cm
li 2.11666667 line 4.724409 / cm
2.11666667 poppy-seed = second 4.724409 / cm
1.81428571 agate-line for print 5.511811 / cm
li 0.635 [*] button-line 15.74803 / cm
0.52916667 shoe-iron 18.89764 / cm
0.396875 [*] shoe-ounce 25.19685 / cm
0.35277778 Adobe-point 28.34646 / cm
0.254 [*] calibre = centinch 39.37008 / cm
0.21166667 gry 47.24409 / cm
0.17638889 hair breadth 56.69291 / cm
0.0254 [*] thou = point 393.70079 / cm
0.0254 [*] mil = millinch 393.70079 / cm
0.01763889 twip 566.92913 / cm
0.00635 [*] silversmithpoint 1574.80315 / cm
Sometimes a pace is falsely called a step.
Foot = International foot = Ordinary foot.
Yard = International yard = Ordinary yard.
Ordinary link (7.92 inch) = Gunter link = Imperial link.
Ordinary chain (792 inch) = Gunter chain = Imperial chain.
Mil (with one L) = milli-inch; Mill (with two L's) = milli-metre.
Thou = one thousandth of an inch.
Twip = one twentieth of an (Adobe-) point.
Button-line = button-thickness-line.
Ounce = old name for 1/12 yard.
Poll = pollex = thumb-witdh.
Palm = palmus = palm-width.
Smoot = length of a scientist at MIT-Boston.
The values in the lower left column of #millimeters are not
exact, except those marked with [*].
[*] = All values in the upper left column (# meters) are exact,
as:
In the Napoleonic system the ordinary decimals are used always to notate the fractions of a meter, decimeter or a centimeter. The above Anglo-Saxon tables show that the feet and inches are split often into non-decimal parts. Some of these are:
metric length
Name part of foot in centimeters [*]
---- ------------ ------------------
foot = Ramden-link 1 30.48
span = palm-length 3 / 4 22.86
shaftment 1 / 2 15.24
finger-length 3 / 8 11.43
palm = ounce 1 / 4 7.62
nail 3 / 16 5.715
fing.width = digit 1 / 16 1.905
hand = fist 1 / 3 10.16
inch = thumb-width 1 / 12 2.54
metric length
Name part of inch in millimetres
---- ------------ --------------
inch 1 25.4 [*]
barley-corn length 1 / 3 8.46666666...
line = poppy-seed 1 / 12 2.11666666...
(shoe-) iron 1 / 48 0.5291666666...
Adobe-point 1 / 72 0.3527777777...
hair breadth 1 / 144 0.1763888888...
button-line 1 / 40 0.635 [*]
gry 1 / 120 0.2116666666...
twip 1 / 1440 0.017638888888...
pin-length 1 / 16 1.5875[*]
shoe-ounce 1 / 64 0.396875 [*]
In the Anglo-Saxon system even a non-decimal system without names is used to notate the fractions of an inch: the BINARY-SPLIT system. This binary inch-splitting means: Break the inch into two equal parts. Each part has the length of a half inch. Then break each half into two equal parts. Each such part has the length of a quarter of an each. Then break each quarter into to equal parts. Each such part has the length of an eighth of an inch. Then break ..., and so on. The table shows the results of this binary splitting until one-sixteenth.
P a r t s o f I n c h Length in Inverse
Binary split Decimal digits Millimeters # / dm.
------------ ---[*]-------- ---[*]----- -------
1 1.0 25.4 3.93700787
15 / 16 0.9375 23.8125 4.19947507
7 / 8 0.875 22.225 4.49943757
13 / 16 0.8125 20.6375 5.72655691
3 / 4 0.75 19.05 5.24934383
11 / 16 0.6875 17.4625 5.72655691
5 / 8 0.625 15.875 6.29921260
9 / 16 0.5625 14.2875 6.99912511
1 / 2 0.5 12.7 7.87401575
7 / 16 0.4375 11.1125 8.998875141
3 / 8 0.375 9.525 10.49868766
5 / 16 0.3125 7.9375 12.59842520
1 / 4 0.25 6.35 15.74803150
3 / 16 0.1875 4.7625 20.99737533
1 / 8 0.125 3.175 31.49606299
pin-length:
1 / 16 0.0625 1.5875 62.99212598
shoe-ounce:
1 / 64 0.015625 0.396875 0.251968504
The old measure system of the USA is still in use for the geodetic surveying, thus for cartography, land measurements and land surveillance. Hence it has been renamed to 'US-Survey'. It uses the same measure names as those in the Surveyor+Chain system. But the corresponding sizes are slightly bigger. It is based on the old value the foot had in the United States. This value had been defined as exactly 1200/3937 metric meters. Thus one meter is exactly 39.37 survey inches long. The number 3937 is a combination of two weird prime numbers: 3937 = 31 * 127
The old British foot was 1200000/3937014 meters long. This value is out of use nowadays. So no references are made to it.
A multiplication factor exists between both measure systems
in the USA. This factor is exactly: (3937*254)/1000000
= 0.999998 herein 254/10000 being the length in
meters of the Survey+Chain inch. So it holds exactly:
# centimeters name inverse
------------- ---- -------
185318.7706375 naut.mile 0.5396107456140/km
160934.7218694 stat.mile 0.6213699494949/km
91.44018288037 yard 1.0936111111111/m
30.48006096012 foot 3.2808333333333/m
2.540005080010 inch 39.37[*] / m
999998 = 3937 * 254 = 31 * 127 * 127 * 2
The inverse of the multiplication factor is 1.000002000004000.
A very good approximation is 1.00000200. Thus the
ratio US-Survey-measure / Surveyor+Chain-measure becomes:
1.000002 = 1+2.0@-6 for linear measures;
1.000004 = 1+4.0@-6 for square measures;
1.000006 = 1+6.0@-6 for cubic measures.
name consists of # metric
---- ----------- --------
US-Survey mile 1.000 00200 ordinary mile 1609.347 218 688 m
US-Survey-foot 1.000 00200 ordinary foot 0.3048 00 6096 m
US-Survey-inch 1.000 00200 ordinary inch 0.0254 000 508 m
US-Survey acre 1.000 00400 ordinary acre 4046.8726 09826 m2
square USur.mile 1.000 00400 square ord.mile 2.58 9998 47029 km2
square USur.yard 1.000 00400 square ord.yard 0.8361 3070 451 m2
square USur.foot 1.000 00400 square ord.foot 929.03411 61216 cm2
cubic int.mile 1.000 00600 cubic ord.mile 4 168 206 834.5 m3
name consists of
---- -----------
circumference of 40227 kilometer
earth equator
-- idem -- 360 degrees of earth equator
degree on earth equator 15 geographical leagues
-- idem -- 20 marine leagues
geographical league 4 international miles
marine league 3 international miles
international mile 1 minute of earth equator
-- idem -- 10 ordinary cable-lengthes
internat. cable-length 608 ordinary feet
This table is not actually used, as some measure values rising from these intentions are slightly contradictory. Besides this one wants the translation of the measures into the metric system not to result into too awkward numbers. So the measure sizes have been adapted slightly. The international nautical mile is defined such that it consists of an integral number of metric meters. Since the same holds for the Canadian landmile this mile is added to the tables. Consequently:
metric equivalents:
name consists of # meters inverse
---- ----------- -------- -------
geograph.league 4 nautical mile 7408 0.13498920 / km
marine league 3 nautical mile 5556 0.17998560 / km
old-Fr.mar.lieue 2.4 [*] naut.mile 4444.8[*] 0.22498200 / km
nautical mile 10 int.cable-len. 1852 0.53995680 / km
int.cable-length 185.2[*] 5.39956803 / km
Canadian league 3 Canadian mile 4827 0.20716801 / km
Canadian mile 1609 0.62150404 / km
metric kilometer 1000 1 / km
ordinary foot 12 ordinary inch 0.3048[*] 3280.839895 / km
US-Survey foot 12 USSurvey inch 0.3048006096 3280.833333 / km
Brit.naut. mile 1.000 6393 nautical mile = 1853.184[*] m
nautical mile 0.999 3611 Brit.naut. mile = 1852 meters
statute mile 1.000 2138 Canadian mile = 1609.344[*] m
Canadian mile 0.999 78625 statute mile = 1609 meters
[*] = This non-integral value is exact.
name # US-Survey feet # ordinary feet
---- ---------------- ---------------
geograph.league 24304.4133333... 24304.4619423
marine league 18228.31 [*] 18228.3464567
old-Fr.mar.lieue 14582.648 [*] 14582.6771654
nautical mile 6076.1033333... 6076.1154856
int.cable-length 607.6103333... 607.6115486
Canadian league 15836.5825 [*] 15836.6141732
Canadian mile 5278.8608333... 5278.8713911
metric kilometer 3280.8333333... 3280.8398950
Brit.naut. mile 6079.98784 [*] 6080
old-Brit.cable-len 607.998784 [*] 608
statute mile 5279.98944 [*] 5280
US-Survey foot 1 1.00000200
ordinary foot 0.999998 [*] 1
metric meter 39.37 [*] USS-inch 39.37007874 inch
Meanings of symbols and abbreviations in this table:
[*] = this value is exact
333... = infinite sequence of the digit 3
ordinary = Surveyor+Chain+British-nautical
marine league = international nautical league
nautical mile = international nautical mile
old-Brit.cable-len = old British nautical cable-length
old-Fr.mar.lieue = old French lieue-maritime (=sea-league)
Other synonyms:
mi = abbreviation for any mile
admiralty mile = British nautical mile
geographical mile = air-mile
= sea-mile
= international nautical mile
short cable-length = international cable length
international foot = ordinary foot
= Surveyor+Chain foot
international yard = ordinary yard
= Surveyor+Chain yard
international-foot and -yard are the official names for
the ordinary-foot and -yard.
There are several miles that are intended to be one sixtieth of the length of one degree on the earth equator. But many of them are approximations only. All have a length between 1852 and 1856 metric meters. So the earth degree is between 59.7 and 60.3 actual miles long. There are also several leagues that are intended to be one fifteenth or one twentieth of one earth degree, and thus contain three or four of such miles. Some of the miles and leagues are listed in the table below. Many of them are called "geographical". In formulas the abbreviation for a mile of any type is often 'mi'.
name consists of # meters inverse
---- ----------- -------- -------
--- values from above ---
statute league 3 statute mile 4828.032 0.20712373 / km
statute mile 5280 ordinary foot 1609.344 0.62137119 / km
US-survey mile 5280 / 0.999998 foot 1609.34722 0.62136995 / km
old-UK-land-mile 5000 ordinary foot 1524 0.6561680 / km
geograph.league 4 Brit.naut.mile 7412.736 0.13490296 / km
Brit.naut.league 3 Brit.naut.mile 5559.552 0.17987061 / km
Brit.naut.mile 6080 ordinary foot 1853.184 0.53961182 / km
radar-data mile 6000 ordinary foot 1828.8 0.54680665 / km
Canadian league 3 Canadian mile 4827 0.20716801 / km
Canadian mile 1609 0.62150404 / km
int.geogr.league 4 int.naut. mile 7408 0.13498920 / km
int.naut.league 3 int.naut. mile 5556 0.17998560 / km
int.naut. mile 1852 0.53995680 / km
old-Fr.sealeague 2.4 int.naut.mile 4444.8 0.22498200 / km
--- other modern values ---
geograph.league 4 geograph. mile 7421.5912 0.13474199 / km
geograph. mile 1855.3978 0.53896798 / km
geograph. mile 6087.2 ordin.foot 1855.37856 0.53897357 / km
geograph. mile 1855.32572 0.53898892 / km
USA-nautic.mile 6080.2 ordin.foot 1853.245 0.53959407 / km
= earth-equator's minute
int.statute mile 1609.347 0.62137003 / km
int.Survey mile 1852 x 1.000002 m. 1852.03704 0.53995572 / km
Telegraph mile 1855.3176 0.53899128 / km
Irish mile 6720 ordinary foot 2048.256 0.4882202 / km
French post-league 2 French mile 3898.0872 0.2565361 / km
French mile 6000 French foot 1949.0436 0.5130715 / km
--- metrical ---
Spanish league 5 kilometre 5000 0.2 / km
ordinary league 4 kilometre 4000 0.25 / km
USA-mile 1.6 kilometre 1600 0.625 / km
European mile 1.5 kilometre 1500 0.6666667 / km
kilometre 1000 1 / km
--- old Roman values --- (metric approximation)
day's march 12.5[*] Roman mile 18500 0.054054054 / km
Roman mile 5000 Roman foot 1480 0.67567568 / km
The old British inch has the length of 2.53998 cm. So the multiplication factor for the linear old-UK measures is: 0.999 99213. This factor has to be used in the same way as the factor in the old US-Survey system.
name consists of meaning of name
---- ----------- ---------------
lieue-de-poste 2 mille post-league
mille 1000 toise mile
arpent (linear) 10 perche <- arepennis = ?
perche (linear) 3 toise perch, log, beam
toise (='fathom') 4 coudee <- tendre = stretch
passe de Haiti 3.5[*] pied Haitian pace
coudee 1.5[*] pied ell, ellbow
pied (de roi) 12 pouce foot
pouce 12 ligne thumb, inch
ligne 12 douzieme line
douzieme one-twelfth
abbr. #meters[*] name inverse
----- ---------- ---- -------
3898.0872 lieue-de-poste 0.2565361 / km
1949.0436 mille 0.5130715 / km
58.471308 (linear) arpent 0.01710238 / m
5.8471308 (linear) perche 0.1710238 / m
1.9490436 toise 0.5130715 / m
1.1369421 passe de Haiti 0.8795523 / m
0.4872609 coudee 2.052286 / m
0.3248406 pied (de roi) 3.078429 / m
0.02707005 pouce 36.94115 / m
2.2558375@-3 ligne 443.29380 / m
1.87986458333@-4 douzieme 5319.53210 / m
At present the exact definition of the arpent is 191.835 foot = 58.471308 meter. This leads to the following table:
equals Anglo-Saxon:
name foot [*] yard [*]
---- -------------------------
lieue-de-poste 12789 4263
mille 6394.5 2131.5
arpent (linear) 191.835 661+1/6
perche (linear) 19.1835
toise (='fathom') 6.3945
passe de Haiti 3.730125
coudee 1.598625
pied (de roi) 12.789 inch
pouce 1.06575 inch
ligne 0.0888125 inch
name consists of [*] # feet
---- --------------- ------
Ireland mile 8 Irish furlong 6720
Ireland furlong 10 Irish chain 840
Ireland chain 4 Irish perch 84
Ireland perch 21 ordinary foot 21
any Irish length = 14/11 (= 1.27272727...) English length
Welsh ridge 3 Welsh leap 81/4 = 20.25
Welsh leap 6 foot + 9 inch 27/4 = 6.75[*]
Jersey foot 11 inch 11/12 = 0.916667
Jersey foot 12 Jersey inch 11/12
Jersey inch 11/144 = 0.0763889
# meters[*] name inverse
----------- ---- -------
2048.256 Irish mile 0.4882202 / km
256.032 Irish furlong 3.905762 / km
25.6032 Irish chain 39.05762 / km
6.4008 Irish perch 0.1562305 / m
6.1722 Welsh ridge 0.1620168 / m
2.0574 Welsh leap 0.4860504 / m
0.3048 ordinary foot 3.280840 / m
0.2794 Jersey-foot 3.579098 / m
0.02328333[~] Jersey-inch 42.949177 / m
name consists of [*] # feet
---- --------------- ------
versta 500 sadzhen, sagene 3500
sadzhen = sagene 3 arshin 7
arshin 28 inch 7/3
arshin 16 vershok, verchok 7/3
vershok = verchok 1.75[*] inch
# meters[*] name inverse
----------- ---- -------
1066.8 versta 0.9373828 / km
2.1336 sadzhen, sagene 0.4686914 / m
0.7112 arshin 1.406074 / m
0.04445 vershok = verchok 22.49719 / m
virsta = vehrsta = versta = verst = werst
name consists of
---- -----------
amsterdam cable-length 120 amst. fathoms
amsterdam fathom 6 amst. feet
abbrev. # meters name inverse
------ -------- ---- -------
203.9 amsterdam cable-length 4.905 / km
1.699 amsterdam fathom 0.589 / m
0.283 amsterdam foot 3.534 / m
0.6858 old Dutch ell 1.458 / m
0.750 old Dutch step 1.333 / m
0.314858 old S.African Cape-foot 3.176035 / m
--- scientists' definition: ---
abbrev. name consists of
------ ---- -----------
m meter 1 / 299 792 458 -th part of
the length travelled by
the light in one second.
The lenght measures of yarn and textiles presented here fit into the the general length system. But for the sake of clarity they are not listed in the general lengths table, but they are in the separate tables of this chapter.
The general length units in these tables refer to the length units defined in the chapter Surveyor + Chain + British-nautical.
name consists of [*] # yard [*]
---- --------------- ----------
+++++ general for linen, cotton and wool +++++
any linen-length = 2.5 cotton-length with same name
any cotton-length = 1.5 wool-length with same name
bundle 20 hank
hank 6 heer
heer 2 cut
cut wool: 46+2/3 yard 46.667[~]
hank 7 skein
skein 1 lea, rap
lea = rap wool: 80 yard 80
+++++ linen +++++
bundle 20 hank 42000
hank 6 heer 2100
heer 2 cut 350
cut 175 yard 175
hank 7 skein 2100
skein 1 lea, rap 300
lea = rap 200 French ell 300
French ell 3 cubit 1.5
+++++ cotton, silk, worsted +++++
bundle 20 hank 16800
spindle 18 hank 15120
hank 6 heer 840
heer 2 cut 140
cut 70 yard 70
hank 7 skein 840
skein 1 lea, rap 120
lea = rap 80 cotton-thread 120
cotton-thread 1 French ell 1.5
French ell 3 cubit 1.5
+++++ wool +++++
bundle 20 hank 11200
hank 6 heer 560
heer 2 cut 93.333[~]
cut 46+2/3 yard 46.667[~]
US-hank 20 skein 1600
hank 7 skein 560
skein 1 lea, rap, wrap 80
lea = rap = wrap 80 yard 80
yard 2 cubit 1
+++++ lint, jute +++++
spindle 4 hasp, hank 14400
hasp = hank 6 heer 3600
heer 2 cut 600
cut 120 lint-thread 300
lint-thread 5 cubit 2.5
+++++ general +++++
gener.bolt-of-cloth 2.5[*] cotton-bolt 100
landcable-length 6 cotton-bolt 240
landcable-length 8 hank-of-cloth 240
cotton-bolt 20 fathom 40
hank-of-cloth 15 fathom 30
wool-, lint-bolt 35 fathom 70
fathom 2 ounce-thread 2
ounce-thread 1 yard 1
yard 2 cubit 1
# inch [*]
+++++ clothings +++++ ----------
wool-bolt-width 20 palm-width 60
cotton-bolt-width 14 palm-width 42
palm-width 3 inch 3
Scottish ell 4 + 1/9 span 37
French ell 6 span 54
English ell 5 span 45
yard 4 span 36
Flemish ell 3 span 27
goad 1 French ell 54
French ell 3 cubit 54
yard 2 cubit 36
cubit 2 breadth-of-flags 18
breadth-of-flags 1 linear-quarter 9
linear-quarter 1 span 9
span 2 finger-length 9
finger-length 2 nail 4.5
nail 2.25 inch 2.25
[~] = These few values are NOT exact !!
In earlier times the Scottish ell was 37.2[*] or 37.0598 inch
long. At present it is redefined to exactly 37 inches.
abbrev. # meters [*] name inverse
------ ------------ ---- -------
bdl 38404.8 linen-bundle 0.02603841 / km
bdl 15361.92 cotton-bundle 0.06509603 / km
13825.728 cotton-spindle 0.07232892 / km
13167.36 lint-spindle 0.07594537 / km
bdl 10241.28 wool-bundle 0.09764404 / km
3291.84 hasp 0.30378147 / km
1920.24 linen-hank 0.52076824 / km
1463.04 US-wool-hank 0.68350831 / km
768.096 cotton-hank 1.301921 / km
548.64 lint-heer 1.822689 / km
512.064 wool-hank 1.952881 / km
320.04 linen-heer 3.124609 / km
274.32 lint-cut 3.645378 / km
274.32 linen-skein 3.645378 / km
274.32 linen-lea, -rap 3.645378 / km
219.456 (land) cable-length 4.556722 / km
160.02 linen-cut 6.249219 / km
128.016 cotton-heer 7.811524 / km
109.728 cotton-skein 9.113444 / km
109.728 cotton-lea, -rap 9.113444 / km
91.44 general-bolt-of-cloth 10.936133 / km
85.344 wool-heer 11.717285 / km
73.152 wool-skein 13.670166 / km
73.152 wool-lea,-rap,-wrap 13.670166 / km
64.008 cotton-cut 15.623047 / km
64.008 lint-bolt 15.623047 / km
42.672 wool-cut 23.434571 / km
36.576 cotton-bolt 27.340332 / km
27.432 hank-of-cloth 36.453777 / km
2.2860 lint-thread 437.44532 / km
fath 1.8288 fathom 546.80665 / km
1.524 wool-bolt-width 656.16798 / km
1.3716 goad 729.07553 / km
1.3716 cotton-thread 729.07553 / km
Fr.e 1.3716 French ell 729.07553 / km
Eng.e 1.143 (English) ell 874.89064 / km
1.0668 cotton-bolt-width 937.38283 / km
Sc.e 0.9398 Scottish ell 1.064056 / m
0.9144 ounce-thread 1.093613 / m
yd 0.9144 yard 1.093613 / m
Fl.e 0.6858 Flemish ell 1.458151 / m
0.4572 cubit 2.187227 / m
ft 0.3048 foot 3.280840 / m
0.2286 breadth-of-flags 4.374453 / m
qr 0.2286 span = linear-quarter 4.374453 / m
0.1143 finger-length 8.748906 / m
0.1016 hand 9.842520 / m
0.0762 palm-width 13.123360 / m
nl 0.05715 nail 17.497813 / m
in 0.0254 inch 39.370079 / m
abbr. name consists of mass/meter
---- ---- ----------- ----------
tex 9 denier 1 mg/m = 1 g/km
tex 10 drex 1 mg/m = 1 g/km
drex 1 dtex 0.1 [*] mg/m
dtex (= deci-tex) 0.1 [*] mg/m
den denier (= 1 g / 9 km) 0.11111 mg/m
poumar 1@-6 (avdp)pound/yard 0.49605465 mg/m
typp 1000 yard/(avdp)pound 2.01590693 m/g
US-run 1600 yard/(avdp)pound 3.22545108 m/g
abbrev. unit meters/hour[*] meters/sec
------ ---- -------------- ----------
kph kilometers per hour 1000 0.27777778
fps feet per second 1097.28 0.3048 [*]
mph statute miles per hour 1609.344 0.44704[*]
knot internat. miles per hour 1852 0.51444444
(knot) UK-nautic. miles per hour 1853.184 0.51477333
mps meters per second 3600 1
Mach speed of sound (typical) 1193760 331.6
[*] = This value is exact.
The speed of sound and so the Mach speed depends on the
temperature and the pressure of the air. Here the value
at 0 degree Celsius and 1 atmosphere is shown. Generally
values from 1060 up to 1230 kph can occur in the air.
In Germany the abbreviation 'kph' is written 'kmh'.
Note that exactly holds:
1 kph = 5/18 mps
and mph = 22/15 fps
and knot = 463/900 mps,
and that roughly holds:
1 mps = 2 knots = 9/4 mph = 10/3 fps = 18/5 kph
and 1 mph = 1.5 fps
and 1 fps = 1.1 kph
name consists of [*] # sq. yard [*]
---- --------------- --------------
sq. geograf.league 16 sq. naut.mile 591462400/9
sq. naut.league 9 sq. naut.mile 36966400
sq. naut.mile 100 sq. cable-len. 36966400/9
sq. cable-length 369664 sq. foot 369664/9
hundred 100 hide 58080000
hide = carucate 4 virgate, yardland 580800
virgate = yardland 2 oxgang, bovate 145200
oxgang = bovate 15 acre 72600
hide = carucate 6 nook 580800
hundred 3 barony 58080000
barony 40 USA-hide 19360000
USA-hide 5 nook 484000
township 4 sq. land-league 111513600
sq. land-league 9 sq. (stat)mile 27878400
sq. (stat)mile 1 USA-section 3097600
USA-section 4 quarter-section 3097600
quarter-section 1 homestead 774400
homestead 2 USA-lot 774400
USA-lot 4 nook 387200
nook 2 sq. furlong 96800
sq. furlong 10 acre 48400
acre 10 sq. chain 4840
sq. chain 16 sq. pole, sq.perch 484
sq. perch = sq. pole 1 sq. rod 30.25
sq. rod 625 sq. link 30.25
sq. link 62.7264 sq. inch 0.0484
sq. (stat)mile 640 acre 3097600
Welsh-cover 2/3 acre 29040/9
acre 4 farthingdale 4840
farthingdale 1 rood 1210
rood 40 sq. rod, perch, pole 1210
sq. rod (sq.perch,
sq.pole) 121 sq. cubit 30.25
sq. fall 225 sq. cubit 56.25
sq. cubit 2.25 sq. foot 1/4 = 0.25
US-football-area 1600 sq. fathom 6400
commerc.acre 1000 sq. fathom 4000
sq. Ramden-chain 100 timber-square 10000/9
timber-square 1 square 100/9
square 100 sq. foot 100/9
(wallpaper-)roll 30 sq. foot 10/3
basebox 128*5*49=31360 sq.inch 1960/81
sq. chain 121 sq. fathom 484
sq. fathom 4 sq. yard 4
sq. yard 9 sq. Ramden-link 1
sq. Ramden-link 1 sq. foot 1/9
super(-ficial) foot 1 sq. foot 1/9
sq. foot 144 sq. inch 1/9
sq. inch 1/1296
[*] = All numeric values in this table are exact!
US-football-area = area of USA football field with end zones
abbrev. # sq.meters name inverse
------- ----------- ---- -------
twp 93.2395720 @+6 township 0.01072506 / sq.km
54.9486550 @+6 sq. geograf.league 0.01819881 / sq.km
30.9086184 @+6 sq. nautic.league 0.03235344 / sq.km
23.3098930 @+6 sq. (land-)league 0.04290024 / sq.km
4.85622771 @+6 hundred 0.2059212 / sq.km
3.43429094 @+6 sq. nautic.mile 0.2911809 / sq.km
mi2 2.58998811 @+6 sq. (statute-)mile 0.3861022 / sq.km
2.58998811 @+6 USA-section 0.3861022 / sq.km
1.61874257 @+6 barony 0.6177635 / sq.km
647497.03 quarter-section 1.5444086 / sq.km
647497.03 homestead 1.5444086 / sq.km
485622.77 hide = carucate 2.0592115 / sq.km
404685.64 USA-hide 2.4710538 / sq.km
323748.51 USA-lot 3.0888173 / sq.km
121405.69 virgate 8.2368460 / sq.km
121405.69 yardland 8.2368460 / sq.km
80937.13 nook 12.355269 / sq.km
60702.85 bovate = oxgang 16.473692 / sq.km
40468.56 sq. furlong 24.710538 / sq.km
5351.215 US-football-area 1.868734 / ha
ac,A 4046.856 acre 2.471054 / ha
3344.50944 [*] commercial-acre 2.989975 / ha
2697.904 Welsh-cover 3.706581 / ha
1011.714 rood 9.884215 / ha
929.0304 [*] sq. Ramden-chain 10.76391 / ha
404.6856 sq. chain 24.71054 / ha
47.032164 sq. fall 212.6205 / ha
25.29285 sq. pole, sq.perch 395.3686 / ha
rd2 25.29285 sq. rod 395.3686 / ha
20.2322176 [*] basebox 494.2612 / ha
9.29 0304 [*] timber-square 0.1076391 / sq.m
9.29 0304 [*] square 0.1076391 / sq.m
3.3445 0944 [*] sq. fathom 0.2989975 / sq.m
2.7870 912 [*] (wallpaper-)roll 0.3587970 / sq.m
yd2 0.8361 2736 [*] sq. yard 1.195990 / sq.m
0.2090 3184 [*] sq. cubit 4.783960 / sq.m
super.ft 0.0929 0304 [*] superficial-foot 10.76391 / sq.m
SF/ft2 0.0929 0304 [*] sq. foot 10.76391 / sq.m
li2 0.0404 6856 sq. link 24.71054 / sq.m
in2 6.4516 sq.cm [*] sq. inch 0.15500 / sq.cm
[*] = This value is exact.
The foot is the ordinary foot.
The ordinary link and chain are the Imperial ones by Gunter.
For the US-Survey square measures, read the section Linear measures: US-Survey + Int.Nautical.
A circular measure gives the area of the largest
circle that fits completely inside the square with
the corresponding name. Its value is pi/4 times the
value of the square. Herein:
pi/4 = 0.7853981633975
Examples are the two circular units in the table below.
# sq.meters name inverse
----------- ---- -------
54878464 sq. int.geograph.league 0.01822208 / km2
30869136 sq. int.nautical league 0.03239482 / km2
3429904 sq. int.nautical mile 0.29155335 / km2
2693840.30 circular int.naut.mile 0.37121725 / km2
2034171.91 circular statute-mile 0.49160054 / km2
name consists of [*] # sq. feet
---- --------------- ----------
Ireland acre 160 sq. Irish-perch 70560
Guernsey-vergee 6/7 Jersey-vergee 16594.286
Jersey-vergee 44 * 44 * 10 sq. foot 19360
Haitian carreau 10000 sq. Haitian-pace 139138.325
sq. Russ.arshin 49/9 sq. foot 5.4444444
South-Africa morgen 1 * 47 * 109 sq.yard 10246 yd2
Welsh stang 5 * 8 * 81 sq.yard 3240 yd2
# sq. meters name inverse
------------ ---- -------
12926.373 Haitian carreau 0.7736122 / ha
8566.961 South-Africa morgen 1.167275 / ha
6555.2385024[*] Irish acre 1.525498 / ha
2709.053 Welsh stang 3.691327 / ha
1798.603 Jersey-vergee 5.559871 / ha
1541.660 Guernsey-vergee 6.486516 / ha
5.0580544[*] sq. arshin 0.1977045 / m2
5188.277465 Cunningham-acre 192.742198 / km2
5188.277465 plantation-acre 192.742198 / km2
4935.190759 Scotland-acre 202.626413 / km2
3418.89386 sq. Paris-arpent 292.492262 / km2
34.18894 sq. Paris-perch 292.492262 / hm2
4.088963 sq. Paris-toise 0.244560783 / m2
name consists of # cu. foot
---- ----------- ----------
++++ nautical & geodetic ++++
cu. Br.naut.-mile 1000 cu. cable-length 224755712@+3
cu. cable-length 224755712 cu.foot 224755712
cu. (statute) mile 512 cu. furlong 147197952@+3
cu. furlong 1000 cu. chain 287496@+3
cu. chain 1331 cu. fathom 287496
cu. fathom 8 cu. yard 216
cu. yard 27 cu. foot 27
++++ transport ++++
(volume-) rod 1 cunit 1000
cunit 1 register-ton 100
register-ton 2.5[*] freight-ton 100
freight-ton 1 USA-shipping-ton 40
USA-shipping-ton 1 marine-ton 40
marine-ton 8 bulk-barrel 40
displacement-ton 7 bulk-barrel 35
forty-ft-e.u. 2 twenty-ft-e.u. 2560
twenty-ft-e.u. 256 sugar-barrel 1280
sugar-barrel 1 bulk-barrel 5
bulk-barrel 5 cu. foot 5
UK-shipping-ton 14 garden-straw-bale 42
++++ wood and timber ++++
London-standard 10 cu. yard 270
cu. fathom 2 stack 216
stack (coal,firewood) 4 cu. yard 108
cu. yard 27 cu. foot 27
register-ton 2 squared-load 100
squared-load 1.25[*] unhewn-load 50
Riga-last-sq.sawn 2 unhewn-load 80
unhewn-load 1 freight-ton 40
freight-ton 2.5[*] cord-foot 40
twenty-ft-e.u. 10 cord 1280
cord 2 face-cord 128
face-cord 4 cord-foot 64
cord-foot 16 cu. foot 16
cord 3 small face-cord 128
small face-cord 1 house-cord 42.66667
house-cord 1 rick, tier 42.66667
rick = tier 512 board-foot 42+2/3
cu. foot 12 super(-ficial)-foot 1
super(-ficial) foot 1 board-foot 0.083333
board-foot 144 cu.inch = 1/12 cu.foot 1/12
London-standard 54 bulk-barrel 270
Petrograd-standard 33 bulk-barrel 165
Riga-last-sq.sawn 16 bulk-barrel 80
Riga-last-round 13 bulk-barrel 65
squared-load 10 bulk-barrel 50
unhewn-load 8 bulk-barrel 40
bulk-barrel 5 cu. foot 5
NorthAmerican-deal 2 whole-deal 2.2916666667
whole-deal 2 split-deal 1.1458333333
split-deal 990 cu. inch 0.5729166667
++++ others & general ++++
masonry-perch 16.5 * 1.5 [*] cu. foot 24.75[*]
mega-acre-foot 1000 kilo-acre-foot 4356 @ 7
kilo-acre-foot 1000 acre-foot 4356 @ 4
acre-foot 12 acre-inch 43560
acre-inch 3630 cu. foot 3630
cu. yard 1 USA-general-load 27
USA-general-load 9 garden-straw-bale 27
garden-straw-bale 3 cu. foot 3
bulk-barrel 60 board-foot 5
USA-dry-barrel 49 board-foot 4.083333
board-foot 144 cu. inch 1/12 = 0.083333
cu. foot 1728 cu. inch 1
cu. inch 5.787037037@-4
note: 3630 = 11 * 11 * 10 * 3
1331 = 11 * 11 * 11
1728 = 12 * 12 * 12
[*] = This value is exact !
Forty-ft-e.u. = forty feet equivalent unit = long freight
container. One such container fits on a lorry.
Twenty-ft-e.u. = twenty feet equivalent unit = short freight
container. Two of these in series fit on a lorry.
Petrograd-standard = st.Petersburg-standard = Pittsburg-standard.
Riga-last-sq.sawn = Riga last square-sawn.
Br.naut.-mile = British nautical mile.
Cable-length = land cable length.
Board-foot = feet-board measure.
The foot is the ordinary foot.
Displacement-ton approximates well the volume of the mass of
one long ton of sea water. The volume of one long ton of fresh
water is 35.84 cu.feet.
The bulk-barrel (= 8640 cu.in) and the USA-dry-barrel
(= 7056 cu.in) are also mentioned in the section about the
USA-dry volumes.
abbrev. # cubic meters name inverse
------ -------------- ---- -------
6.364373017380 km3 cu. Br.naut.mile 0.1571247 / cu.km
4.168181825441 km3 cu.(statute)mile 0.2399128 / cu.km
Maf 1.2334818 km3 mega-acre-foot 0.8107132 / cu.km
8140980.1 cu. furlong 122.83533 / cu.km
6364373.0 cu. cable-length 157.12467 / cu.km
kaf 1233481.8 kilo-acre-foot 810.7132 / cu.km
af,ac.ft 1233.4818 acre-foot 810.7132 / cu.hm
8140.9801 cu. chain 122.8353 / cu.hm
102.79015 acre-inch 9728.5583 / cu.hm
FEU 72.491127 forty-ft-e.u 0.01379479 / cu.m
TEU 36.245564 twenty-ft-e.u 0.02758958 / cu.m
28.316847 volume-rod 0.03531467 / cu.m
7.645549 London-standard 0.13079506 / cu.m
6.116439 cu. fathom 0.1634938 / cu.m
4.672280 Petrograd-standard 0.2140283 / cu.m
3.624556 cord 0.2758958 / cu.m
3.058219 stack 0.3269877 / cu.m
RT 2.831685 register-ton 0.3531467 / cu.m
2.831685 cunit 0.3531467 / cu.m
2.265348 Riga-last-sq.sawn 0.4414333 / cu.m
1.840595 Riga-last-round 0.5433026 / cu.m
1.812278 face-cord 0.5517917 / cu.m
1.415842 squared-load 0.7062933 / cu.m
1.208185 small face-cord 0.8276875 / cu.m
1.208185 house-cord 0.8276875 / cu.m
1.208185 rick = tier 0.8276875 / cu.m
1.189308 UK-shipping-ton 0.8408254 / cu.m
1.132674 USA-shipping-ton 0.8828666 / cu.m
FT 1.132674 freight-ton 0.8828666 / cu.m
1.132674 marine-ton 0.8828666 / cu.m
1.132674 unhewn-load 0.8828666 / cu.m
DT 0.9910896 displacement-ton 1.0089905 / cu.m
0.7645549 USA-general-load 1.3079506 / cu.m
cy 0.7645549 cu. yard 1.3079506 / cu.m
0.7008420 masonry-perch 1.4268552 / cu.m
0.4530695 cord-foot 2.2071666 / cu.m
0.1415842 bulk-barrel 7.0629333 / cu.m
0.1415842 sugar-barrel 7.0629333 / cu.m
bbl 0.1156271 USA-dry-barrel 8.6484898 / cu.m
84.950540 cu.dm garden-straw-bale 11.7715556 / cu.m
64.892773 cu.dm NorthAmerican-deal 15.4100364 / cu.m
32.446387 cu.dm whole-deal 30.8200728 / cu.m
ft3 28.316847 cu.dm cu. foot 35.3146667 / cu.m
16.223193 cu.dm split-deal 61.6401456 / cu.m
super.ft 2.359737 cu.dm super-foot 0.4237760 / cu.dm
BF/fbm 2.359737 cu.dm board-foot 0.4237760 / cu.dm
in3 16.387064 cu.cm [*] cu. inch 61.0237441 / cu.dm
[*] = This value is exact !
The USA-dry-volumes system has been derived from the old British dry-system. Therefore some old British striked (= not-heaped) dry-units are included in the tables. If such unit has the same name as an American unit, but a different size, then it is marked with the prefix OB = old-British.
name consists of # cu.inch[*] # gallon
---- ----------- ------------ --------
bulk-barrel 128.57 quart 8640 32.14
barrel 105.00 quart 7056 26.25
last 2 horse-load 172033.6 640
horse-load 1 wey 86016.8 320
wey 5 quarter 86016.8 320
chaldron 4 fatt 77415.12 288
fatt 2 OB-barrel 19353.78 72
OB-barrel 9 bucket 9676.89 36
big sack 5 bushel 10752.1 40
fatt 3 bag 19353.78 72
bag = sack 3 bushel 6451.26 24
berries-tray 3 quartern 403.20375 3/2
trug-of-grain 2/3 bushel 1433.613333[~] 16/3
US-citrus:
field-box 10 US-c-box 34406.72 128
box 2 US-c-carton 3440.672 12.8[*]
carton 0.1 [*] quarter 1720.336 6.4[*]
tun = ton 2 Scott.quarter 68813.44 256
Scott.quarter 2 quarter, seam 34406.72 128
quarter = seam 2 coomb(e) 17203.36 64
coomb(e) 2 strike 8601.68 32
strike 2 bushel 4300.84 16
bushel 2 bucket 2150.42 8
bucket 2 peck 1075.21 4
peck 2 gallon 537.605 2
gallon 2 pottle, quartern 268.802 5 1
pottle=quartern 2 quart 134.401 25 1/2
quart 2 pint, chopine 67.200 625 1/4
pint = chopine 2 cup, demiard 33.600 3125 1/8
cup = demiard 2 gill, roquille 16.800 15625 1/16
gill = roquille 8.400 078125 1/32
7056 = 144 * 49 .
[*] = All values in the cu.inch-column are exact, except
the one indicated with [~].
The barrel and the bulk-barrel (= sugar barrel) belong to the
cubic-measure system of Surveyor+Chain+Big-cargo.
Therefore they are also mentioned in that section. Consequently
their values 105.00 and 128.57 in the left column and their values
26.25 and 32.14 in the right column are not exact.
Gallon = Queen-Elisabeth-1 gallon = old-British corn-gallon
= old-British grain-gallon.
Bushel = Winchester bushel of 1696. In spite of its name it has
no relation to the Winchester quart. In early days the size of
this bushel was exactly 2150 cubic inch. At present the size
is 2150.42 cubic inch. The corresponding sizes of the gallon
are: old = 268.75 in3, nowadays = 268.8025 in3.
Note the difference in the meanings of the very similarily
spelled words Quart and Quarter.
Chalder = chaldron = chauldron = cauldron = large kettle.
Scott.quarter = Scottish quarter.
OB = old-British dry-system.
abbrev. # cu.dm name inverse
------ ------- ---- -------
2819.1256 last 0.3547199 / m3
1409.5628 horse-load 0.7094398 / m3
1409.5628 wey 0.7094398 / m3
chal/chd 1268.6065 chaldron 0.7882665 / m3
1127.6502 tun = ton 0.8867998 / m3
563.82512 Scott.quarter 1.7735996 / m3
563.82512 US-citr.field-box 1.7735996 / m3
317.15163 fatt 3.153066 / m3
qtr/qr 281.91256 quarter = seam 3.547199 / m3
176.19535 big-sack 5.675519 / m3
158.57582 OB-barrel 6.306132 / m3
141.58423 bulk-barrel 7.062933 / m3
140.95628 coomb(e) 7.094398 / m3
bbl 115.62712 barrel 8.648490 / m3
sk 105.71721 bag = sack 9.459198 / m3
70.478140 strike 14.18880 / m3
56.382512 US-citrus-box 17.735996 / m3
bu(sh) 35.239070 bushel 28.37759 / m3
28.191256 US-citrus-carton 35.47199 / m3
23.492713 trug-of-grain 42.56639 / m3
17.619535 bucket 56.75519 / m3
pk 8.8097675 peck 0.1135104 / dm3
6.6073257 berries-tray 0.1513472 / dm3
gal 4.4048838 gallon 0.2270207 / dm3
2.2024419 pottle = quartern 0.4540415 / dm3
qt 1.1012209 quart 0.9080830 / dm3
pt 0.5506105 pint = chopine 1.816166 / dm3
0.2753052 cup = demiard 3.632332 / dm3
gi 0.1376526 gill = roquille 7.264664 / dm3
The exact value of the bushel is 35.239 070 166 88 litre.
OB = Old-British unit with same name as an USA-unit.
The USA-liquids-volumes system has been derived from the old British wine-system. Therefore some old British wine-units are included in the tables. If such unit has the same name as an American unit, but a different size, then it is marked with the prefix OB = old-British.
name consists of # gal/in3
---- ----------- ---------
+++++ trade and industry +++++ # gallon
--------
oil-drum 55 gallon 55
oil-tanker 2 000 000 petroleum-barrel 84 @ 6
oil-barge 25 000 petroleum-barrel 105 @ 4
wine-puncheon 2 petroleum-barrel 84
petroleum-barrel 1 wine-tierce 42
wine-tierce 4 tenhalf 42
tenhalf 10.5 [*] gallon 10.5[*]
tun = ton 2 butt, pipe 252
butt = pipe 1 puncheon 126
puncheon 2 hogshead 126
hogshead 2 wine-barrel 63
wine-barrel 3 tenhalf 31.5[*]
tenhalf 10.5 [*] gallon 10.5[*]
beer-barrel 2 beer-keg 31
beer-keg 2 ponykeg 15.5[*]
ponykeg 7.75 [*] gallon 7.25[*]
tun = ton 3 tierce, tertian 252
tierce = tertian 1 thirdendel 84
thirdendel 1 wine-puncheon 84
wine-puncheon 2 wine-tierce 84
wine-puncheon 7 wine-keg 84
wine-keg 12 gallon 12
hogshead 7 firkin 63
runlet = rundlet 1 kilderkin 18
kilderkin 2 firkin 18
firkin 2 pin 9
pin 2 beer-case 4.5[*]
beer-case 9 quarts 2.25[*]
unit-case 6 quarts 1.5[*]
proof-spirit-barrel 4 anker 40
anker 2 sales-bucket 10
sales-bucket 5 flagon 5
flagon 1 gallon 1
++++++ domestic +++++ # cu. inch
----------
gallon 3 * 7 * 11 cu.inch 231
gallon 160 OB-ounce 231
gallon 5 (wine-)fifth 231
(wine-) fifth 1 whiskey-bottle 46.2[*]
whiskey-bottle 2 can, (wine)tenth 46.2[*]
can = (wine-)tenth 16 OB-ounce 23.1[*]
gallon 32 gill, roquille 231
gill = roquille 5 OB-ounce 7.21875[*]
OB-ounce 1.44375[*]
gallon 128 ounce 231
gallon 6 champagne-bottle 231
champagne-bottle 64/3 = 21+1/3 ounce 38.5[*]
champagne-bottle 2/3 quart 38.5[*]
champagne-quart 1 wine-bottle 46.921875[*]
wine-bottle 26 ounce 46.921875[*]
soda-bottle 12 ounce 21.65625[*]
gallon 2 pottle 231
pottle 2 milk-bottle 115.5[*]
milk-bottle 1 quart 57.75[*]
quart 2 pint, chopine 57.75 [*]
pint = chopine 2 OB-chopin 28.875 [*]
OB-chopin 1 cup, demiard 14.4375[*]
cup = demiard 1 tumbler, glass 14.4375[*]
tumbler = glass 2 quartern 14.4375[*]
quartern 1 wine-glass 7.21875[*]
wine-glass 1 butter-stick 7.21875[*]
butter-stick 1 gill, roquille 7.21875[*]
gill = roquille 2 double 7.21875[*]
double 2 ounce 3.609375[*]
ounce 1.8046875[*]
+++++ cans +++++
number-10-can 105 ounce 189.4921875[*]
number-5-can 7 cup = 56 oz 101.0625[*]
number-3-can 4 cup = 32 oz 57.75[*]
number-2.5-can 3.5[*] cup = 28 oz 50.53125[*]
number-2-can 19 ounce 34.2890625[*]
number-1-can 10 ounce 18.046875[*]
cup 8 ounce = 2 gill 14.4375[*]
+++++ apothecary and cooking +++++
ounce 1 shot, pony 1.8046875[*]
shot = pony 1 coffeemeasure 1.8046875[*]
coffeemeasure 2 bartender-count 1.8046875[*]
bartender-count 1 tablespoon 0.90234375[*]
tablespoon 2 papspoon 0.90234375[*]
papspoon 2 bart.teaspoon 0.451171875[*]
bart.teaspoon 1 dram 0.22558594
dram 3 scruple 0.22558594
scruple 1 saltspoon 0.075195313
saltspoon 2 pinch, smite 0.075195313
pinch = smite 2 dash 0.037597656
dash 5 drop 0.018798828
drop 1 minim 0.003759766
minim 0.003759766
dash 6 old-kitchen-drop 0.018798828
old-kitchen-drop 0.003133138
ounce 3 dessertspoon 1.8046875[*]
tablespoon 3 teaspoon 0.90234375[*]
dessertspoon 2 teaspoon 0.6015625[*]
teaspoon 2 coffeespoon 0.30078125[*]
coffeespoon 2 saltspoon 0.150390625[*]
saltspoon 1 scruple 0.075195313
scruple 20 drop 0.075195313
drop 0.003759766
+++++ bartender (= bart. = b.) +++++
soda-bottle 12 ounce = 3 gill 21.65625[*]
soda-bottle 2 soda-split 21.65625[*]
soda-split 2 b.snit 10.828125[*]
b.snit 2 b.jigger 5.4140625[*]
b.jigger 4 b.tablespoon 2.70703125[*]
b.tablespoon 3 b.teaspoon 0.67675781
b.jigger 1.5[*] shot, pony 2.70703125[*]
b.shot 1.25[*] shot, pony 2.255859375[*]
shot, pony 1 ounce 1.8046875[*]
ounce 2 b.count 1.8046875[*]
b.count 4 b.teaspoon 0.90234375[*]
b.teaspoon 1 dram (drachm) 0.22558594
dram (drachm) 4 b.dash, b.splash 0.22558594
b.dash = b.splash 0.05639648
[*] = This value is exact.
Note: 1 gill = 4 ounce (not 5 as in UK-Imperial and Old-British-Beer).
A Minim is roughly the size of one droplet of water.
Gallon = 1707 Queen-Anne's wine gallon.
OB = old-British wine-system.
Tenhalf = unit invented by the author.
Oil-tanker = roughly the size of most crude-oil super-tank-ships.
Petroleum-barrel = oil-barrel = the famous volume-unit used
by the oil producing and exporting countries (OPEC) when
determinating the price of crude oil.
abbrev. # cu.dm name inverse
------ ------- ---- -------
317974600 crude-oil super-tanker 3.144905 / hm3
3974682.4 petr.oil-barge 251.5924 / hm3
953.9238 tun = ton 1.048302 / m3
476.9619 butt = pipe 2.096604 / m3
pun(ch) 476.9619 puncheon 2.096604 / m3
317.9746 tierce, tertian 3.144905 / m3
317.9746 thinderdel 3.144905 / m3
317.9746 wine-puncheon 3.144905 / m3
hhd/hka 238.4809 hogshead 4.193207 / m3
208.1976 oil-drum 4.803128 / m3
158.9873 wine-tierce 6.289811 / m3
bo/bbl 158.9873 petrol.-barrel 6.289811 / m3
151.4165 proof-spirit-barrel 6.604301 / m3
bbl 119.2405 wine-barrel 8.386414 / m3
bbl 117.3478 beer-barrel 8.521679 / m3
68.13741 run(d)let 14.67623 / m3
68.13741 kilderkin 14.67623 / m3
58.67388 beer-keg 17.04336 / m3
45.42494 wine-keg 22.01434 / m3
39.746824 tenhalf 25.15924 / m3
ank 37.854118 anker 26.41721 / m3
fir 34.068706 firkin 29.35245 / m3
29.33694133 ponykeg 34.08672 / m3
18.92705892[*] sales-bucket 52.83441 / m3
17.03435303 pin 58.70490 / m3
8.517176514[*] beer-case 0.11740980 / dm3
5.678117676[*] unit-case 0.17611470 / dm3
3.785411784[*] flagon 0.26417205 / dm3
gal 3.785411784[*] gallon 0.26417205 / dm3
3.105220604 number-10-can 0.32203831 / dm3
1.892705892[*] pottle 0.52834410 / dm3
1.656117656 number-5-can 0.60382183 / dm3
0.946352946[*] number-3-can 1.05668821 / dm3
0.946352946[*] milk-bottle 1.05668821 / dm3
qt 0.946352946[*] quart 1.05668821 / dm3
0.828058828 number-2.5-can 1.2076437 / dm3
0.768911769 wine-bottle 1.300539 / dm3
0.768911769 champagne-quart 1.300539 / dm3
0.7570823568[*] fifth 1.320860 / dm3
0.7570823568[*] whiskey-bottle 1.320860 / dm3
0.630901964 champagne-bottle 1.585032 / dm3
0.561897062 number-2-can 1.779685 / dm3
pt 0.473176473[*] pint = chopine 2.113376 / dm3
can 0.378541178 can 2.641721 / dm3
0.354882355 soda-bottle 2.817835 / dm3
0.295735296 number-1-can 3.381402 / dm3
0.236588237 OB-chopin 4.226753 / dm3
0.236588237 cup = demiard 4.226753 / dm3
0.236588237 tumbler = glass 4.226753 / dm3
0.177441177 soda-split 5.635670 / dm3
gi 0.118294118 gill = roquille 8.453506 / dm3
0.118294118 wine-glass 8.453506 / dm3
0.118294118 butter-stick 8.453506 / dm3
0.118294118 quartern 8.453506 / dm3
0.088720589 bartender-snit 11.27134 / dm3
0.059147059 double 16.90701 / dm3
0.044360294 bartender-jigger 22.54268 / dm3
0.036966912 bartender-shot 27.05122 / dm3
0.029573530 shot = pony 33.81402 / dm3
0.029573530 coffeemeasure 33.81402 / dm3
fl.oz 0.029573530 ounce 33.81402 / dm3
0.023658824 OB-ounce 42.26753 / dm3
14.78676 cu.cm bart.-count 67.62805 / dm3
tblsp 14.78676 cu.cm tablespoon 67.62805 / dm3
11.09007 cu.cm bart.-tablespoon 90.17073 / dm3
dssp 9.857843 cu.cm dessertspoon 101.44207 / dm3
7.393382 cu.cm papspoon 135.25609 / dm3
tsp 4.928922 cu.cm teaspoon 202.88414 / dm3
fl.dr 3.696691 cu.cm dram 270.51218 / dm3
3.696691 cu.cm bart.-teaspoon 270.51218 / dm3
2.464461 cu.cm coffeespoon 405.76827 / dm3
ssp 1.232230 cu.cm saltspoon 811.53654 / dm3
1.232230 cu.cm scruple 811.53654 / dm3
0.92417280 cm3 bartender-dash 1.082049 / cm3
0.92417280 cm3 bart.-splash 1.082049 / cm3
0.61611520 cm3 pinch = smite 1.623073 / cm3
0.30805760 cm3 dash 3.246146 / cm3
gt/ggt 0.061611520 cc drop 16.23073 / cm3
min 0.061611520 cc minim 16.23073 / cm3
0.051342933 cc old-kitchen-drop 19.47688 / cm3
bo = barrel of oil.
bbl = brl = bl = barrel (general).
tblsp = tbsp = Tsp = tablespoon.
gt = ggt = gutta = Latin word for drop.
hm3 = cu.hm = cubic hectometer = 1 000 000 000 litre.
cc = cm3 = cu.cm = cubic centimeter = 0.001[*] litre.
OB = Old-British-wine unit with same name as an USA-unit.
In early British times the gallon was ca. 0.18 cu.inch
bigger: 3.7884 liters.
The volume of the transparent water can on top of the water coolers in offices and convenience shops is one sales-bucket. Everyday people should drink at least half a gallon = 8 glasses of water or 'thin' non-alcoholic beverages (e.g. lemon-juice, not thick lentil-soup); when sporting much much more, maybe one or even two gallons a day! The best and cheapest sports-drink is the humble water.
name consists of # gallon
---- ----------- --------
+++++ trade and industry +++++
wine-bottle 80/3 ounce 1/6 = 0.16666...
reputed-quart 2 reputed-pint 1/6 = 0.16666...
reputed-pint 1/3 quart 1/12 = 0.083333..
herrings-cran 37.5 [*] gallon 37.5[*]
wine-butt 12 tenhalf 126
wine-hogshead 5 tenhalf 52.5[*]
tierce 4 tenhalf 42
wine-barrel 3 tenhalf 31.5[*]
tenhalf 10.5 [*] gallon 10.5[*]
claret-hogshead 46 gallon 46
butt = pipe 2 hogshead 108
hogshead 3 runlet, rundlet 54
chaldron 4 fatt 288
fatt 2 barrel 72
barrel 2 runlet, rundlet 36
runlet=rundlet 1 kilderkin 18
kilderkin 2 firkin 18
firkin 2 pin 9
pin 4.5 [*] gallon 4.5[*]
last 2 wey 640
wey 1 horse-load 320
horse-load 5 seam 320
horse-load 8 big-sack 320
puncheon 7 anker 70
alcohol-barrel 5 anker 50
big sack 4 anker 40
anker 5 peck 10
chaldron 9 coomb(e) 288
water-ton 7 coomb(e) 224
coomb(e) 4 bushel 32
fatt 3 bag, sack 72
boll 2 bag, sack 48
bag = sack 2 firlot 24
firlot 1.5 [*] bushel 12
big sack 5 bushel 40
heaped bushel 1.278 bushel 10.224
Scott.chalder 2 tun, ton 512
tun = ton 2 Scott.quarter 256
Scott.quarter 2 seam 128
seam 1 (dry) quarter 64
(dry) quarter 2 amber 64
amber 1 coomb(e) 32
coomb(e) 2 strike 32
strike 2 bushel 16
bushel 2 bucket 8
bucket 2 peck 4
peck 2 gallon 2
gallon 277.42 cu. inch 1
+++++ domestic +++++ # cu. inch
----------
gallon 1 congius 277.4194327916
congius 2 pottle 277.4194327916
pottle 1 dry-quartern 138.7097
dry-quartern 2 quart 138.7097
quart 2 pint, chopine 69.35486
pint = chopine 1 octarius 34.67743
octarius 2 old-chopin 34.67743
old-chopin 1 breakfast-cup 17.33871
breakfast-cup 1 tumblerful 17.33871
tumblerful 1 Australian middy 17.33871
Austral. middy 2 gill, roquille 17.33871
gill = roquille 1 noggin, teacup 8.669357
noggin = teacup 1 fluid-quartern 8.669357
fluid-quartern 2 wineglass 8.669357
wineglass 2.5[*] ounce 4.334679
small-teacup 3 ounce 5.201614
small-wineglass 2 ounce 3.467743
pint 3 large-teacup 34.67743
large-teacup 11.559143
ounce 2 tablespoon 1.733871
tablespoon 2 dessertspoon 0.8669357
dessertspoon 2 teaspoon 0.4334679
teaspoon 1 drachm (dram) 0.2167339
drachm (dram) 3 scruple 0.2167339
scruple 1 coffeespoon 0.07224464
coffeespoon 20 drop 0.07224464
drop 1 minim 0.003612232
minim 0.003612232
scruple 24 old-kitchen-drop 0.07224464
old-kitchen-drop 0.0030101935
wineglass 3 nip, pub-tot 4.334679
nip = pub-tot 1.444893
wineglass 4 medic.tablespoon 4.334679
med.-tablespoon 4 medical-teaspoon 1.083670
medical-teaspoon 0.2709174
[*] = This value is exact.
Note: 1 gill = 5 ounce (not 4 as in USA-fluid).
A Minim is roughly the size of one droplet of water.
Dry-quartern = Winchester-quart. In spite of its name it
has no relation to the Winchester-bushel.
Note the difference in the meanings of the very similarly
spelled words Quart, Quarter and Quartern.
Med. = medi. = medic. = medical .
Chalder = chaldron = chauldron = cauldron = large kettle.
Tenhalf = unit invented by the author.
The Scottish volumes are dry-general.
abbrev. # cu.dm name inverse
------ ------- ---- -------
2909.4976[*] last 0.34370195 / m3
2327.59808[*] Scottish-chalder 0.42962744 / m3
1454.7488[*] wey 0.6874039 / m3
1454.7488[*] horse-load 0.6874039 / m3
chal/chd 1309.27392[*] chaldron 0.7637821 / m3
1163.79904[*] tun 0.8592549 / m3
1163.79904[*] ton 0.8592549 / m3
1018.32416[*] water-ton 0.9820056 / m3
581.89952[*] Scottish-quarter 1.718510 / m3
572.80734[*] wine-butt 1.745788 / m3
490.97772[*] butt 2.036753 / m3
490.97772[*] pipe 2.036753 / m3
327.31848[*] fatt 3.055128 / m3
pun(ch) 318.2263[*] puncheon 3.142418 / m3
qtr/qr 290.94976[*] (dry) quarter 3.437020 / m3
290.94976[*] seam 3.437020 / m3
hhd 245.48886[*] hogshead 4.073505 / m3
hhd 238.669725[*] wine-hogshead 4.189890 / m3
227.3045[*] alcohol-barrel 4.399385 / m3
218.21232[*] boll 4.582693 / m3
209.12014[*] claret-hogshead 4.781940 / m3
190.93578[*] tierce 5.237363 / m3
181.8436[*] big sack 5.499231 / m3
170.478375[*] herrings-cran 5.865847 / m3
bbl/bl 163.65924[*] barrel 6.110257 / m3
145.47488[*] amber 6.874039 / m3
145.47488[*] coomb(e) 6.874039 / m3
143.201835[*] wine-barrel 6.983151 / m3
sk 109.10616[*] sack 9.165385 / m3
109.10616[*] bag 9.165385 / m3
run 81.82962[*] run(d)let 12.22051 / m3
81.82962[*] kilderkin 12.22051 / m3
72.73744[*] strike 13.74808 / m3
54.55308[*] firlot 18.33077 / m3
47.733945[*] tenhalf 20.94945 / m3
46.479224 heaped bushel 21.51499 / m3
ank 45.4609[*] anker 21.99692 / m3
fir 40.91481[*] firkin 24.44103 / m3
bu(sh) 36.36872[*] bushel 27.49616 / m3
20.457405[*] pin 48.88206 / m3
18.18436[*] bucket 54.99231 / m3
pk 9.09218[*] peck 109.98462 / m3
gal 4.54609[*] gallon 0.21996925 / dm3
4.54609[*] congius 0.21996925 / dm3
2.273045[*] pottle 0.4399385 / dm3
2.273045[*] dry-quartern 0.4399385 / dm3
qt 1.1365225[*] quart 0.8798770 / dm3
0.75768167 reputed-quart 1.3198155 / dm3
0.75768167 wine-bottle 1.3198155 / dm3
pt 0.56826125[*] pint 1.759754 / dm3
0.56826125[*] chopine 1.759754 / dm3
0.56826125[*] octarius 1.759754 / dm3
0.37884083 reputed-pint 2.639631 / dm3
0.2841306 old-chopin 3.519508 / dm3
0.2841306 breakfast-cup 3.519508 / dm3
0.2841306 tumblerful 3.519508 / dm3
0.2841306 Austral. middy 3.519508 / dm3
0.1894204 large-teacup 5.279262 / dm3
gi 0.1420653 gill 7.039016 / dm3
0.1420653 noggin 7.039016 / dm3
0.1420653 roquille 7.039016 / dm3
0.1420653 fluid-quartern 7.039016 / dm3
0.1420653 teacup 7.039016 / dm3
0.08523919 small-teacup 11.731693 / dm3
0.07103266 wineglass 14.07803 / dm3
0.056826125[*] small-wineglass 17.59754 / dm3
fl.oz 0.02841306 ounce 35.19508 / dm3
0.02367755 nip 42.23410 /dm3
0.02367755 pub-tot 42.23410 /dm3
0.01775816 med.tablespoon 56.31213 / dm3
tbsp/Tsp 0.01420653 tablespoon 70.39016 / dm3
dssp/dsp 7.103266 cu.cm dessertspoon 140.7803 / dm3
4.439541 cu.cm medi.teaspoon 225.2485 / dm3
tsp 3.551633 cu.cm teaspoon 281.5606 / dm3
fl.dr 3.551633 cu.cm drachm (dram) 281.5606 / dm3
1.183878 cu.cm scruple 844.6819 / dm3
gt/ggt 0.05919388 cu.cm drop 16.89364 / cu.cm
min 0.05919388 cu.cm minim 16.89364 / cu.cm
0.04932823 cu.cm old-kitchen-drop 20.27237 / cu.cm
name consists of # gallon
---- ----------- --------
tun = ton 2 pipe, butt 216
pipe = butt 2 beer-hogshead 108
puncheon = tertian 2 beer-barrel 72
beer-hogshead 3 kilderkin 54
beer-barrel 2 kilderkin 36
kilderkin 2 firkin 18
firkin 9 gallon 9
ale-hogshead 1.5[*] ale-barrel 51
ale-barrel 34 gallon 34
strike 2 bushel 16
bushel 8 gallon 8
# cu.inch[*]
------------
gallon 2 * 3 * 47 cu.inch 282
gallon 2 pottle 282
pottle 2 quart 141
quart 2 pint 70.5
pint 2 (old)-chopin 35.25
(old)-chopin 2 gill 17.625
gill 5 ounce 8.8125
ounce 1.7625
[*] = These values are exact.
Note: 1 gill = 5 ounce (not 4 as in USA-fluid).
abbrev. # cu.dm name inverse
------ ------- ---- -------
998.1688 tun = ton 1.001835 / m3
499.0844 pipe = butt 2.003669 / m3
pun(ch) 332.7229 puncheon 3.005504 / m3
332.7229 tertian 3.005504 / m3
hhd 249.5422 beer-hogshead 4.007338 / m3
235.6788 ale-hogshead 4.243064 / m3
bbl 166.3615 beer-barrel 6.011007 / m3
157.1192 ale-barrel 6.364596 / m3
83.18074 kilderkin 12.02201 / m3
fir 41.59037 firkin 24.04403 / m3
73.93843 strike 13.52477 / m3
bu(sh) 36.96922 bushel 27.04953 / m3
gal 4.621152 gallon 216.3963 / m3
2.310576 pottle 432.7925 / m3
qt 1.155288 quart 865.5850 / m3
pt 0.5776440 pint 1.731170 / dm3
0.2888220 (old)-chopin 3.462340 / dm3
gi 0.1444110 gill 6.924680 / dm3
fl.oz 0.02888220 ounce 34.62340 / dm3
To construct the conversion-to-metrics table the size of the
cubic present-day-inch is taken and not that of an cubic old-inch.
Thus the exact value of the gallon is 4.621 152 048 litre.
The official name for this gallon is Queen-Elizabeth-1 gallon.
Large wine-bottles often have been christened with the names of old-testamentical priests and kings. These are:
# wine- # m i l l i l i t e r s
name bottles USA-fluid UK-Imperial Metric
---- ------- --------- ----------- ------
picolo, split 1/4 192.22794 189.42042 187.5[*]
quarter-bottle 1/4 192.22794 189.42042 187.5[*]
chopine 1/3 256.30392 252.56056 250
demi 1/2 384.45588 378.84083 375
UK-reputed-pint 1/2 -- 378.84083 --
metric tenth 1/2 -- -- 375
metric fifth 1 -- -- 750
UK-reputed-quart 1 -- 757.68167 --
US-champag.quart 1 768.91177 -- --
standard 1 768.91177 757.68167 750
magnum 2 1537.8235 1515.3633 1500
marie-jeannne 3 2306.7353 2273.045[*] 2250
UK-half-gallon 3 -- 2273.045[*] --
UK-pottle 3 -- 2273.045[*] --
double-magnum 4 3075.6471 3030.7267 3000
jeroboam 4 3075.6471 3030.7267 3000
'metric one-th' 5 -- -- 3750
bordeaux-jeroboam 6 4613.4706 4546.09[*] 4500
rehabeam,rehoboam 6 4613.4706 4546.09[*] 4500
UK-gallon 6 -- 4546.09[*] --
imperial 8 6151.2941 6061.4533 6000
methusalah 8 6151.2941 6061.4533 6000
salmanazar 12 9226.9412 9092.18[*] 9000
UK-peck 12 -- 9092.18[*] --
balthasar 16 12302.588 12122.907 12000
nebuchadnezzar 20 15378.235 15153.633 15000
melchior 24 18453.882 18184.36[*] 18000
UK-bucket 24 -- 18184.36[*] --
solomon 28 21529.530 21215.087 21000
sovereign 100/3 25630.392 25256.056 25000
primat 36 27680.824 27276.54[*] 27000
melchizedek 40 30756.471 30307.267 30000
--BASIC UNITS--
gallon - 3785.411784[*] 4546.09[*] --
ounce - 29.573530 28.4130625[*] 30
gallon - 128 ounce 160 ounce --
stand.wine-bottle 1 26 ounce 26+2/3 ounce 25 ounce
Note:
The metric one-th bottle does not exist actually.
UK-imperial bottle is about 1% larger than Metric bottle.
USA-fluid bottle is about 2.5% larger than Metric bottle.
For the US-Survey cubic measures, read the section Linear measures: US-Survey + Int.Nautical.
abbrev. #cu.kilometer[*] name inverse
------ ---------------- ---- -------
406.539661312 cu. geograph. league 0.0024597846 / km3
171.508919616 cu. marine league 0.0058306005 / km3
cubim 6.352182208 cu. int.naut. mile 0.1574262147 / km3
# liters name inverse
-------- ---- -------
1439.661 volume tonneau = 42 cu.pied 0.6946080 / m3
34.27764 cubic pied 29.17354 / m3
E Q U A L S
| kilometers | miles per | miles per |
| per liter | USA-gallon | UK-gallon |
-----------------+------------+------------+------------+
D kilometres | | | |
I per litre | 1 | 2.352146 | 2.824809 |
S -------------+------------+------------+------------+
T miles per | | | |
A USA-gallon | 0.4251437 | 1 | 1.200950 |
N -------------+------------+------------+------------+
C miles per | | | |
E UK-gallon | 0.3540062 | 0.8326742 | 1 |
-----------------+------------+------------+------------+
Reading of the table:
1 kilometre per litre = 2.352146 mile per USA-gallon.
1 mile per UK-gallon = 0.3540062 kilometre per liter.
Examples:
24 mile per USA-fluid-gallon
= 24 * 0.4251437 kilometre per litre
= 10.20 kilometer per liter
30 miles / UK-gallon = 10.62 kilometre / litre
Herein is:
UK-gallon = Imperial gallon
USA-gallon = USA-liquid gallon
1 mile = 1 land-mile = 1 statute-mile = 1.609344[*] kilometer
The tables in this section only list the Avoirdupois weight units that are generally used. Several units used in specific branches of trade and industry are listed in the specials section.
abbrev. British name USA-name # pounds
------ ------------ -------- --------
++++++++ long weights ++++++++
ton long ton 2240
U-L-quarter - long quarter 560
hundredweight long hundredweight 112
B-L-quarter long quarter - 28
st stone - 14
long assay-ton - 0.07202
++++++++ short weights +++++++
short ton ton 2000
U-S-quarter - short quarter 500
cental short hundredweight 100
B-S-quarter short quarter - 25
st - wool-stone 12.5[*]
- short assay-ton 0.06430
++++++++ small weights +++++++
lb.avdp pound pound 7000 troy grain
gr troy grain troy grain 0.064 798 91 [*] gram
- = no name
Single-letter abbreviations:
U-L = USA-long; U-S = USA-short;
B-L = British-long; B-S = British-short.
Example: B-L-quarter = British-long-quarter.
Quarter, another word is Quartermass.
NOTE: In ancient times 'hundred' meant every number between 100 and 120. Great-hundred = 120.
name consists of # pounds
---- ----------- --------
+++++++ long + Brit. weights +++++++
U-L-quarter 7776 long assay-ton 560
long assay-ton 112 assay-element 0.07202
deadweight-ton 1 long ton 2240
long ton 4 U-L-quarter 2240
U-L-quarter 5 coal-sack 560
coal-sack 1 long hundredweight 112
long hundredweight 2 (general) truss 112
(general) truss 1 firkin 56
firkin 2 B-L-quarter 56
B-L-quarter 1 (wool-) tod 28
(wool-) tod 2 stone 28
stone 2 (wool-) clove 14
bushel 9 (wool-) clove 63
(wool-) clove 1 brick 7
brick 2 quartern 7
quartern 3.5 pound 3.5[*]
wey 9 B-L-quarter 252
B-L-quarter 7 loaf-quartern 28
Scottish stone 4 loaf-quartern 16
loaf-quartern 4 pound 4
box 9 gallon 90
frail (-of-raisins) 5 gallon 50
score 2 (Imp.) gallon 20
(Imp.) gallon 2 block 10
block 5 pound 5
head 6+3/4 = 27/4 pound 6.75[*]
+++++++ short + USA. weights +++++++
U-S-quarter 7776 short assay-ton 500
short assay-ton 100 assay-element 0.06430
short ton 2 kip (= kilopound) 2000
kip (= kilopound) 2 U-S-quarter 1000
U-S-quarter 5 cental 500
cental 1 quintal 100
quintal 1 short hundredweight 100
short hundredweight 4 B-S-quarter 100
B-S-quarter 2 USA-wool-stone 25
USA-wool-stone 2.5 [*] block 12.5[*]
block 5 pound 5
elvis 51 block 255
# troy grains
-------------
++++++++++ physics weights +++++++++
slinch = snail 12 slug 2702620.08
slug 1 geepound 225218.34
geepound 32.174049 pound 225218.34
+++++++++++ small weights ++++++++++
pound 2 marc, marco 7000
marc = marco 2 US-butter-stick 3500
US-butter-stick 4 ounce 1750
ounce 16 dram (drachm) 437.5 [*]
dram (drachm) 27.34 375 [*] troy grain
ounce 18 scruple 437.5 [*]
dram (drachm) 9/8 = 1.125[*] scruple
scruple 24.30 555 556 troy grain
assay-element 4.501 0288 066 troy grain
(Avdp-)pound 7000 troy grain 7000
troy grain 64.798 91 [*] milligram 1
Factorial: 7776 = 6 * 6 * 6 * 6 * 6
The name 'assay-element' is invented by the author.
abbrev. # kilograms name inverse
------ ----------- -------------- -------
dwt 1016.04690 deadweight-ton 0.9842065 / t
tn/t 1016.04690 (long,Brit.) ton 0.9842065 / t
sh.tn/t 907.18474[*] (short,US) ton 1.102311 / t
kip 453.59237[*] kilopound 2.204623 / t
qtr/qr 254.0117 U-L-quarter 3.936826 / t
qtr/qr 226.7962 U-S-quarter 4.409245 / t
175.12683525 slinch = snail 5.710147 / t
115.6661 elvis 8.645579 / t
wey 114.3053 wey 8.748502 / t
50.80235 coal-sack 19.68413 / t
cwt 50.80235 long-hundredweight 19.68413 / t
cwt/ctl 45.359237[*] short-hundredweight 22.04623 / t
ctl 45.359237[*] cental 22.04623 / t
ctl 45.359237[*] quintal 22.04623 / t
40.8233133[*] box 24.49581 / t
28.576319 bushel 34.99401 / t
25.401173 truss (general) 39.36826 / t
25.401173 firkin 39.36826 / t
14.59390294 geepound = slug 68.52177 / t
12.70059 (wool-) tod 78.73652 / t
qtr/qr 12.70059 B-L-quarter 78.73652 / t
qtr/qr 11.33981 B-S-quarter 88.18490 / t
9.0718474[*] score 110.2311 / t
7.257478 Scottish-stone 137.7889 / t
st 6.350293 stone 157.4730 / t
5.669905 USA-wool-stone 176.3698 / t
4.5359237[*] (Imper.) gallon 220.4623 / t
3.175147 (wool-)clove 314.9461 / t
3.175147 brick 314.9461 / t
3.0617485 head 326.6108 / t
2.26796185 [*] block 440.9245 / t
1.81436948 [*] loaf-quartern 551.1557 / t
1.587573 quartern 629.8922 / t
lb.avdp 453.59237 g [*] pound 2.204623 / kg
226.7962 g marc, marco, mark 4.409245 / kg
113.39809 g US-butter-stick 8.818490 / kg
32.66612 g long assay-ton 30.61276 / kg
29.16618 g short assay-ton 34.28629 / kg
oz.avdp 28.349523 g ounce 35.27396 / kg
dr.avdp 1.771845 g dram = drachm 564.3834 / kg
s.avdp 1.574974 g scruple 634.9313 / kg
0.2916618 g assay-element 3.428629 / g
gr 64.798 91 mg [*] troy grain 15.43236 / g
Grain = 0.064 798 91 gram [*]
Pound = 0.453 592 37 kilogram [*]
[*] = This value is exact !
Letter g means metrical gram (=0.001[*] kg)
Letter t in inverse-column means metrical ton (=1000 kg).
The name 'assay-element' is invented by the author.
U-L = USA-long; U-S = USA-short;
B-L = British-long; B-S = British-short.
quintal = kintal = kantal = cental.
slinch = slug-inch = mug = many-slug.
elvis = the weight of Elvis Presley at the time of his death.
The assay units are jewellers units.
An (Imperial-) gallon is the weight of around one Imperial
gallon of water.
The background of the geepound is described in the section
'other weights'.
The basis of the Anglo-Saxon weight-system is the Troy-system Herein during the last millennium many pounds and ounces have been applied. And most of them have already been abolished. The following table shows some of them. This table also shows that the present-day Avoirdupois-system is a direct descendant of the Troy-system.
Remarkably enough, the weight of the grain did not change during this long time. Its definition only got more accurate. In earlier days it equalled the average weight of the barley-corn grain which equals to 4/3 of that of the wheat-grain. At present it is tightly connected to the metric system, so its relative accuracy is determined by the definition of the metric kilogram.
pound- #grains #grains #ounces
type per pound per ounce per pound
------ --------- --------- ---------
'French'-merchant 7680 480 16
old-Avoirdupois 7200 450 16
old-London =^ 7200 450 16
English-merchant 6750 450 15
Apothecary 5760 480 12
Troy =^ 5760 480 12
old-Saxon 5400 450 12
old-Tower =^ 5400 450 12
Scottish-tron 9520 476 20
(new) Avoirdupois 7000 437.5[*] 16
old-wool 6992 - -
=^ means this pound-type equals the pound type above it.
Factorial: 6992 = 16 * 19 * 23
name equals [*]
---- ------------
old-London-pound 15/16 = 0.9375 'French'-merchant-pound
Engl.merch-pound 225/256 = 0.87890625 'French'-merchant-pound
Troy-pound 3/4 = 0.75 'French'-merchant-pound
old-Tower-pound 45/64 = 0.703125 'French'-merchant-pound
Engl.merch-pound 15/16 = 0.9375 old-London-pound
Troy-pound 4/5 = 0.8 old-London-pound
old-Tower-pound 3/4 = 0.75 old-London-pound
Engl.merch-pound 75/64 = 1.171875 Troy-pound
old-Tower-pound 4/5 = 0.8 English-merchant-pound
old-Tower-pound 15/16 = 0.9375 Troy-pound
old-London-ounce 15/16 = 0.9375 'French'-merchant-ounce
Troy-ounce 1 'French'-merchant-ounce
Engl.merch-ounce 1 old-London-ounce
old-Tower-ounce 1 old-London-ounce
wheat-grain 3/4 = 0.75 Troy-grain
(barley-) grain 1 Troy-grain
abbrev. # grams [*] name inverse (# /kg)
------ ----------- ---- ---------------
--- pounds ---
616.8856232 Scottish-tron 1.621046
497.6556288 'French'-merchant 2.009422
466.552152 old-London 2.143383
466.552152 old-Avoirdupois 2.143383
lb.avdp 453.59237 (new) Avoirdupois 2.204623
453.07398 old-wool 2.207145
lb.merc 437.3926425 English-merchant 2.286275
lb.ap 373.2417216 Apothecary 2.679229
lb.tr 373.2417216 Troy 2.679229
349.914114 old-Tower 2.857844
349.914114 old-Saxon 2.857844
--- ounces ---
31.1034768 'French'-merchant 32.15075
oz.ap 31.1034768 Apothecary 32.15075
oz.tr 31.1034768 Troy 32.15075
30.84428116 Scottish-tron 32.42092
oz.merc 29.1595095 English-merchant 34.29413
29.1595095 old-London 34.29413
29.1595095 old-Avoirdupois 34.29413
29.1595095 old-Saxon 34.29413
29.1595095 old-Tower 34.29413
oz.avdp 28.349523125 (new) Avoirdupois 35.27396
--- grains ---
gr 0.06479891 barley 15432.36
gr 0.06479891 Troy 15432.36
0.0485991825 wheat 20576.48
Note: The 'French'-merchant pound and ounce differ only 1.7 percent from the pound and ounce of old-Paris and Quebec. See the Other-Weights section. The grains are more different.
For the Assay weights: see the above section
Avoirdupois-General.
In the table below, 'pound' and 'ounce' without preceding
name mean 'Troy-pound' and 'Troy-ounce'.
name consists of # grains[*]
---- ----------- -----------
------- O L D W E I G H T S -------
old London-stone 12.5 [*] old-Lond.pound 90 000
mast 2 old-London-pound 14 400
old London-pound 15 ounce 7 200
old London-pound 16 old-Tower-ounce 7 200
Engl.merch.pound 14.0625 [*] ounce 6 750
Engl.merch.pound 15 old-Tower-ounce 6 750
old Tower-pound 11.25 [*] ounce 5 400
old Tower-pound 12 old-Tower-ounce 5 400
old Tower-ounce 20 old-silver-penny 450
old silv.penny 1 English-merch.-penny 22.5
Engl.merch.penny 22.5 [*] grain 22.5
old silv.penny 30 wheat-grain 22.5
Scot.tron-stone 16 Scot.tron-pound 152320
Scot.tron-pound 20 Scot.tron-ounce 9520
Scot.tron-ounce 16 Scot.tron-drop 476
Scot.tron-drop 29.75 [*] grain 29.75
----- P R E S E N T - D A Y W E I G H T S -----
ton 20 hundredweight 11520 000
hundredweight 4 quarter 576 000
quarter 10 mast 144 000
mast 2.5 [*] pound 14 400
pound 6 mancus 5 760
mancus 2 ounce 960
hundredweight 3 gold-bar 576 000
gold-bar 400 ounce 192 000
ounce 8 drachm (dram) 480
dram (drachm) 3 scruple 60
scruple 20 grain 20
dram (drachm) 2.5 [*] pennyweight 60
pennyweight 24 grain 24
pennyweight 32 wheat-grain 24
wheat-grain 0.75[*] grain 3/4
ounce 30 AngloSaxon-gram 480
pennyweight 1.5 [*] AngloSaxon-gram 24
AngloSaxon-gram 16 grain 16
grain 1 barleycorn-weight 1
barleycorn-weight 1 minim 1
minim 20 mite 1
mite 24 doite 0.05
doite 1/480
(Troy-)pound 5760 grain 5 760
grain 64.798 91 [*] milligram 1
abbrev. # grams [*] name inverse
------ ----------- ---- -------
746.4834432 kg ton 0.13396 / t
cwt 37.32417216 kg hundredweight 26.79229 / t
12.44139072 kg gold-bar 80.37687 / t
9.8701699712 kg Scot.tron-stone 101.3154 / t
qr 9.33104304 kg quarter 107.1692 / t
5.8319019 kg old-London-stone 171.4706 / t
933.104304 mast 1.071692 / kg
616.8856232 Scott.tron-pound 1.621046 / kg
466.552152 old-London-pound 2.143383 / kg
lb.merc 437.3926425 Engl.merch.pound 2.286275 / kg
lb.tr/ap 373.2417216 pound 2.679229 / kg
349.914114 old-Tower-pound 2.857844 / kg
62.2069536 mancus 16.07537 / kg
oz.tr/ap 31.1034768 ounce (=toz =ozt) 32.15075 / kg
30.84428116 Scott.tron-ounce 32.42092 / kg
29.1595095 old-Tower-ounce 34.29413 / kg
dr.tr/ap 3.8879346 dram (drachm) 257.2060 / kg
1.9277675725 Scot.tron-drop 518.7347 / kg
dwt 1.55517384 pennyweight 643.0149 / kg
1.457975475 Engl.merch.penny 685.8826 / kg
1.457975475 old-silver-penny 685.8826 / kg
s.tr/ap 1.2959782 scruple 771.6179 / kg
1.03678256 AngloSaxon-gram 964.5224 / kg
gr 64.79891 mg grain 15.43236 / g
64.79891 mg minim 15.43236 / g
64.79891 mg barleycorn-weight 15.43236 / g
48.5991825 mg wheat-grain 20.57648 / g
3.2399455 mg mite 30.86472 / g
0.13499773[~]mg doite 740.75320 / g
Grain = 0.064 798 91 gram [*]
Pound = 0.373 241 721 6 kilogram [*]
[*] = All values in the left column are exact, except the doite
which is indicated with [~].
Letter t in inverse-column means metrical ton (=1000 kg).
dwt = denier weight. Denier is a very old French word for penny.
The subdivision of the old-Tower-pound and Troy-pound was the basis of the English monetary structure until 1970:
name consists of # pence
---- ----------- --------
Sterling-pound 20 shilling 240
shilling 12 penny 12
penny 1
There are two types of Carat (= ct) for indicating the weight
of diamonds and gem stones. And there is one Karat (= kt) for
indicating the part of gold in an alloy.
NOTE: Do not exchange the words Carat and Karat! Some
people do this falsely.
The Carat indicates the weight (but not the economical value) of a diamond or another gem stone. In previous times its definition was based on the weight of the carob seed. These seeds are astonishingly equal in weight, and this weight is scarcely influenced by the local soil and weather conditions the carob tree lives in. It is around 0.2 grams.
Later on the carat was redefined to be more accurate. Alas, every country created its own definition, that in general differed slightly from those of its neighbouring countries (e.g. in USA: 1 carat = 0.2056 grams). Consequently several slightly different values of the carat arose, all around 0.2 grams. In 1907 one started to define it as an exact value in the metric weight-system. At present since 1914 this definition is in use everywhere.
The two most important carat-weights are:
measure system # grams # troy-grains
-------------- ------- -------------
Imperial-1877 0.20530 3.168263
Metric 0.2 [*] 3.086472
The carat is subdivided into smaller units, and some pearl-units have been related to it.
name consists of # points
---- ----------- --------
carat 4 carat-quarter 100
carat-quarter 1 carat-grain 25
carat-grain 25 carat-points 25
carat-point 1
**** pearl units ****
momme 18.75[*] metric-carat 1875
pearl-grain 1 Imp-1877-carat-grain 25
abbr # Troy-grain name inverse
---- ------------ ---- -------
**** Imp-1877 carat ****
ct 3.168263 carat 0.3156303 / gr
0.7920658 quarter 1.262521 / gr
0.7920658 grain 1.262521 / gr
0.7920658 pearl-grain 1.262521 / gr
0.03168263 point 31.56303 / gr
**** metric carat ****
57.871344 momme 0.017279709 / gr
ct 3.0864717 carat 0.32399455 [*] / gr
0.77161792 quarter 1.2959782 [*] / gr
0.77161792 grain 1.2959782 [*] / gr
0.030864717 point 32.399455 [*] / gr
abbr #milligram name inverse
---- ---------- ---- -------
**** Imp-1877 carat ****
ct 205.30 carat 4.870921 / g
51.325 quarter 19.48368 / g
51.325 grain 19.48368 / g
51.325 pearl-grain 19.48368 / g
2.0530 point 487.0921 / g
**** metric carat ****
3750 momme 0.266667 / g
ct 200 carat 5 / g
50 quarter 20 / g
50 grain 20 / g
2 point 500 / g
[*] = These non-integral values are exact.
Momme = Japanese pearls weight unit. The metricalized version
mentioned here equals 75 carat-grain = 15/4 gram.
--- Synonyms: ---
Old-London carat = Imperial-1877 carat
Metric-1914 carat = Metric carat
jeweller's grain = carat grain
The Karat is a ratio for indicating the fineness (= purity) of gold or another precious metal in an alloy:
1 gram of gold
kt = Karat = -------------------- = 4.1666667 %
24 gram of mixture
This Karat can be used easily in conjunction with the Troy+Apothecary weight system. As one Troy pennyweight consists of 24 Troy grains, the number of karats equals the number of grains of pure gold in the pennyweight of alloy. Thus for example, one pennyweight of a 9 Karat alloy contains 9 grains of pure gold.
A modern measure for the fineness of gold or another precious metal in an alloy is simply called: Fineness. Its definition is:
1 gram of gold
(metric) Fineness = -------------------- = 0.1 %
1000 gram of mixture
The tables in this section list several Avoirdupois weight units that are or were used in only one or a very few branches of trade and industry. Most of them are British. The units for general use are listed in the general-units section. A few of those general units are also listed in the present section to establish the connections between the tables in both.
In the following table many weight units are prefixed,
what they in reality are not. The prefix indicates the type
of the product:
w = wool
c = coal
f = flour
b = butter + cheese
h = hay + straw
Example: c-sack = coal sack; f-sack = flour sack; w-sack =
wool sack.
name consists of # pounds
---- ----------- --------
+++ multiplication chains based on seven-pounder +++
c-ship-load 20 c-keel, c-barge 949760
c-barge = c-keel 8 c-chalder 47488
c-chalder 53 hundredweight 5936
c-barge = c-keel 21.2 [*] long-ton 47488
c-barge = c-keel 3 c-room + 4 c-sack 47488
c-room 7 long ton 15680
long ton 10 b-barrel 2240
h-load-old-hay 9 b-barrel 2016
b-barrel 1 c-large-sack 224
c-large-sack 2 long hundredweight 224
long hundredweight 1 c-sack 112
c-sack 1 b-dutch-cask 112
b-Dutch-cask 2 f-bushel 112
f-bushel 1 b-firkin 56
b-firkin 1 pig 56
pig 1 h-truss-old-hay 56
h-truss-old-hay 1 (general) truss 56
(general) truss 2 B-L-quarter 56
cotton-candy 7 long hundredweight 784
long ton 4 U-L-quarter 2240
U-L-quarter 5 long hundredweight 560
h-load-old-hay 6 b-Essex-wey(?) 2016
b-Essex-wey(?) 3 long hundredweight 336
long hundredweight 2 B-L-quarter 112
w-sack 13 B-L-quarter 364
f-barrel 7 B-L-quarter 196
U-L-quarter 2 salt-barrel 560
salt-barrel 1 f-sack 280
f-sack 2 f-bag 280
f-bag 1 USA-cotton-sack 140
USA-cotton-sack 5 B-L-quarter 140
wey 3 b-tub 252
potatoes-sack 2 b-tub 168
b-tub 3 B-L-quarter 84
w-last 6 w-sarpler 4368
w-sarpler 2 w-sack 728
w-sack 2 w-wey 364
w-wey 13 stone 182
B-L-quarter 1 w-tod, tod 28
w-tod = tod 2 stone 28
stone 2 w-clove 14
w-clove 7 pounds 7
++++++++ other multiplication chains ++++++
USA-Short-quarter 10 frail-of-raisins 500
beef,fish,pork-barrel 2 nails-keg 200
nails-keg 1 USA-f-sack 100
USA-f-sack 2 frail-of-raisins 100
frail-of-raisins 4 USA-w-stone 50
USA-w-stone 12.5[*] pound 12.5[*]
new lead-fother 19.5[*] long-hundredw. 2184
old lead-fother 1 h-load-new-hay 2160
h-load-new-hay 30 fotmal 2160
fotmal 9 butcher-stone 72
beef,fish,pork-barrel 5 f-poll 200
f-poll 5 butcher-stone 40
w-pack 2 iron-fagot 240
iron-fagot 1 glass-seam 120
glass-seam 5 UK-old-w-stone 120
UK-old-w-stone 3 butcher-stone 24
Scottish stone 2 butcher-stone 16
b-clove 1 butcher-stone 8
sugar-stone 1 butcher-stone 8
butcher-stone 8 pound 8
h-load-new-hay 36 h-truss-new-hay 2160
h-truss-new-hay 10 sixpounder 60
h-load-of-straw 36 h-truss-of-straw 1296
wey 7 h-truss-of-straw 252
h-truss-of-straw 6 sixpounder 36
sixpounder 6 pound 6
+++++++ small and no chains +++++++
mercury-flask: UK 76 pound 76
USA 75 pound 75
general 76.5 [*] pound 76.5[*]
bone-dry-unit 1.2[*] bone-dry ton 2400
bone-dry-ton 1 short ton 2000
fothers 6 Canada-cement-barrel 2100
Canada-cement-barrel 2 lead-wey 350
lead-wey 2.5 [*] lead-fotmal 175
lead-fotmal 5 stone 70
stone 14 pound 14
lead-wey 2 Canada-cement-bag 175
Canada-cement-bag 7 USA-wool-stone 87.5[*]
USA-wool-stone 1 lead-stone 12.5[*]
lead-stone 12.5[*] pound 12.5[*]
USA-cement-barrel 4 USA-cement-bag 376
USA-cement-bag 2 * 47 pound 94
b-Suffolk-wey 4 * 89 pound 356
USA-salt-sack 5 * 43 pound 215
soap-firkin 2 * 31 pound 62
USA-b-stick 1/4 pound 0.25[*]
cotton-bale-of:
Egypt (old) 1.5 USA-cott.bale old 750
Egypt (present) 1.5 USA-cott.bale new 720
Egypt (average) 719 pound 719
USA (old) 1 USA-Short-quarter 500
USA (at present) 480 pound 480
USA (average) 477 pound 477
India (old) 400 pound 400
East-India (avg) 396 pound 396
Brazil + Peru (old) 250 pound 250
Brazil (new) 220 pound 220
pound 7000 troy grain 1
old wool-pound 6992=16*19*23 troy-grain 0.9988571
The factorials (e.g. 2*47) are given by the author.
The name 'sixpounder' is an invention of the author.
Chalder = chaldron = chauldron = cauldron = large kettle.
U-L = USA-long; B-L = British-long.
Concrete-sack = cement-bag.
Mercury = quicksilver.
abbrev. # kilograms name inverse
------ ----------- -------------- -------
430 803.889 coal-ship-load 0.002321242 / t
21 540.194 coal-barge 0.04642484 / t
21 540.194 coal-keel 0.04642484 / t
7112.328 coal-room 0.1406009 / t
2692.524 coal-chalder 0.3713987 / t
1981.291 wool-last 0.5047213 / t
1088.622 bone-dry-unit (wood) 0.9185928 / t
1016.04690 long-ton 0.9842065 / t
990.6457 new-lead-fother 1.009443 / t
979.7595 old-lead-fother 1.020659 / t
979.7595 load-new-hay 1.020659 / t
914.4422 load-old-hay 1.093563 / t
90.718474[*] bone-dry-ton (wood) 1.102311 / t
90.718474[*] short ton 1.102311 / t
587.8557 load-of-straw 1.701098 / t
355.6164 cotton-candy 2.812019 / t
340.1943 old cotton-bale-Egypt 2.939497 / t
330.2152 wool-sarpler 3.028328 / t
326.5865 new cotton-bale-Egypt 3.061976 / t
326.1329 avg cotton-bale-Egupt 3.066235 / t
254.0117 USA-Long-quarter 3.936826 / t
226.7962 USA-Short-quarter 4.409245 / t
226.7962 old cotton-bale-USA 4.409245 / t
217.7243 new cotton-bale-USA 4.592964 / t
216.3636 avg cotton-bale-USA 4.621850 / t
181.4369 old cotton-bale-India 5.511557 / t
179.6226 avg cotton-bale-East-India 5.567229 / t
170.5507 USA-cement-barrel 5.863358 / t
165.1076 wool-sack 6.056656 / t
161.4789 Suffolk-butter-wey 6.192760 / t
158.7573 Canadian-cement-barrel 6.298922 / t
152.4070 Essex-butter-wey(?) 6.561377 / t
127.0059 flour-sack 7.873652 / t
127.0059 salt-barrel 7.873652 / t
wey 114.3053 wey 8.748502 / t
113.3981 old cotton-bale-Brazil+Peru 8.818490 / t
108.8622 wool-pack 9.185928 / t
101.6047 large-coal-sack 9.842065 / t
101.6047 butter-barrel 9.842065 / t
99.79032 new cotton-bale-Brazil 10.02101 / t
97.52236 USA-salt-sack 10.25406 / t
95.2543977[*] fothers 10.49820 / t
90.718474[*] beef,fish,pork-barrel 11.02311 / t
88.90410 flour-barrel 11.24807 / t
82.55381 wool-wey 12.11331 / t
79.37866 lead-wey 12.59784 / t
76.20352 potatoes-sack 13.12275 / t
63.50293 flour-bag 15.74730 / t
63.50293 USA-cotton-sack 15.74730 / t
54.43108 iron-fagot 18.37186 / t
54.43108 glass-seam 18.37186 / t
cwt 50.80235 long-hundredweight 19.68413 / t
50.80235 Dutch-butter-cask 19.68413 / t
50.80235 coal-sack 19.68413 / t
45.359237[*] nails-keg 22.04623 / t
45.359237[*] USA-flour-sack 22.04623 / t
42.63768 USA-cement-bag 23.45343 / t
39.68933 Canadian-cement-bag 25.19569 / t
38.10176 butter-tub 26.24551 / t
34.69982 general-mercury-flask 28.81860 / t
34.47302 UK-mercury-flask 29.00819 / t
34.01943 USA-mercury-flask 29.39497 / t
32.65865 fotmal 30.61976 / t
31.75147 lead-fotmal 31.49461 / t
28.12273 soap-firkin 35.55843 / t
27.21554 truss-new-hay 36.74371 / t
25.40117 truss-old-hay 39.36826 / t
25.40117 truss (general) 39.36826 / t
25.40117 flour-bushel 39.36826 / t
25.40117 butter-firkin 39.36826 / t
25.40117 pig 39.36826 / t
22.67962 frail-of-raisins 44.09245 / t
18.14369 flour-poll 55.11557 / t
16.32933 truss-of-straw 61.23952 / t
12.70059 tod = wool-tod 78.73652 / t
qr 12.70059 British-Long-quarter 78.73652 / t
10.88622 UK-old-wool-stone 91.85928 / t
7.257478 Scottish-stone 137.7889 / t
st 6.350293 stone 157.4730 / t
5.669905 lead-stone 176.3698 / t
5.669905 USA-wool-stone 176.3698 / t
3.628739 sugar-stone 275.5778 / t
3.628739 butcher-stone 275.5778 / t
3.628739 butter-clove 275.5778 / t
3.175147 wool-clove 314.9461 / t
2.721554 sixpounder 367.4371 / t
lb.avdp 453.59237 g[*] pound 2.204623 / kg
453.07398 g old-wool-pound 2.207145 / kg
113.39809 g USA-b-stick 8.818490 / kg
Grain = 0.064 798 91 gram [*]
Pound = 0.453 592 37 kilogram [*]
[*] = This value is exact !
Letter g means metrical gram (=0.001[*] kg)
Letter t in inverse-column means metrical ton (=1000 kg).
One dry bushel (= 2150.42 cu.inch) of alfalfa weights approximately 60 pounds. Therefore the alfalfa-bushel is fixed to exactly 60 pounds. This is 27.22 kilograms. So 36.74 of these bushels fit into one metric ton. Now the bushel is not any more a volume measure, but it has become a weight measure.
Similar has been done to the bushels of more food stuffs. Their appointed weight values are listed in the table below. This table also shows that (for example:) cowpeas, flax and the different kinds of clover have got the same weight values as alfalfa has.
stuff #pound #kilograms[*] #bushels/ton
----- ------ ------------- ------------
general 63 28.57631931 34.9940099
Grass: blue 14 6.35029318 157.473044
brome (smooth)
fescue (tall)
orchard
redtop
Turnip-greens, dry 16 7.25747792 137.788914
Turnip-greens, wet 18 8.16466266 122.479035
Mustard-greens
Spinach 20 9.07184740 110.231131
Field-peas 25 11.33980925 88.184905
Ocra 26 11.79340162 84.793178
Grass, sudan 28 12.70058636 78.736522
Pole-beans
Snap-beans 30 13.60777110 73.487421
Lima-beans, unshelled
English-peas, in hull
Cotton 32 14.51495584 68.894457
Oats (not in Canada)
Egg-plant 33 14.96854821 66.806746
Canada-oats 34 15.42214058 64.841842
Grass, timothy 45 20.41165665 48.991614
Rice
Barley 48 21.77243376 45.929638
Apples
Cucumbers
Millet 50 22.67961850 44.092452
Muscadines
Peaches
Sorghum, forage
Sweet-potatoes, dry
Tomatoes 53 24.04039561 41.596653
Turnips, without tops 54 24.49398798 40.826345
Sweet-potatoes, green 55 24.94758035 40.084048
Corn, shelled 56 25.40117272 39.368261
Sorghum, grain
Rye
Onions 57 25.85476509 38.677590
Alfalfa 60 27.21554220 36.743710
Clover: alsike
crimson
ladino
sweet
white
red
Cowpeas
Flax
Rape
Soybeans
Trefoil, birdsfoot
Vetch
Wheat
Corn, in ear 70 31.75146590 31.494609
Sunflower, oil-type 24 to 10.88621688 91.859276
32 14.51495584 68.894457
Lespedeza 40 to 18.14369480 55.115566
50 22.67961850 44.092452
volume #cu.inch[*] #liters #bushels/m3
------ ----------- ---------- -----------
USA-dry-bushel 2150.42 35.2390702 28.3775933
name consists of meaning of name
---- ----------- ---------------
tonneau 20 quintal tun, ton, tonne
quintal 100 livre cental
livre 2 marc pound
marc 2 quatreron
quatreron 4 once four-ounces
once 2 lot ounce
lot 4 gros
gros 1 drachme
drachme 3 denier drachme
denier 1 scrupule from: denarius
scrupule 24 grain small itchy pebble
grain 1 grain e.g. wheat granule
grain 0.053 115 234 375 [*] metric gram
abbr. # grams [*] name inverse
----- ----------- ---- -------
979020 tonneau 1.0214296 / t
48951 quintal 20.42859 / t
489.51 livre 2.042859 / kg
244.755 marc 4.085718 / kg
122.377 5 quarteron 8.171437 / kg
30.5943 75 once 32.68575 / kg
15.2971 875 lot 65.37149 / kg
3.82429 6875 gros 261.4860 / kg
3.82429 6875 drachme 261.4860 / kg
1.27476 5625 denier 784.4579 / kg
1.27476 5625 scrupule 784.4579 / kg
53.1152 34375 mg grain 18.82699 / gram
[*] = The values in the left column are exact.
The biological effect (= activity) of many vitamins and drugs depends on the way they have been prepared. So there is no direct relation between the weight of a quantity of such stuff and its effect. Therefore this effect is compared to the effect of a quantity-unit of the stuff prepared in the standardized way. If both effects are equal, then the dose of 'unknown' stuff is said to be 1 IU (= international unit).
For some stuffs the weight of one IU of the standard specimen is:
stuff: 1 IU weights:
------ -------------
Penicilline 0.6 micro-gram
Insuline 45.5 micro-gram
Vitamin A 0.3 micro-gram
Vitamin C 50 micro-gram
Vitamin D 25 nano-gram
Vitamin E 2/3 = 0.66667 milli-gram
Example: The theoretical biological activity of a beta-carotene molecule equals twice that of a vitamin-A molecule. However in the reality it is only one-third! Thus six grams of beta-carotene perform the same biological effect in the human body as one gram of vitamin-A. So 1 IU of beta-carotene weights 1.8 micrograms.
All mammals must consume twelve vitamins. A few of them, cavia, primate apes and human, even one more: vitamin C = ascorbic acid. Four vitamins are fat soluble: A, D, E and K. Three vitamins are anti-oxydants: A, C and E.
abbrev. # kilograms name inverse
------ ----------- ---- -------
175.12683525 slinch = snail 5.710147 / t
14.59390294 geepound = slug 68.52177 / t
9.80665 mug = hyl 101.97162 / t
Several masses have been devised for simulating the
force of earth gravity in horizontal equipment. Three of
them are:
Geepound (= G-pound) = Slug = the mass of a body which,
when acted upon by a force of one poundforce, acquires
an acceleration of one foot per second per second.
Slinch (= Slug-inch) = Snail = the mass such that a force
of one poundforce accelerates this mass by one inch per
second per second.
Mug (= Metric slug) = the mass accelerated at one meter per
second per second by a force of one kilogramforce. Other
names for it are: Techma = Technische Masse-Einheit = TME =
Unite de Masse = UdM = Par = Hyl.
-- Herein is:
Poundforce = the force given by the earth gravity to a
body with a mass of one pound.
-- Do not confuse this with:
Poundal = the force required to impart an acceleration
of one foot per second per second to a body with a mass
of one pound.
Poundfoot = the torque caused by one poundforce on a lever
with a length of one foot (in Newton-meter).
Footpound = the enery delivered by one poundforce over a
displacement of one foot (in Joule).
-- Densities for textile-yarn are:
Poumar = pound per million yard = a density of textile-yarn.
Typp = thousand yard per pound = in fact the inverse of poumar.
US-run = # 1600-yard wool-hanks per pound.
When we look at the values only, and not at the types of the units (e.g. time or length or mass), then the following equations hold, some of them ONLY in the METRIC system:
mug = hyl = kilogramforce = kgf = earth-gravity
poundforce = pound(avdp) * earth-gravity
footpound = poundfoot = poundforce * foot
geepound = poundforce / foot
slinch = poundforce / inch = 12 * geepound
poundal = poundfoot / earth-gravity = pound(avdp) * foot
poumar = pound(avdp) / ( foot * 3@+6 )
typp = 3000 * foot / pound(avdp) = 0.001 / poumar
US-run for wool-yarn = 1.6 * typp
pound-per-square-inch = psi = poundforce / square-inch
pound-per-square-foot = psf = geepound / foot = psi / 144
water-atmosphere = watm = water-density * earth-gravity * 10
technical-atmosphere = at = kgf/cm2 = 10000 * earth-gravity
In the metric system their values are:
mug = 9.80665
poundforce = 4.4482216
poundfoot = 1.35581795
footpound = 1.35581795
geepound = 14.593903
slinch = 175.12684
poundal = 0.13825495
poumar = 0.49605465 @-6
typp = 2.01590693 @+3
US-run = 3.22545108 @+3
psf = 47.880259
psi = 6894.7573
watm = 98063.754
at = 98066.5
See also the sub-section "Inter-measure coefficients" in Pressures: Basic units and Coefficients.
The user has to write one of these prefixes before the basic measure unit of the right class to form the desired measure unit.
sci. every-day name
abbrev. name 10 to power of cont.Europe USA
------ ---- -------------- ----------- -----------
Y yotta +24 quadrillion septillion
Z zeta +21 trilliard sextillion
E exa +18 trillion quintillion
P peta +15 billiard quadrillion
T tera +12 billion trillion
G giga + 9 milliard billion
M mega + 6 million million
myria + 4 tenthousand tenthousand
k kilo + 3 thousand thousand
h hecto + 2 hundred hundred
da deca,deka + 1 ten ten
[none] 0 one one
d deci - 1
c centi - 2
m milli - 3
u,mc micro - 6
n nano - 9
p pico -12
f femto -15
a atto -18
y yocto -21
z zepto -24
Myria has no symbol.
dk This symbol is obsolete for deka.
The classes and the basic units on which the metric measure system is based, and which are used by the everyday man, are:
abbreviation of
class basic unit basic-unit name
----- ---------- ---------------
mass kilogram kg
length meter (or: metre) m
time second s
electric current Ampere A
Yes indeed folks, that is all!
At present these units themselves are defined by using the physical properties of atoms and light waves. Some results of this 'higher science' are described in the section Physical constants: Definition of Meter and Second.
By combining a prefix with a basic name, every user can make
the name for every measure unit he likes. He/she is never urged
to search for an (unprefixed) name. No hyphen or space should be
written between the prefix and the basic name. Examples:
ms = millisecond = 1/1000-th of a second
dm = decimeter = 1/10-th of a meter
km = kilometer = 1000 meters
ns = nanosecond = 1 milliardth of a second
Ms = megasecond = 1 million seconds
uA = micro-ampere = 1 millionth of an Ampere
Areas are always derived from the length class by using the
adjective 'square' (= sq.) or the suffix 2. Thus: sq.km = km2
Volumes are always derived from the length class by using the
adjective 'cubic' (= cu.) or the suffix 3. Thus: cu.dm = dm3
The electric tension (in Volt) is derived from all four classes
together.
The combination of the area- or volume-adjective together with a prefix leads to a snag that is dealt with extensively in the chapter Metric pitfalls: Square and Cubic.
The name of the unit of mass, kilogram, has a snag too. It is
made up from the prefix 'kilo' and an old mass-unit called 'gram'
abbreviated as 'g'. When it is prefixed, the prefix merges itself
with the built-in prefix 'kilo', thus making a new prefix in front
of the old unit 'gram'.
Examples:
kg = kilogram = 1@3 gram = 1000 g
g = gram = 1/1000 kilogram
kkg = kilo-kilogram = 1@(3+3) gram ==> 1@+6 gram = megagram = Mg
mkg = milli-kilogram = 1@(3-3) gram ==> gram = g [without any prefix]
ukg = micro-kilogram = 1@(3-6) gram ==> 1@-3 gram = milligram = mg
dkg = deci-kilogram = 1@(3-1) gram ==> 1@+2 gram = hectogram = hg
dakg = deka-kilogram = 1@(3+1) gram ==> 1@+4 gram = myriagram
nkg = nano-kilogram = 1@(3-9) gram ==> 1@-6 gram = microgram = ug
Why not simply saying: the basic unit of mass is the gram? The reason is that in calculations of force and energy the kilogram is the basic unit. The names of the other three basic units do not have this illogical snag.
In Europe some ancient names are still in use. They are not many, and the values they stand for fit quite well in the metric system. Several of these names are listed here.
abbrev. name value
------ ---- -----
spat 1 @ +12 m
myriameter 10000 m
league 4000 m
mile 2000 m
cable 220 m
Dutch-rood 10 m
toise 2 m
pace 1.5 m
step 75 cm
foot 1/3 m = 33.333... cm
thumb, inch 27.5 mm
line 2.3 mm
Q,kyu quarter 0.25 mm (= metric-point)
pm perm 0.1 mm
u,um micron 1 @ -6 m
A Angstrom 1 @ -10 m
uu,pm bicron 1 @ -12 m (micronmicron = bi-micron)
F Fermi 1 @ -15 m
abbrev. name consists of # sq.m
------ ---- ----------- ------
Dutch-bannier (bunder) 1 hectare 10 000
Dutch-morgen 0.85 hectare 8 500
ha hectare 2 soccer-fields 10 000
soccer-field 5 dekare 5 000
da dekare 10 Dutch (sq.-)rood 1 000
Du.(sq.)rood 1 are 100
a are 100 centiare 100
ca centiare 1
barn = Fermi (F) 1 @ -24 sq.cm 1@-28
soccer = European-style football
name # liters
---- --------
dekastere 10000
Dutch-load 3000
stere (s,st) 1000
raummeter (Rm) 1000
festmeter (Fm) 1000
drum 200 or 205 or 208
decistere 100
Dutch sack 100
name # cu.cm
---- -------
Winchester-quart 2500
milk-bottle 1000
liter (ltr, lt, L) 1000
wine-quart 1000
wine-fifth 750
wine-bottle (btl) 750
pint 500
demipint, large cup 250
cup, glass, butcher 200
seven (= ca. 7 fl.oz) 200
French champaign-split 200
wine-split (= 1/4 btl) 187.5[*]
fluid ounce 30
shot 25
big tablespoon 20
(small) tablespoon 15
thimble 10
pap-spoon 8 or 7.5[*]
(big) tea-spoon (tsp) 5
small tea-spoon 3
coffee-spoon 1.25[*]
cc 1
drop 0.05
lambda 0.001
Note:
1 m3 = 1 cu.m = 1000 cu.dm = 1000 dm3
1 liter = 1 cu.dm = 1 dm3 = 1000 cm3 = 1000 cu.cm
1 cc = 1 cu.dm = 1 cu.cm = 1000 cu.mm = 1000 mm3
1 lambda = 1 cu.mm = 1 mm3 = 1 uL
name consists of metrical
---- ----------- --------
commercial-load 3 ton, tonne 3000 kg
German-load 2 ton, tonne 2000 kg
deadweight-ton (dwt) 1 ton, tonne 1000 kg
bone-dry metr.ton (bdmt) 1 ton, tonne 1000 kg
ton = tonne (t) 10 quintal 1000 kg
quintal = Russ.centner 2 hundredweight 100 kg
hundredweight = centner 1 sack, bag 50 kg
sack = bag 5 myriagram 50 kg
myriagram 10 kilogram 10 kg
kilogram 2 pound 1000 g
pound 5 Dutch-ounce 500 g
Dutch-ounce 100 glug 100 g
glug 1 gram 1 g
gram 5 carat 1000 mg
carat 4 (wheat-)grain 200 mg
German-grain 1 drugs-grain 60 mg
drugs-grain 30 point 60 mg
(wheat-) grain 25 point 50 mg
point 2 milligram 2 mg
milligram 1000 gamma 1000 ug
gamma 1 microgram 1 ug
kg = kilogram = 1 @ +3 g
mg = milligram = 1 @ -3 g
ug = microgram = 1 @ -6 g
g = gram
[*] = All values in these tables are exact.
Note, the metric quintal is not 100 pound, but it is 100 kg.
In early days the litre was defined as the volume of one
kilogram of water at four degrees Celsius. This value
approximates very well the size of one cubic decimeter, but
does not match it exactly. It is a very little bit more.
This very small difference does not make any sense in the
ordinary daily life. Nowadays since 1964 one litre is defined
as one cubic decimeter. So one litre of water weighs slightly
less than one kilogram. The old liter has also been fixed by
definition and thus also been detached from the actual water
density. Thus:
1 old-litre = 1.000028 [*] dm3
1 litre = 1 dm3
Ton is (approx.) the weight of 1 m3 filled with water.
This is a proposal of a set of new and existing names that may ease the daily use of the metric system. The values given to the originally Anglo-Saxon names are in the neighbourhood of the values these names represent actually.
VOLUME [*] AREA [*]
Name dm3 Name m2
---- --- ---- --
dekastere 10 000 hectare 10 000
stere 1 000 soccer-field 5 000
barrel=oil-drum 200 acre 4 000
oil-barrel 160 rood = dekare 1 000
decistere = bag 100 are 100
bushel 40 roomfloor 20
big-bucket 20 kitchen-floor 10
peck 10
house-bucket 10
half-bucket 5 WEIGHT [*]
gallon 4 Name kg
triple-liter 3 ---- --
pottle = oil-can 2 ton 1000
liter=milk-bottle 1 double-cental 100
wine-bottle 0.75 cental 50
pint 0.5 house-bucket 10
soda-bottle 3.75 stone 5
mug = big-cup 0.25 brick 2.5
cup = glass 0.2 kilogram 1
gill 0.125 pound 0.5
deciliter 0.1 Dutch-ounce 0.1
APOTHECARY, VOLUME AND/OR WEIGHT [*]
Name cm3 or gram
---- -----------
deciliter, Du.ounce 100
ounce 30
big-tablespoon 20
small-tablespoon 15
dessertspoon 10
papspoon 7.5
big-teaspoon 5
drachme, dram 3.75
small-teaspoon 3
coffee-spoon 2.5
pennyweight 1.5
salt-spoon, scruple 1.25
cc, gram 1
pinch 0.625
dash 0.3125
carat 0.2 = 1/5
minim, grain 0.0625 = 1/16
drop, small-grain 0.05 = 1/20
[*] = All values in these tables are intended to be exact.
A unit of pressure (stress) or strain is expressed in force
per unit of surface. Several units of pressure and strain are
used as a consequence of different methods of measuring a
pressure or strain. The units can be translated into each other
by multiplications with constant values. Strain can be seen as
the opposite of pressure. The four main methods of measuring
the pressure and their corresponding units are:
The relations between a pressure unit and its scale division units are defined as:
abbrev. name consists of
------- ---- -----------
atm,atmos physical/ordinary atmosphere 760 torr
torr Torricelli 1 mmHg
mmHg millimeter mercury-column
watm water atmosphere 10 mH2O
mH2O meter water-column
at technical atmosphere 1 kgf/cm2
kgf/cm2 kilogramforce per square cm. 9.80665 N/cm2
psi poundforce per square inch 144 psf
psf poundforce per square foot
Bar Bar 100 pieze
pieze 10 mBar
mBar millibar 1 hPa
hPa hecto-pascal 100 Pa
Pa Pascal 10 Barye
uBar,ba Barye = microbar 0.1 N / sq.m
Bar Bar 10 N / sq.cm
Pa Pascal 1 N / sq.m
N Newton 1 kg.m/s2
The numeric notation of a pressure value in one system can be easily translated into the corresponding notation of another system. The coefficients that connect the four systems and are used in these translations are:
torricelli = 0.001 333 2237 Bar
earth gravity = 9.806 65 [*] m/s2
water density = 0.999 972 kg/dm3
pound (avdp) = 0.453 592 37 [*] kg
square inch = 6.451 6 [*] cm2
[*] = This value is exact by definition. The other
values in this table are measured values.
The formulas to derive the different types of pressure
from these basic coefficients are:
psi = pound * earth-gravity / square-inch
psf = pound * earth-gravity / square-foot
watm = 10 * water-density * earth-gravity
bar = 100000 * Newton / square-meter
at = 10000 * earth-gravity * kg/m2
On 18 may 2003 the NIST published the redefinition of the ordinary atmosphere. Its value has become 1.01325 bar exactly. In the construction of the inter-unit-coefficients table in the section below the definitions of the above tables are used, not this redefinition of the atmosphere. Nevertheless no contradiction will occur since this 'new' value lies within the accuracy of six to eight digits used in making the inter-unit-coefficients table. Therefore none of the values in that table need to be recalculated. They remain correct.
Now we have all tools to calculate every coefficient between the one unit or scale division and any other unit or scale division. Put together all coefficients form a table. The most important ones are listed below. The table thus created consists of eight by eight cells.
For the ease of the user the table has got additional organisation. That is written in the following paragraphs up to the 'Note'.
The rows and columns have been ordered in such a way that the number in a cell is greater when the cell is located in a higher row and/or a more right column.
The numeric values below the 1-1-1 diagonal are the inverses of those above this diagonal. Example: The inverse of 51.714932 is 0.019336775
For the sake of easy reading and printing on small computer peripherals the table is split into four two-column tables.
NOTE: Many of the listed numbers are written with an
accuracy of eight or nine digits. This is done to avoid
cumulative calculation errors in complex and cascade-like
calculations. The actual accuracy of the most of the
numbers is only six digits, since the accuracy of the
water-density and that of the gravity are six digits !!
The table should be read as follows:
One unit written alongside the vertical axis ('row name')
equals one unit written alongside the horizontal
axis ('column name') times the numeric value in
the table cell.
Example: 1 psi = 51.714932 torr
| atm | bar |
--------+-------------------+-------------------+
atm | 1 | 1.01325001 |
--------+-------------------+-------------------+
bar | 0.986 923 26 | 1 |
--------+-------------------+-------------------+
at | 0.967 841 09 | 0.980 665 [*] |
--------+-------------------+-------------------+
watm | 0.967 813 99 | 0.980 637 54 |
--------+-------------------+-------------------+
psi | 0.068 045 963 | 0.068 947 573 |
--------+-------------------+-------------------+
torr | 0.001 315 789 5 | 0.001 333 223 7 |
--------+-------------------+-------------------+
hPa | 0.000 986 923 26 | 0.001 [*] |
--------+-------------------+-------------------+
psf | 0.000 472 541 41 | 0.000 478 802 59 |
--------+-------------------+-------------------+
| at | watm |
--------+-------------------+-------------------+
atm | 1.033 227 47 | 1.033 256 40 |
--------+-------------------+-------------------+
bar | 1.019 716 2 | 1.019 744 77 |
--------+-------------------+-------------------+
at | 1 | 1.000 028 0 |
--------+-------------------+-------------------+
watm | 0.999 972 | 1 |
--------+-------------------+-------------------+
psi | 0.070 306 958 | 0.070 308 927 |
--------+-------------------+-------------------+
torr | 0.001 359 509 8 | 0.001 359 547 9 |
--------+-------------------+-------------------+
hPa | 0.001 019 716 2 | 0.001 019 744 77 |
--------+-------------------+-------------------+
psf | 0.000 488 242 76 | 0.000 488 256 43 |
--------+-------------------+-------------------+
| psi | torr |
--------+-------------------+-------------------+
atm | 14.695 949 | 760 |
--------+-------------------+-------------------+
bar | 14.503 774 | 750.061 67 |
--------+-------------------+-------------------+
at | 14.223 343 | 735.559 23 |
--------+-------------------+-------------------+
watm | 14.222 945 | 735.538 64 |
--------+-------------------+-------------------+
psi | 1 | 51.714 932 |
--------+-------------------+-------------------+
torr | 0.019 336 775 | 1 |
--------+-------------------+-------------------+
hPa | 0.014 503 774 | 0.750 061 67 |
--------+-------------------+-------------------+
psf | 0.006 944 444 4 | 0.359 131 47 |
--------+-------------------+-------------------+
| hPa | psf |
--------+-------------------+-------------------+
atm | 1 013.250 01 | 2 116.216 6 |
--------+-------------------+-------------------+
bar | 1000 | 2 088.543 4 |
--------+-------------------+-------------------+
at | 980.665 [*] | 2 048.1614 |
--------+-------------------+-------------------+
watm | 980.637 54 | 2 048.104 1 |
--------+-------------------+-------------------+
psi | 68.947 573 | 144 |
--------+-------------------+-------------------+
torr | 1.333 223 7 | 2.784 495 6 |
--------+-------------------+-------------------+
hPa | 1 | 2.088 543 4 |
--------+-------------------+-------------------+
psf | 0.478 802 59 | 1 |
--------+-------------------+-------------------+
One can conclude from the above table that the units atm, bar, at and watm can be supposed to be equal when an inaccuracy of 3.5% or more is allowed. Then the table shrinks into the following very small layout:
| bar | psi | torr | hPa | psf |
-----+----------+--------+--------+--------+--------+
bar | 1 | 14.5 | 750 | 1000 | 2000 |
-----+----------+--------+--------+--------+--------+
psi | 0.07 | 1 | 52.5 | 70 | 144 |
-----+----------+--------+--------+--------+--------+
torr | 0.001333 | 0.019 | 1 | 1.3333 | 2.6667 |
-----+----------+--------+--------+--------+--------+
hPa | 0.001 | 0.0145 | 0.750 | 1 | 2 |
-----+----------+--------+--------+--------+--------+
psf | 0.0005 | 0.007 | 0.375 | 0.5 | 1 |
-----+----------+--------+--------+--------+--------+
Herein: atm = bar = at = watm
The inter-unit-coefficients table would become too big when all fluid-column pressures were added to it. Therefore in the following table they are compared to the bar only. This table must be read as follows: One foot of mercury equals 0.406 bar.
BAR-pressure in case of:
| water | mercury |
---------+-------------------+-------------------+
inch | 0.00 249 081 936 | 0.033 863 882 0 |
---------+-------------------+-------------------+
foot | 0.02 988 983 23 | 0.406 366 584 |
---------+-------------------+-------------------+
yard | 0.08 966 949 69 | 1.219 099 751 |
---------+-------------------+-------------------+
meter | 0.09 806 375 42 | 1.333 223 7 |
---------+-------------------+-------------------+
ft-hd = foot-of-head = foot of water-column.
in-WC = in-wg = inch of water-column = inch of water-gauge.
The blood pressure in a human body (except in the lungs)
is measured in the the neighbourhood of the heart, e.g. on
an upper arm. It is expressed in mmHg or Torr. Two values
that can be obtained easily by every physician are very
important:
Systolic pressure: This is the maximum pressure value during
the heartbeat. A healthy value is 125 mmHg.
Diastolic pressure: This is the minimum pressure that occurs
during the resting phase of the heart between two beats. A
healthy value is 75 mmHg.
Thus in a healthy person the value of the blood pressure
moves constantly back and forth between one sixth and one
tenth of an atmosphere, i.e. between 1.6 and 1 mH2O.
Higher pressures make that the heart has to work harder thus causing more wear and tear, and that the bloodvessels are more strained which in the long time may lead to tiny cracks in their walls. These cracks cause bloodclots and thrombosis which on their turn may cause strike attacks in the heart and the head with irreversible damage.
Some scientists suggest that the intense use of salt makes
the blood pressure to increase slowly during the aging of a
person. This increase can be stopped, but not made undone by
stopping the excessive salt consumption.
Too much fat tissue also increases the blood pressure as it
pinches several blood vessels in the belly. This is similar
to pinching a garden hose to increase the water pressure.
Then in case of physical strain the head feels to explode.
This over pressure can be made undone simply by slimming.
The table below gives the distances in metric hecto-meters covered by a recreational runner at his maximum effort during twelve minutes. This is called the Cooper-test. The table shows the dependence on the gender and the age of the person.
NOTE: This table is not applicable for people who perform very few body exercise or none at all.
C O O P E R T E S T
Form Gender Distance in hectometers in 12 minutes run
Age ---> 0-29 30-39 40-49 50-59 60-...
Very poor F 0-15 0-14 0-12 0-11 0-10
M 0-16 0-15 0-14 0-13 0-12
Poor F 15-18 14-17 12-15 11-14 10-13
M 16-20 15-19 14-17 13-16 12-15
Mediocre F 18-22 17-20 15-19 14-17 13-16
M 20-24 19-23 17-21 16-20 15-19
Good F 22-27 20-25 19-23 17-22 16-21
M 24-28 23-27 21-25 20-24 19-23
Very good F 27-31 25-29 23-27 22-26 21-25
M 28-32 27-31 25-29 24-28 23-27
Excellent F 31-35 29-33 27-31 26-30 25-29
M 32-36 31-35 29-33 28-32 27-31
Distances have been rounded to integral hectometer-units.
Hectometer equals hundred meters.
Age is given in years.
Gender: M = Male; F = Female.
Example: A 34 years old woman runs 1830 meters (= 18.3 hm) during twelve minutes. The Coopertest table says that her sports form is mediocre.
Three tables are given in relation to the windforce
as defined by Francis Beaufort (1774-1857) and later on
refined by others. The abbreviations in these three
tables are:
index = Beaufort number
psi = pounds per square inch
mps = meters per second
kph = kilometers per hour
mph = statute miles per hour
knot = internat. miles per hour
23-> = 23->> = 23 and more
At present the Beaufort index is determined by averaging the wind speed over a period of ten minutes. So the incidental gusts are ruled out and thus unable to lift up the index to a higher number. The measurements are done on an open water or open land area at the height of ten meters.
The primary base of the Beaufort scale is not the speed of the wind, but the force it exerts on objects like ships and buildings. Therefore the first table shows the pressure by the wind and the resulting wave size in giant open waters. The pressure is measured with a disk of one square foot in area.
average
index pressure sea wave height description
(psi) (m,cm) (ft,in)
----- -------- ------- ------- -----------
0 0.0 0 cm 0 in calm, no wind
1 0.01 7 cm 3 in light air
2 0.08 13 cm 5 in light breeze
3 0.28 60 cm 2.0 ft gentle breeze
4 0.67 1 m 3.5 ft moderate breeze
5 1.31 2 m 6.5 ft fresh breeze
6 2.3 3 m 9.5 ft strong breeze
7 3.6 4 m 13.5 ft near gale / moderate gale
8 5.4 5.5 m 18 ft gale / fresh gale
9 7.7 7 m 23 ft strong gale
10 10.5 9 m 29 ft storm / whole gale
11 14.0 11 m 37 ft violent storm / storm
12 17-> 14-> m 45-> ft hurricane, tyfoon, cyclone
In case of a double description with '/' the right part is the description used by Francis Beaufort himself. The left part is the one used in the modern days.
The wave heights are the typical heights at open seas or giant lakes. The "freak waves" are left out of sight. At the stormy windforces of ten or more such unpredictable rogue waves may suddenly occur. Such a wave rises out of the water as a 25 to 30 meters high wall, breaks like a surf wave and then falls down on the ship. Thus it can swallow the largest freight or passenger ship entirely. Often the ship disappears without any sign left.
Beaufort made a table that describes the effect of the wind on a ship and how the sailors must handle to keep the ship safe at sea. In 1926 meteorologists added a list of the effects by the wind at the inland.
index effects on land
----- ---------------
0 smoke rises vertically
1 smoke drift shows direction of wind
2 wind felt on face; leaves rustle;
ordinary vane moves
3 leaves and small twigs in constant motion;
wind extends light flag
4 raises dust and loose paper; small branches move;
hair is disordered
5 small trees in leaf begin to sway;
crested wavelets form on inland waters
6 large branches in motion; difficult to use
umbrellas; whistling heard in telegraph wires
7 whole trees in motion; inconvenience felt when
walking against wind
8 breaks twigs off trees; generally impedes walking
9 small structural damage (chimney post, roof tiles
and slates removed)
10 trees uprooted; considerable structural damage;
adult people are overthrown
11 widespread damage in forests and buildings
12 widespread damage, apocalyptic like in the hell.
Windforce 10 is seldomly experienced inland; windforce 11 and 12 very rarely. When the windforce index is 12 or more, the storm is named a hurricane or tyfoon or cyclone (all three words are the same). The intensity of such storms is listed by the Scale of Saffir-Simpson.
index speed(mps) speed(kph) speed(mph) speed(knot)
----- ---------- ---------- ---------- -----------
0 0.0 - 0.3 0 - 1 0 - 1 0 - 1
1 0.3 - 1.5 1 - 5 1 - 3 1 - 3
2 1.6 - 3.3 6 - 11 4 - 7 4 - 6
3 3.4 - 5.4 12 - 19 8 - 12 7 - 10
4 5.5 - 7.9 20 - 28 13 - 18 11 - 16
5 8.0 - 10.7 29 - 38 19 - 24 17 - 21
6 10.8 - 13.8 39 - 49 25 - 31 22 - 27
7 13.9 - 17.1 50 - 61 32 - 38 28 - 33
8 17.2 - 20.7 62 - 74 39 - 46 34 - 40
9 20.8 - 24.4 75 - 88 47 - 54 41 - 47
10 24.5 - 28.4 89 - 102 55 - 63 48 - 55
11 28.5 - 32.6 103 - 117 64 - 75 56 - 63
12 32.7 ->> 117 ->> 75 ->> 64 ->>
The four definitions of the wind speeds that border the zone of one Beaufort index do not match exactly, although they are the definitions used by the official weather institutes. The wind pressure and the wave heights in the first table are those in the midst of the zone.
The scale made in 1935 by Charles Richter (1900 - 1985) is not based on the effects by the earthquakes, but on the amplitudes of the ground motions. The amplitude selected for this measure is not simply the maximum sway of the ground. The determination of the right amplitude size is much more complicated because of the following reasons:
Therefore the seismologists have the difficult task to calculate an 'average sway' having the 'average amplitude' in the epicenter. The epicenter is the location on the earth surface right above the source (= center) of the quake. The total duration of the quake is not taken into account, and also not the noisy vibrations that feel like a giant lorry near the house.
For easiness not the average amplitude itself, but its
logarithm is published to the news press. This value is
called the "Richter magnitude". Its value is:
RichterMagnitude = log ( AverageAmplitude )
This formula shows that the amplitude is ten times bigger
when the magnitude increases by one.
A few days after the quake the seismic data are evaluated more meticulously. Often this leads to a correction of the average amplitude. Then the Richter magnitude may change with a value of up to 0.3
In a woodland a quake does not harm. In mountain areas it can break rocks. When under the see it can create hughe tidal waves called "tsunami"s. These can be dangerous when trapped in a harbor or impeded by a long coast line. The table below lists the earthquake damages in populated areas on land.
Richter
magnitude effects on land
--------- ---------------
under 2.0 micro-earthquake; not felt.
under 3.5 generally not felt, but recorded only;
sometimes felt as a small vibration.
3.5 - 5.4 moderate earthquake; often felt, rarely damage,
some chimneys may topple off.
under 6.0 at most slight damage to well-designed buildings,
major damage to poorly constructed buildings
over small regions.
6.1 - 6.9 strong earthquake; destructive in populated
areas up to about 100 kilometers.
7.0 - 7.9 major earthquake; serious damage in larger areas.
8 or more great earthquake; serious damage in areas several
hundred kilometers across.
The time the earth needs to circle around the sun is called the "solar year" or "tropical year". This solar year has not always the same length. In the course of time it gets shorter slightly. Therefore the scientists, like astronomers and physicists, use the solar year of 1900 as the reference year for their definitions of date and time. That year had the duration of 365.242198781 days = 31556925.9747 seconds. This is 365 days, 5 hours, 48 minutes and (approx.) 46 seconds.
At present the solar year lasts shorter for over half
a second. The duration of the solar year of 2000 is
31556925.444 seconds = 365.24219264 (1900-)days. This is
365 (1900-)days, 5 hours, 48 minutes and 45.444 seconds.
The scientifically determined length of a day in 2000 is
86400.002 seconds. So the 'solar day' does not match
exactly the 'calendar day' too!. And a lunar month also
does not match an ordinary month:
lunar month = 29.53059 days = 2551442.976 seconds.
The solar year is very important for our civilization as it dictates the seasons and thus the periodicity of the weather types. By this way it dictates the human food production by the agriculture and cattle raising. For a good grow one must know when (and how) to plow, sow, mow and stow and cover the cow. These activities must be performed months in advance of harvesting and collecting the resulting food.
Alas, the solar year has not an integral number of days. Therefore humans introduced the approximating "calendar year" or "civil year" which has an integral number of days. This 'integralization' makes its duration slightly different from that of the solar year. Consequently, due course of time the calendar year would loose totally its relation with the solar year and thus render itself useless. In order to avoid this slip we must use two types of calendar years, each having its own integral number of days, and place them in an intermixed sequence.
The two types of calendar year are the "normal year" (with 365 days) and the "leap year" (with 366 days). The eternal time is divided into sets of four calendar years, each set consisting of three normal years and one leap year. This results into the well-known rule that each year with a number dividable by four is a leap year, e.g. 1904, 1908, 1912, and so on. The others are normal years.
In a very few sets the leap year is replaced by a normal year. This is done only once in a period of 100 or 200 years. It is not done within the 199 years period from 1901 to 2099. The years 1900 and 2100 are normal years that replace leap years. But the year 2000 stays a leap year. By these ways we can keep the difference between the solar year and the current calendar year always less than one day.
In old medieval times efforts had already been made to determine the length of the solar year. At first this lead to the Julian and later to the more accurate Gregorian year.
Note that the year 0 does not exist. So the year -1 = 1 BC is followed immediately by the year +1 = 1 AD. The reason is that until the year 700 the number 'zero' was not known in Europe. The Hindus have invented it.
The following table shows the relations between the man-made calendar-units of time, except months.
abbrev name consists of # seconds
------ ---- ----------- ---------
+++ present-day calendar +++
Gregorian year 365.2425[*] day 31556952
Julian year 365.25[*] day 31557600
a, y, yr leap year 366 day 31622400
a, y, yr normal year 365 day 31536000
fortnight 2 sennight 1209600
se(ve)nnight 1 week 604800
w week 7 day 604800
d day 6 ship-watch 86400
ship-watch 2 ship-dog-watch 14400
ship-dog-watch 2 hour 7200
h hour 2 ship-bell 3600
ship-bell 2 quarter 1800
quarter 15 minute 900
m minute (= ') 60 second 60
s second (= ") 60 third 1
third (= "') 0.0166667
+++ medieval +++
h hour 5 point 3600
point 8 moment 720
moment 12 ounce 90
ounce 47 atom 7.5[*]
atom 1/376 minute 0.1595745
+++ old-Roman +++
hour 24 scrupulus 3600
scrupulus [*] 2.5 (modern) minute 150
+++ metric +++
day 10 m.hour 86400
m.hour 100 m.minute, beat 8640
m.minute = beat 100 m.second, blink 86.4[*]
m.second = blink 0.864[*]
+++ scientists' definition: +++
s second = 9 192 631 770 wave periods of
the light emitted by an
excited Cesium-133 atom
When put together the facts described above make a large table. The part of it with the most-commonly used time-units forms the following table, that for the ease of printing on paper has been split into two parts. This table must be read as follows: One column item consists of cell-number row items. Example: one day consists of 1440 minutes.
solar year
leap year 1900 normal year
+-----------+---------------+-----------+
second | 31622400 | 31556925.9747 | 31536000 |
+-----------+---------------+-----------+
minute | 527040 | 525948.766245 | 525600 |
+-----------+---------------+-----------+
hour | 8784 | 8765.81277075 | 8760 |
+-----------+---------------+-----------+
day | 366 | 365.242198781 | 365 |
+-----------+---------------+-----------+
week | 52.285714 | 52.1774569688 | 52.142857 |
+-----------+---------------+-----------+
normal | 1.0027397 | 1.0006635583 | 1 |
year +-----------+---------------+-----------+
solar | 1.0020748 | 1 |
year +-----------+---------------+
leap | 1 |
year +-----------+
week day hour min. sec.
+--------+-------+------+-----+-----+
second | 604800 | 86400 | 3600 | 60 | 1 |
+--------+-------+------+-----+-----+
minute | 10080 | 1440 | 60 | 1 |
+--------+-------+------+-----+
hour | 168 | 24 | 1 |
+--------+-------+------+
day | 7 | 1 |
+--------+-------+
week | 1 |
+--------+
The several man-made periods of time in a calendar are supposed to have a constant duration. There is one type of period that has not: the month. Every of the twelve months in a year has its own length. That is an integral number from 28 to 31 days. The following table shows the length in days of every month and the day-in-the-year-number of the day immediately before the first day of the month.
normal year leap year
month name length day before length day before
---------- ------ ---------- ------ ----------
january 31 0 31 0
february 28 31 29 31
march 31 59 31 60
april 30 90 30 91
may 31 120 31 121
june 30 151 30 152
july 31 181 31 182
august 31 212 31 213
september 30 243 30 244
october 31 273 31 274
november 30 304 30 305
december 31 334 31 335
next-year's
january 31 365 31 366
The way of calculating the daynumber in the year is
given by an example.
5 MAY in a normal year: 120 + 5 = 125
5 MAY in a leap year:
121 + 5 = 126
1 JANUARY: 0 + 1 = 1
initial-degree-type calculation degree-type-target
----------- ----------- ----------
Kelvin K - 273.15 = C Celsius
Kelvin (K - 273.15) * 9/5 + 32.0 = F Fahrenheit
Kelvin (K - 273.15) * 4/5 = R Reaumur
Kelvin K * 9/5 = A Rankine
Celsius C + 273.15 = K Kelvin
Celsius C * 9/5 + 32.0 = F Fahrenheit
Celsius C * 9/5 + 491.67 = A Rankine
Celsius C * 4/5 = R Reaumur
Rankine A * 5/9 = K Kelvin
Rankine A - 459.67 = F Fahrenheit
Rankine (A - 491.67) * 5/9 = C Celsius
Rankine (A - 491.67) * 4/9 = R Reaumur
Fahrenheit (F - 32.0) * 5/9 + 273.15 = K Kelvin
Fahrenheit (F - 32.0) * 5/9 = C Celcius
Fahrenheit (F - 32.0) * 4/9 = R Reaumur
Fahrenheit F + 459.67 = A Rankine
Reaumur R * 5/4 + 273.15 = K Kelvin
Reaumur R * 5/4 = C Celsius
Reaumur R * 9/4 + 32.0 = F Fahrenheit
Reaumur R * 9/4 + 491.67 = A Rankine
In this table:
A = Rankine
R = Reaumur
C = Celcius
F = Fahrenheit
K = Kelvin
273.15 * 9/5 = 491.67 = 459.67 + 32.0
One degree difference in Kelvin = one degree difference in Celsius
Synonym: Centigrade = degree Celcius
Example with some equivalents of Celsius and Fahrenheit:
Celsius Fahrenheit Celsius Fahrenheit
------- ---------- ------- ----------
100 212 22 71.6
93.33 200 20 68
60 140 10 50
50 122 4 39.2
40 104 0 32
39 102.2 -10 14
37.78 100 -17.78 0
37 98.6 -20 -4
30 86 -40 -40
The temperature of the indicator fluid in the process of
measuring a volume or a pressure is very important for an accurate
result. The temperatures of the indicators in our tables are:
Meter, by Napoleon Bonaparte and his geodetical engineers:
(metric) meter =
Circumference of earth minus measurement error of 8 km
----------------------------------------------------------
40 million
Meter, in 1963 by the physics scientists:
(metric) meter = 1 650 763.73 wave lengths of
the light emitted by an
excited Krypton-86 atom.
Meter, at present, since 1983 by the physics scientists:
(metric) meter = 1 / 299 792 458 -th part of
the length travelled by
the light in one second,
in an absolute vacuum.
Second, as defined by astronomists in earlier days:
second =
1/86400-th part of the average length
of the days in a year.
Second, at present by the physics scientists:
second = 9 192 631 770 wave periods of
the light emitted by an
excited Cesium-133 atom.
Second, proposed in may 2005 by scientists in Tokyo:
second = 429 228 004 952 wave periods of
the light emitted by an
excited Strontium atom
emprisoned by laser beams.
Kilogram is the mass of a platinum-iridium cylinder stored in the French Bureau-International-des-Poids-et-Mesures at Sevres near Paris.
speed of light = c 2.99792458 @ 8 [*] m/s
9.83571056 @ 8 ft/s
1.86282397 @ 5 mile/s
astronomical unit (1996) 1.49597870691 @ 11 m
= au = ua 9.29558072674 @ 8 mile
spat 1 @ +12 m
6.68458712267 astronom.unit
light year 9.460528405 @ 15 m
5.878499814 @ 12 mile
6323.972635 astronom.unit
parallax second = parsec 3.08567758 @ 16 m
1.91735116 @ 13 mile
206264.80625 astronom.unit
3.2616334409 light year
Hubble 1 @ +9 lightyear
9.460528405 @ 24 m
specific density of water (at 4`C) 0.999 9724 kg / cu.dm
thus: 1 old litre 1.000 028 cu.dm
norm volume of idealized gas 22.4129 ltr / mol
-- idem -- 22.414 cu.dm / mol
number of particles
in one mol = Avogadro's-nr. 6.022142 @ 23
amu = unit of atomic mas = Dalton
= 1/ Avogadro's-number 1.660539 @ -27 kg
bes = hyle 1000.29 kg
crith (1L H2 at 0.01'C & 1 atm) 89.2295583 mg
density of seawater (at 4`C) 1.026493 * density of normal
water at 4 centigrades
nautical speed: 1 knot = 1852 m/h = 0.5144 m/s
airplane speed: 1 mach = (approximated)
typical 1193.4 km/h = 331.5 m/s
at sea-level 1223.1 km/h = 760 miles/h
at high altitude 1062.2 km/h = 660 miles/h
speed of sound of 0 Hz at 0 deg.C 1193.4 km/h
speed of light: c = 299 792 458 m/s
G = grav = standard acceleration
by earth gravity 9.80665 [*] m/s2 = 32.174 ft/s2
kilogram-force (kgf) 9.80665 [*] N
poundforce (lbf) 4.4482216 N
poundal 0.13825495 N
Newton (N) 0.2248089 poundforce =
0.1019716 kilogramforce =
7.2330139 poundal
sthene 1 kN = 1000 N
dyne (dyn) 10 uN = 1 @ -5 N [*]
erg 1 @ -7 J = 0.1 uJ [*]
footpound 1.35581795 J
British thermal unit (Btu) 1055.05585262 J [*]
calory (cal; chemical) 4.1840 J
calory (cal; IT-steam) 4.1868 J [*]
food-Calorie (=1000 IT-st.cal) 4186.8 J [*]
joule (J) 0.239 cal
watt-hour 3600 J (= 0.859845228 Cal)
kilowatt-hour (kWh) 3.6 MJ [*] (= 859.845228 Cal)
gas-constant R (in PV=RT) 8.31432 J / mol / Kelvin
horsepower:
Euro-continent (pk/ps) 735.5 W = 75 kgf.m/s
USA (hp) 745.7 W = 550 lbf.ft/s
waterpump 746.043 W = 550.253 lbf.ft/s
donkey-power 250 W (= ca. 1/3 horsepower)
USA-man-power 74.57 W (= 1/10 horsepower)
[*] = This value is exact.
square-root of 2 1.41421 35623 73095
square-root of 3 1.73205 08075 68877
square-root of 5 2.23606 79774 99790
square-root of 7 2.64575 13110 64591
square-root of 10 3.16227 76601 68379
pi (of circle circumference) 3.14159 26535 89793
e (the natural number) 2.71828 18284 59045
e-log 10 = ln 10 2.30258 50929 94046
10-log e = 1 / e-log 10 0.43429 44819 03252
gamma (of factorial calcul's) 0.57721 56649 01533
golden ratio of beauty = (1+sqrt(5))/2 = 1.618034
Pythagoras-constant = sqrt(2)
Archimedes-constant = pi
Euler-constant = Euler-Mascheroni constant = gamma
base of Napier-logarithm = e
Rough approximation Deviation in %
------------------- --------------
pi = 3,1415926535897932384626433832795
10-log( pi ) =~= 1/2 = 0.5 +0.6
sqrt( pi ) =~= 1 + 3/4 = 1.75 -1.3
pi^2 =~= 10 +1.4
pi^3 =~= 31 -0.02
e = 2,7182818284590452353602874713527
10-log( e ) =~= 4/9 = 0.4444 +2.25
sqrt( e ) =~= 1 + 2/3 = 1.667 +1.25
e^2 =~= 7.5 +1.667
e^3 =~= 20 -0.5
10-log(2) = 0,30102999566398119521373889472449
10-log( 2 ) =~= 0.30103000 +15@-7
10-log( 2 ) =~= 0.30 -0.35
Some physical constants:
gravity =~= 10 +2.2
calory =~= 4.2 +0.4
horsepower =~= 750 +2
light-speed =~= 3 @ 8 +0.07
The name PI stands for the first letter of the Greek word Perimeter, which means Circumference.
For thousands of years the mathematicians tried to find the exact value of PI. Until the Renaissance era they believed that it can be expressed as the ratio of two integral numbers. Some of them (e.g. Ahmes) even thought each of these numbers itself is the square value of another integral number. This is the so-called quadrature of the circle. Therefore they zealously tried to find this rational quotient. They could approach the actual value of PI very closely, but never found it exactly.
Of course they never found this value by that way because PI is an irrational and even transcendental number. This has been proven by Lambert (1728-1777) in 1766, by Legendre (1752-1833) in 1794, and by F.Lindeman in 1882. Therefore the value of PI should be calculated by an infinite polynomial. For this several polynomials are available. In the actual calculation some of these converge very quickly, whilst other ones converge very slowly like the one of Leibniz in 1673.
Some of the old rational approximations are listed here, in the order of increasing accuracy. The factorial subdivisions of the Indian and the Ptolemaian values into prime numbers are made by the author of this history, not by the discoverers of those values. Nowadays in some cases the simple approximation 22/7 by Archimedes is still in use.
Old-Babylon and Biblical Old-Testament (1-Kings 7:23):
pi = 3
A rough modern-day approximation might be:
pi = sqrt (10) = 3.162277660168379332
Ahmes (ca. 2000-1600 BC):
pi = (16/9)^2 = 256 / 81 = 3.160493827160
Archimedes (287-212 BC):
pi lies between 22 / 7 = 3.142857142857
and 223 / 71 = 3.140845070423
Ptolemaios (ca. 125-150 AD):
pi = 29*13/120 = 377 / 120 = 3.141666666....
in India (ca. 0 - 700 AD), e.g. Aryabhata in 476 A.D.:
pi = (2^3)*3*7*11*17 / 10000 = 3.1416 ['exact']
Actual value (see above):
pi = 3.14159 26535 89793 23846 26433 83279 50288
circle with radius R:
circumference = perimeter length = 2 * PI * R
disc area = PI * R*R = PI * R^2
globe, ball with radius R:
surface area = 4 * PI * R*R = 4 * PI * R^2
volume = (4/3) * PI * R*R*R = (4/3) * PI * R^3
At first a list of the used names and abbreviations:
abbreviation meaning
------------ -------
rad radian
deg arcdegree = circular degree
min = ' arcminute = circular minute
sec = " arcsecond = circular second
gon centesimal grade
angular-mil centesimal deci-grade
centigon centesimal minute = centigrade
[no abbrev.] centesimal second
mil NATO-artillery mil
rhumb nautical rhumb = compass point
The mathematical relations between the deg, gon, mil and rhumb are quite easy. Read the table as by this example: 1 rhumb = 25/2 gon = 12.5 gon.
unit deg gon mil rhumb
---- --- --- --- -----
deg 1 10/9 160/9 4/45
gon 9/10 1 16 2/25
mil 9/160 1/16 1 1/200
rhumb 45/4 25/2 200 1
The following numerical relations hold beteen the rad, deg, gon, mil and rhumb. Read the table as by this example: 1 gon = 16 mil.
unit rad deg
---- --- ---
full circle 6.28318531 360
rad 1 57.2957795
deg 0.01745329252 1
gon 0.01570796327 0.9[*]
mil 0.000981747704 0.05625[*]
rhumb 0.196349541 11.25[*]
unit gon mil rhumb
---- --- --- -----
full circle 400 6400 32
rad 63.6619772 1018.59164 5.09295818
deg 1.11111111 17.7777778 0.08888889
gon 1 16 0.08
mil 0.0625[*] 1 0.005
rhumb 12.5[*] 200 1
Some relations with the other units are:
circular degree 60 min
circular degree 3600 sec
circular minute 60 sec
centesimal grade 54 min
centesimal grade 3240 sec
centesimal grade 10 angular-mil
centesimal deci-grade 10 centigon
centesimal minute 100 centesimal-seconds
radian 57deg 17' 44.80625"
radian 57.29577 95131 deg
radian 3437.74677 07849 min
radian 2 06264.80625 sec
circular degree 0.01745 32925 19943 rad
circular minute 0.00029 08882 08666 rad
circular second 0.00000 48481 36811 rad
The circular degree and its derivatives the minute and the second are the types of angular units most often used in the technical applications of the goniometry.
A circle is often divided into parts, e.g. quadrants. The table below lists the names and numerical sizes of these parts. Read the table as by this example: An octant is one-eight part of a circle and contains 45 degrees.
name part of circle rad deg
---- -------------- --- ---
revolution,cycle 1/1 6.28318531 360
half circle 1/2 3.14159265 180
third circle 1/3 2.09439510 120
quadrant 1/4 1.57079633 90
sextant 1/6 1.04719755 60
octant 1/8 0.7853981634 45
sign 1/12 0.5235987756 30
hour 1/24 0.2617993878 15
name gon mil rhumb
---- --- --- -----
revolution,cycle 400 6400 32
half circle 200 3200 16
third circle 133.33... 2133.33... 10.666...
quadrant 100 1600 8
sextant 66.66... 1066.66... 5.333...
octant 50 800 4
sign 33.33... 533.33... 2.666...
hour 16.66... 266.66... 1.333...
In this chapter the circular degrees are used, of which 360 units make a full circle.
The following table is a contraption for easy remembrance of some very important sinus-values.
sin ( 0 ) = sqrt(0) / 2 = 0
sin ( 30 ) = sqrt(1) / 2 = 0.5 [*]
sin ( 45 ) = sqrt(2) / 2 = 0.7071067811865
sin ( 60 ) = sqrt(3) / 2 = 0.8660254037844
sin ( 90 ) = sqrt(4) / 2 = 1
[*] means this value is exact.
The following table gives the derivatives of the sinus values for every value of x in the range from 0 to 90 degrees.
cos ( x ) = sin ( 90-x )
tan ( x ) = sin(x) / cos(x)
cot ( x ) = cos(x) / sin(x) = 1 / tan(x)
secans ( x ) = 1 / sin(x)
cosec ( x ) = 1 / cos(x)
The goniometric function values of the angles other than
those mentioned in the contraption table and in the range
from 0 en 90 degrees can roughly be gained by linear
interpolation. Example for 50 degrees:
50 = 45 * 2/3 + 60 * 1/3
sin(50) =(approx.)= sin(45) * 2/3 + sin(60) * 1/3
= 0.70711 * 2/3 + 0.86603 * 1/3
= 0.76008
The actual value is 0.76604444
40 = 30 * 1/3 + 45 * 2/3
cos(50) = sin(90-50) = sin(40)
sin(40) =(approx.)= sin(45) * 2/3 + sin(30) * 1/3
= 0.70711 * 2/3 + 0.50000 * 1/3
= 0.63807
The actual value is 0.64278761
tan(50) = sin(50) / cos(50) = 0.76008/0.63807 = 1.19122
The actual value is 0.76604444 / 64278671 = 1.1917536
Similarily the values of the cotangens, the secans and the cosecans can be calculated.
For better accuracy between sin(60) and sin(90) and thus between cos(30) and cos(0) and the derivative functions in these areas, use quadratic approximation in stead of linear approximation. The formulas for this approximation are:
for sinus between 60 and 90 degrees:
sin(x) = 1 - 0.0001488606624618 * (90-x) * (90-x)
for cosinus between 0 and 30 degrees:
cos(x) = 1 - 0.0001488606624618 * x * x
Example:
sin(75) = cos(15) =(approx.)=
= 1 - 0.000148861 * 15 * 15
= 1 - 0.000148861 * 225
= 1 - 0.033494
= 0.966506
The actual value is: 0.9659258262891
When x is near zero, the value of the sinus can be calculated by a very simple formula. The value of the tangens will be equal to it. Similar holds for the value of the cosinus and that of the cotangens for x near 90 degrees. In that area the value of the tangens is also very simple. The value of the cotangens is simple for x near zero degrees. These formulas are:
For x near 0 degrees:
sin(x) = tan(x) =(approx.)= 0.01745329252 * x
cot(x) = 1 / ( 0.01745329252 * x )
For x near 90 degrees:
cos(x) = cot(x) =(approx.)= 0.01745329252 * (90-x)
tan(x) = 1 / ( 0.01745329252 * (90-x) )
The more x approximates the 0 or 90 degrees, the more accurate the formulas will become. At x = 13 resp. 77 degrees the inaccuracy of the formulae for the sinus or cosinus is only just 1 percent. And then the tangens and cotangens formulae are 2 percent inaccurate.
Of course, when the other scale-units are used, they must be converted into degrees before they are used in the goniometric formulae given here. Example: sin(800 mil) = sin(50 gon)= sin(4 rhumb) = sin(1 octant) = sin(45 degree) = 0.7071068
Now everyone can calculate the goniometric-function values with an inaccuracy of only a few percents by using a simple office calculator, even an ancient mechanical one!
The sections with the measure-unit tables are split into two parts: The Old-Testamentical part and the (Greco-)Roman part which embraces the New-Testamentical measure units. For many units the tables mention the Biblical location of only one verse wherein the unit is used.
It was very difficult to collect the right and consistent values. So the tables may have errors very likely. These can be reported to the author.
A "number" is the sequence of symbols (letters or digits) representing a numeric value. There are several ways of making numbers. At present the extended Indian system is the system most common in use. Today the clumsy Roman numbers are in use for romantic purposes only.
Up to medieval times the Europeans used the Greek, the Jewish and above all the Roman system for the notation of numeric values. These systems have two disadvantages compared with the today's notation system.
The first although minor disadvantage of these systems was that the digits were not represented by graphical symbols put apart for the digits only, but by some letters of the alphabet. This may hamper the readability of a text wherein numeric values are used. In the Indian system the symbols of the digits differ from those for the letters. The letters and their numeric values used by the ancient Romans are:
M = 1000 (mille)
D = 500 (demi-mille)
C = 100 (centum)
L = 50 (lira)
X = 10 (easy notation of two V's?)
W = VV = 10
U = V = 5 (unknown; abstraction of spreaded hand?)
Y = IJ = II = 2
I = J = 1 (bare bar, see text far below)
In this Roman system an upperscore (= line above the letter) means that the value of the letter is multiplied by 1000. So an X with an upperscore has the value of 10000. Here the value of the letter is changed by adding a line to it. This worsens even readability. Note that I with upperscore equals M, and Y with upperscore equals MM.
The second and major disadvantage of the Roman, Greek and Hebrew notation systems is the cumbersome way of representing a numeric value. The value is difficult to read. This makes this notation inept for writing down intermediate results in long calculations. Therefore an abacus is often needed. The final result of the abacus calculation must be 'translated' before it is written down on paper.
In general the value of a number is calculated by adding
together the values of all digits in that number. But, the value
of a digit is subtracted in stead of added when this digit has
a right neighbour with a greater value. A digit between two of
greater value is subtracted from the right one. Then the left one
is added to this result (or when smaller subtracted from it). These
rules imply that a numeric value can be notated in different ways.
Example:
MDCCCCLXXXYY = MCMXXCIV = 1984.
Indian numbers
At around 700 A.D. the Muslim Arabs copied from Hinduistic India a system for writing numbers quite different from the Roman system. It is much easier in use, and so they tried to export it to Europe, in which they succeeded a few centuries later. Therefore often it is unjustly called the Arabic number system. In the past five centuries the European colonialism spread it over the entire world.
Around the year 500 A.D. the Indians invented the digit for the notation of 'nothing': the zero. Also all values between zero and ten got their own digit. So there were ten digits for the ten values from zero up to nine. The values of ten and more did not get a digit at all. These inventions enabled the invention of the main characteristic of the Indian system:
The value of the digit is determined by the position of its symbol in the number. One position to the left means multiplying with the factor ten. One position to the right means dividing by ten. Never additional lines or serifs are added to the symbol to mark its actual value. Simply its position suffices. The total value of the number is always the addition of the values represented by the individual digits. No subtraction is in use. Example: 1984 = 1*thousand + 9*hundred + 8*ten + 4*one
This notation system has great advantages. First a numeric value can be represented in only one way. There never are two notations for the same numeric value. Second enormously big values can be displayed without the creation of new symbols. The ten digit-symbols suffice always. (Remarkably the Arabs use other symbols for these 'Arabic' digits than the Europeans and the rest of the world do). When the value increases the number becomes longer. Thus the length of the number already gives a rough indication of the bigness of the value. Example: The value of 2000 is displayed with more digits than the smaller value of 37. In the Roman system it is with less digits: MM and XXXVII (= XXCIIIX).
Also the numbers are very well readable. So this notation can be used both for the final result and for the intermediate values in a long calculation. Also the final result can be used directly as input for an other calculation. The abacus becomes superfluous. Therefore the invention of position dependency is invaluably great. It has enabled the steep rise of the modern mathematics and science.
The German baron Gottfried Wilhelm von Leibniz (or: Leibnitz) (1646-1716) invented a similar system with only two digits, 0 and 1: the binary system. Herein the numbers become roughly three times as long as in the Indian decimal system. They are less readable for humans, but they are more apt for the use in mechanical calculators like the modern electronic computers. Example: BIN-11111000000 = DEC-1984
By the Indian way only integral values could be displayed. Two extensions were added in later times. To show the broken numbers the notation of the fractional part was added. Its length shows the accuracy with which the number approximates the actual value. The exponent notation was added to ease the display of extremely large or small values. Both are applied in the binary system too.
In all number systems the bare bar indicates the digit one.
It is derived from a single stroke in the sand or a straight
finger (called 'dik' by modern etymologists). A finger bent in
the fist is not to be counted. Perhaps this was the basis of the
notation for the zero: a circle.
In different languages the Indian word SIFR (=> cipher) has got
different meanings: Encryption code, Digit (one out of 0 to 9),
Digit zero or Value zero.
For several lengths only one verse is mentioned wherein they are used.
metrical
Hebrew name consists of meters English name where
----------- ----------- -------- ------------ -----
amma 2 zeret 48 cm cubit Deut 3:11
zeret 3 tofach 24 cm hand-span Ex 28:16
tofach 4 esba 8 cm hand-breadth Ex 25:25
esba 2 cm finger Jer 52:21
metrical
Greco-Roman name consists of meters English name where
---------------- ----------- -------- ------------ -----
---- in the Bible ----
pechys 48 cm Greek ell John 21: 8
sabbat.journey 2000 Grk ell 960 m Acts 1:12
milion,miliarium 8 stadia 1480 m Roman mile Matt 5:41
stadion(-um) 100 orguia 185 m furlong Luke 24:13
orguia 5 palmipes 185 cm fathom Acts 27:28
---- in general ----
milestones-distance 1520 m
schoenus 4 milion 5920 m
leuga, leuca 1.5[*] milion 2220 m Gaulish/Celtic mile
milion, -arium 1000 passus 1480 m from: mille = 1000
milion, -arium 8 stadion 1480 m Roman mile
stathmos 100 stadion 18.5 km day's march
stadion(stadium) 125 passus 185 m
actum(circumfer.) 4 actum(len.) 142 m
actum (length) 6 actum-minor 35.5 m
actum-minor 2 decimpeda 592 cm
decimpeda 2 passus 296 cm perch, ten-feeter
passus 5 pes 148 cm foot step
cubitus-maior 7 palmus 51.8 cm long cubit
cubitum(cubitus) 6 palmus 44.4 cm cubit, ellbow
palmipes 5 palmus 37 cm big foot
pes 4 palmus 29.6 cm foot
palmus-major 3 palmus 22.2 cm stretched-hand length
palmus (-minor) 3 uncia 7.4 cm width of hand-palm
palmus (-minor) 4 digitus 7.4 cm palm-width
pes, pedes 3 manus 29.6 cm foot
manus 4 uncia 9.867 cm hand
pes-naturalis 10 uncia 24.67 cm natural foot
uncia (='1/12-th') 2.467 cm inch, ounce, thumb-width
digitus 1.85 cm finger-width
400-BC.Greek Olympia stadion 192.28 m
At present the sabbatical journey is 2000 meters.
Other distances for the Roman foot have been: 29.42 cm, 29.73 cm,
33.3 cm, 33.35 cm
Many people think that in medieval times in Europa only a very few and rudimentary measurement devices did exist. So the medieval craftsmen would perform every measure by their expert eyes, even when building a hughe cathedral or castle. This is not true. Those people were clever enough to make and use sophisticated and accurate masurement devices.
At building sites they used the so-called Twelve-Knots-rope. This is a circular rope with twelve knots distributed equally over its full length. The rope must be very flexible and the knots must not shift over it.
With this rope several geometric figures can be made with always a knot on every corner point. These figures are parallograms (= slanted rectangles) and triangles. Between the corners the rope is pulled straight, so the intervals between the knots all have the same length, e.g. one ell.
Important shapes are:
metrical
Roman name consists of sq. meters
---------- ----------- ----------
saltus 8 centuria 201.87 hectare
centuria 50 geredium 25.23 hectare
geredium,heredium 2 iugerum 5047.
iugerum 2 acnua 2523. (day's-work of oxes)
acnua 1 sq. actum 1262. (120^2 ft2)
sq. actum 4 clima 1262.
clima 9 sq.act.minor 315.4
sq. actum-minor 4 sq.decimpeda 35.05
sq. decimpeda 100 sq. pes 8.7616 (when foot exactly
sq. pes 36/25 sq.pes.natur. 0.087616 equals 29.6 cm)
sq. pes-natur. 0.058411
sq = square = quadratus. Example sq.actus = actus quadratus
For several volumes only one verse is mentioned wherein they are used.
metrical
Hebrew name consists of liters English name where
----------- ----------- -------- ------------ -----
--- dry ---
homer 1 kor 365. Levi 27:16
kor 2 lethek 365. cor Ez 45:14
lethek 5 ephah 182.5
ephah 10 (g)omer 36.5 epha Judge 6:19
gomer = omer 3.65 Exod 16:16
ephah 3 seah 36.5 epha
seah 6 cab 12.17
cab 2.03
--- liquid ---
homer 10 bath 365.
bath 3 seah 36.5 Ez 45:10
seah 2 hin 12.17
hin 12 log 6.1 Exod 29:40
log 0.5
metrical
Gr.Roman name consists of liters English name where
------------- ----------- -------- ------------ -----
---- in Bible: fluid + dry ----
metretes = Greek-amphora 38.8 measure John 2: 6
koros (grain) 10 bath 345.8 cor Luke 16: 7
batos = bath 4 modios 34.58 bath Luke 16: 6
modios (grain) 8 choinix 8.64 bushel Matth 5:15
choinix (grain) 1.08 measure Revel 6: 6
---- Greco-Roman volumes in general ----
-- connection to foot --
cubic-foot 1 quadrantes 25.934336 (when foot exactly
quadrantes 3 modius/-os 25.934336 equals 29.6 cm)
-- fluid --
dolium 20 amphora 518.7
amphora 1 quadrantes 25.93 Roman amphora
quadrantes 2 urna 25.93 flu+dry
urna 4 congius 12.97
congius 6 sextarius 3.24
sextarius 2 h/gemina 0.540 flu+dry
g/hemina 2 quartarius 0.270
quartarius 2 acetabulus 0.135 flu+dry
acetabulus 6 ligula 0.0675
ligula 0.0113
congius 8 octarius 3.24
octarius 3 quartarius 0.405
quartarius 0.135
-- dry --
koros 10 batos 345.8
batos 4 modios 34.58
modios/-us 2 semodius 8.64
semodius 4 choinix 4.32
choinix 2 sextarius 1.08
sextarius 3 ciate 0.540 flu+dry
ciate 4 dry-hemina 0.180 flu
dry-hemina 4 ligula 0.0450
ligula 0.0113 flu
Ltr = Litre = cu.dm = dm3 .
metrical
Hebrew name consists of grams English name
----------- ----------- -------- ------------
talent 50 early-mina 30. kg
talent 60 later-mina 30. kg
mina (early) 60 shekel 600. pound
mina (later) 50 shekel 500. pound
shekel 3/2 = 1.5 pim 10.
pim 4/3 = 1.33 beka 6.67
shekel 2 beka 10.
beka 2 rebah 5.
rebah 5 gerah 2.5 quarter
gerah 0.5 gram
During the exile in Babylon the weight units were twice as heavy. Then a talent weighted around 60 kilograms.
metrical
Greek name consists of grams English name
---------- ----------- -------- ------------
talanton 60 mina 25.86 kg
mina, mna, mnea 25 tetradrachme 431. pound
tetradrachme 4 drachme 17.24
drachme 3 diobolos 4.31
diobolos 2 obolos 1.437
obolos 8 halk 0.718
halk 0.0898
For one weight the verse is mentioned wherein it is used.
metrical
Roman name consists of grams comments
---------- ----------- -------- --------
centenarius 100 libra 32749.
centumpondus 100 libra 32749.
pondus = litra = 327.5 'pound', see John 12:3
= libbra = libra 12 uncia equals 0.722 avdp-pound
uncia 2 semiuncia 27.29
semiuncia 2 sicilicus 13.65
sicilicus 2 denarius 6.823
denarius 3 scrupulus 3.411
uncia 3 duella 27.29
duella 2 solidus 9.097
solidus 4 scrupulus 4.549
mina (=Greek-lb.) 5/3 libra 545.8
mina (=Greek-lb.) 20 uncia 545.8
uncia 5 milliaresium 27.29
milliaresium 24/5 scrupulus 5.458
uncia 8 drachma 27.29
drachma 3 scrupulus 3.411
scrupulus 2 obolus 1.137
obolus 0.569
The name Centenarius came to us, westerners, by the Arab way. Roman centenarius -> Arabic cantar -> Arabic qintar -> European quintal -> European cental.
The money in the way we know it has been invented by the state of Lydia (in present-day Turkey) at around 700 B.C. The richest king of this state was Croesus who lived at around 500 B.C. So before the exile in Babylonia the Israelites did not have coins. They paid with rods and rings of silver of which the values were determined by their weight. One talent is approximately 30 to 60 metric kilograms of silver. It contains: 1 talent = 60 pounds = 3000 shekels. See the table of Old-Testamentical weights in the weights-section.
In this section the money denominations mentioned in the New Testament of the Christian Bible are tabulated, which are the Greco-Roman ones. In the section following the table the explanations and additional notes are written.
In the money table one Denarion is supposed to be equal to
50 Euro. This estimation is valid for the years around 2000.
See the elucidation after the table.
For every denomination only one Biblical verse is mentioned
wherein it is used.
Biblical name #Denar English name (est.)# Euro where
------------- ------ ------------ ------------ -----
Denarion 1 penny 50 Matth 20: 4
Drachme 1 drachma 50
Didrachme 2 didrachma 100 Matth 17:24
2 tribute money 100
Tetradrachme 4 tetradrachma 200
Stater (silver) 4 stater 200 Matth 17:27
Argurion 4 piece of silver 200 Matth 27: 3
4 silver shekel 200
Stater (gold) 20 1 000
Mna, mnea 100 minas, pound 5 000 Luke 19:13
Sestertium 250 sestertium 12 500
Talanton 6000 talent 300 000 Matth 18:24
Sestertius 1/4 sesterce 12.5
As, Assarion 1/16 farthing 3.1 Luke 12: 6
Kodrantes 1/64 quadrans 0.8 Matth 5:26
Lepton 1/128 mite 0.4 Marc 12:42
Sestertium is shorthand of mille sestertium = 1000 sesterces.
During the years around 2000 one US-Dollar equalled one Euro
very roughly. And also very roughly one British-Pound equalled
one and a half Euro. So the values in the table can be translated
into the USA- and British currency by the formulas:
Amount of Dollars = Amount of Euros,
Amount of Pounds = Amount of Euros * 2 / 3.
Estimations of the present-day values of the different money denominations are given. These are based on the exact multiplication factors between the different denominations and the words of Jesus in Matt.20:1-16 about the value of one of them. In that paragraph Jesus told about a 'right wage for a day's work'. He means the buying power of the wage of one day's work. This value is one Roman coin called Denarion, which has been translated into the English word Penny. At present (around the year 2000), a (not big, but still) right wage for a day's work is 50 Euro. So in the table the Denarion is put on a par with 50 Euro.
Inflation was unknown in the Greek and Roman empire before Christ. So the Denarion-Euro ratio holds for several hundreds of years, and the table can be applied to the Greek period of 500 years earlier.
In many books (even new ones) one can see figures for the conversion between Roman and present-day currencies that are unrealistic small. These figures are derived from a very old table. This table can be found easily by dividing the number of Euros in the upper table by 250. See the next table:
estimated number of Euros
Biblical name #Denar upper table old tables
------------- ------ ----------- ----------
Talanton 6000 300 000 1200
(mille) Sestertium 250 12 500 50
Mna, mnea 100 5 000 20
Stater (gold) 20 1 000 4
Argurion 4 200 0.8
Stater (silver) 4 200 0.8
Tetradrachme 4 200 0.8
Didrachme 2 100 0.4
Drachme 1 50 0.2
Denarion 1 50 0.2
Sestertius 1/4 12.5 0.05
As, Assarion 1/16 3.1 0.0125
Kodrantes 1/64 0.8 0.0031
Lepton 1/128 0.4 0.0016
The values of the upper table give a much better insight in the meaning of the amounts of money mentioned in the several locations in the Bible. They show that similarly to us the people in those times sometimes liked to think big and at other moments they thought too small. Here are some Biblical and non-biblical examples:
Betrayal by Judas = 30 silverpieces = 120 denarii = 6000 Euro (Matthew 26:15). This is in fact a very small amount of money for such an important deal.
Pouring of 325 grams of nard balm = 300 denarii = 15000 Euro! (Mark 14:5). One can buy a rather nice car for it, e.g. a simple BMW. At present only famous fashion houses like Dior, Chanel, Gucci, etc. may sell such expensive perfume bottles.
A very big value is mentioned in the parable of the merciless slave (Matthew 18:23-35). The debt of the second slave was 5000 Euro. The debt of the merciless slave was 3@9 (= 3 milliard-billion) Euro! Perhaps this slave had wrongly invested in a giant Manhattan-like real-estate project. Only Bill Gates can remit a debt of this size without getting much pain.
The yearly salary of an Athenian citizen in 450 B.C. was on average 500 drachmes. The building of the Acropolis then costed 'several thousands of talents' with a today's value of 10@9 (= one EUR-milliard = one USA-billion) Euros. At that time Athens became a rich state as the silver mines of Laurion delivered 3000 tons of pure silver in total during their hundred years of existence.
On 1-jan-1999 the European Central Bank at Frankfurt connected the value of the Euro-currency to the national currencies according to the following EXACT six-digit values:
abbrev. 1 Euro eqls currency type #Euros (*1000)
------- --- [*] --- ------------- --------------
IEP 0.787564 Irish pound 1269.7381
DEM 1.95583 German mark 511.29188
NLG 2.20371 Netherlands gulden 453.78022
FIM 5.94573 Finnish markka 168.18793
FRF 6.55957 French franc 152.44902
ATS 13.7603 Austrian schilling 72.672834
BEF/LUF 40.3399 Belgian + Luxemburg franc 24.789353
ESP 166.386 Spanish peseta 6.010121
PTE 200.482 Portuguese escudo 4.987979
SIT 239.640 Slovenijan tolar (1-jan-2007) 4.172926
GDR 340.750 Greek drachme (1-jan-2001) 2.9347029
ITL 1936.27 Italian lire 0.5164569
GBP --.-- British pound did not join the EMU -.--
[*] = All values in the column '1-Euro-equals' are exact.
The values in the column '#Euros' are approximations. This
column is the inverse of the other column.
Example on how to read the table: One Euro equals (exactly)
40.3399 Belgian francs. Thousand Belgian francs together equal
(approximately) 24.789353 Euro.
Confusing are the three names for a small country in Nothwestern
Europe: Netherlands = Holland = Dutch country. Its currency also
had two names: Gulden and Florijn. From the latter comes the old
abbreviation DFL = Dutch florine. To enhance the confusion: One
of its neighbouring countries calls itself Deutschland.
Numbers of six digits are not easy for use in daily life. Here simple approximations are often satisfactory, like the following rules of thumb:
currency country actions to be performed
-------- ------- -------------------------------------
IEP Ireland multiply with 10, then divide by 8
DEM Germany divide by 2
NLG Netherlands divide by 2, then subtract 10 %
FIM Finland divide by 6
FRF France multiply with 3, then divide by 20
ATS Austria multiply with 3, then divide by 40
BEF/LUF Belgium+Lux divide by 40
ESP Spain multiply with 6, then divide by 1000
PTE Portugal divide by 200
SIT Slovenija divide by 240
GDR Greece multiply with 3, then divide by 1000
ITL Italy divide by 2000
rough: SIT Slovenija multiply with 4, then divide by 1000
currency country actions to be performed
-------- ------- -------------------------------------
IEP Ireland multiply with 8, then divide by 10
DEM Germany multiply with 2
NLG Netherlands multiply with 2, then add 10 %
FIM Finland multiply with 6
FRF France multiply with 20, then divide by 3
ATS Austria multiply with 40, then divide by 3
BEF/LUF Belgium+Lux multiply with 40
ESP Spain multiply with 1000, then divide by 6
PTE Portugal multiply with 200
SIT Slovenija multiply with 240
GDR Greece multiply with 1000, then divide by 3
ITL Italy multiply with 2000
rough: SIT Slovenija multiply with 1000, then divide by 4
During the years around 2000 one US-Dollar equalled one Euro very roughly. And also very roughly one British-Pound equalled one and a half Euro.
The Dutch people should not throw away their Euro-calculators as they can use them for a rough calculation of the avdp-pounds and the brit.imp.gallons. The following table shows the conversion numbers and between parentheses the percentage of the inaccuracy that will occur when the NLG-Euro-calculator is used.
1 Euro = 2.20371 NLG
1 kilogram = 2.20462 avdp-pounds (inacc. = 0.05 %)
10 litres = 2.1997 brit.imp.gallon (inacc. = 0.2 %)
1 NLG = 0.45378 Euro
1 avdp-pound = 0.45359 kilogram (inacc. = 0.05 %)
1 brit.imp.gallon = 4.5461 litres (inacc. = 0.2 %)
Note: 0.1% = 1 gram per kilogram
Perhaps the Euro-calculators of other countries can be used for similar conversions between the metric and the Anglo-Saxon measure systems.