A Dictionary of Units of Measurement

A Dictionary of Units of Measurement (uploader's note: if you wish to use the dictionary with all links activated, please, go to the following homepage: http://www.unc.edu/~rowlett/units/) For information on a specific unit, click on the first letter of its name:

ABC D E F G H I J K L M N O P Q R S T U V W X Y Z Answers to the three most frequently asked questions: How many micrograms (µg, ug or mcg) in a milligram (mg)? 1000 micrograms = 1 milligram, and 1000 milligrams = 1 gram. How can I convert from international units (IU) to milligrams or micrograms? Generally speaking, you can't. IU's measure the potency of a drug, not its mass or weight. What countries besides the U.S. have not adopted the metric system? Many U.S. teachers think the answer is "Liberia and Burma" (make that Myanmar). Let's give Liberia and Myanmar a break! All countries have adopted the metric system, including the U.S., and most countries (but not the U.S.) have taken steps to eliminate most uses of traditional measurements. However, in nearly all countries people still use traditional units sometimes, at least in colloquial expressions. Becoming metric is not a one-time event that has either happened or not. It is a process that happens over time. Every country is somewhere in this process of going metric, some much further along than others.

Commentary and Explanation

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Using the Dictionary o Using Numbers and Units o Roman and Arabic Numerals o Names of Large Numbers o Symbols and Abbreviations The International System (SI) o SI Base (Fundamental) Units o SI Derived Units o Metric Prefixes o SI Units for Clinical Data in Medicine The English Customary Systems The Metric System o CGS and MKS Units o Spelling of Metric Units o The Metric System in the United States ISO and IOC country codes Links to Related Sites

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Bibliography

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What's New • • • • • • • • • •

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measuring the size of dice in hun the French encablure, 120 brasses a cent of land in southern India the fibrin unit for nattokinase the Pfiff, a small unit for beer the French brasse, a nautical unit like the fathom measuring erosion in Bubnoff units the tithing, an old English land area unit stock tank barrels in the oil industry Enhanced Fujita scale for tornado intensity photosynthetic radiation in microeinsteins

Introduction Americans probably use a greater variety of units of measurement than anyone else in the world. Caught in a slow-moving transition from customary to metric units, we employ a fascinating and sometimes frustrating mixture of units in talking about the same things. We measure the length of a race in meters, but the length of the long jump event in feet and inches. We speak of an engine's power in horsepower and its displacement in liters. In the same dispatch, we describe a hurricane's wind speed in knots and its central pressure in millibars. Furthermore, our English customary units do not form a consistent system. Reflecting their diverse roots in Celtic, Roman, Saxon, and Norse cultures, they are often confusing

and contradictory. There are two systems for land measurement (one based on the yard and the other on the rod) and a third system for distances at sea. There are two systems (avoirdupois and troy) for small weights and two more (based on the long and short tons) for large weights. Americans use two systems for volumes (one for dry commodities and one for liquids) and the British use a third (British Imperial Measure). Meanwhile, only a few Americans know that the legal definitions of the English customary units are actually based on metric units. The U. S. and British governments have agreed that a yard equals exactly 0.9144 meter and an avoirdupois pound equals exactly 0.453 592 37 kilograms. In this way, all the units of measurement Americans use every day are based on the standards of the metric system. Since 1875, in fact, the United States has subscribed to the International System of Weights and Measures, the official version of the metric system. This dictionary began as a collection of notes describing the relationship between various English and metric units. It gradually grew until it finally became too large a wordprocessing document; I couldn't find my way around in it any more. So I turned it into a folder of html documents and added it to my Internet site. For many months, no one looked at the site except me and my students. Then, gradually, the dictionary began to attract users from around the world. Many users were kind enough to point out errors; others suggested additions and improvements. Questions about units began to appear in my email inbox. Sometimes I could answer the questions, sometimes not. Today the dictionary has become a kind of interactive resource. It grows slowly and steadily, mostly through suggestions from readers and my efforts to answer questions posed by readers. You can participate in this process! Please let me know if you find any errors on the site, or if you can't find what you wanted to know, or if you know of units used in your field of study or in your part of the world that aren't included. I hope you find the dictionary useful and informative.

Formalities Written by: Russ Rowlett, Director, Center for Mathematics and Science Education University of North Carolina at Chapel Hill. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2005 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this or any page of the dictionary. Please do not copy the

contents of any page of the dictionary to another site. The material at this site is updated frequently as new information is added, so linking to the site rather than copying it is in the best interests of everyone. The information contained in the dictionary is as accurate as I can make it; please notify me if you find any errors. Neither the author nor the University of North Carolina assumes any liability for uses made of the information presented by this web site. The dictionary is not designed to promote any system of measurement. Its only purpose is to present information useful to anyone interested in the subject. July 11, 2005

Using the Dictionary This dictionary includes: • • • • • •

all the units of the International System of Units (SI); many other units of the metric system used in everyday life or in science, either currently or recently; various non-metric scientific units such as the astronomical unit, the electronvolt, and the parsec; all the units of the English traditional systems I've encountered that can be defined with reasonable precision; selected traditional units from cultures other than English; and certain measurement terms and notations which are not "units of measurement" in a strict sense, but which are used much as if they were.

Each unit's definition includes conversion factors you can use to convert that unit into other units measuring the same concept. In the case of the traditional units, remember that in many cases the "precise" definition for an older unit (such as the league or the hogshead) was not established until the nineteenth century. It's not wise to rely too much on these definitions when reading older works. Also, many units which have precise meanings now, such as the barrel and the gallon, formerly had a variety of special meanings when applied to particular commodities; there isn't space in the dictionary for all these meanings. For many units, an abbreviation or symbol is given in parentheses, like this: gram (g). Generally speaking, symbols do not appear as separate entries, except in those cases where one could not guess from the symbol which page the unit appears on. So if all you know is a symbol or abbreviation, it's necessary to scan the appropriate page and search for the abbreviation. For example, for the unit abbreviated "Pa" look on the "P" page.) It is often necessary to use scientific (powers of ten) notation, like this: 106. If that doesn't show up on your screen as 10 raised to the 6th power, then similar problems will occur throughout the dictionary. In addition, there are several Greek letters used as symbols. Most Internet browsers will now display the "micro" symbol µ (lower case Greek letter mu), because it belongs to the international character set known as ISO Latin 1 and it is supported in both Windows and Mac OS. The lower case pi and gamma and upper case omega are not available in ISO Latin 1, so the dictionary represents them as English words in red. The dictionary observes certain standard conventions on using numbers and units. The dictionary contains a huge number of links intended to cross-reference between units. If you find such a link that doesn't work, please let me know so I can fix it.

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2004 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. January 6, 2000; latest update July 14, 2004.

Using Numbers and Units In science, there are definite rules of syntax for using numbers and units. This dictionary tries to follow those rules. Large numbers: How many is a billion? In America, the word "billion" means the number 1 000 000 000, or 109. In Britain, this number is (or was) traditionally called "one milliard" or "one thousand million," and "billion" means the number 1 000 000 000 000 or 1012, which is what Americans call a "trillion." Most other European languages have similar expressions, such as mil millones for 109 and billón for 1012 in Spanish. The Dictionary uses the American definitions for large number names. Although the General Conference on Weights and Measures endorsed the European names in 1948, the American definitions seem to be gaining ground in Britain and perhaps elsewhere. See Names for Large Numbers for more on this question. There's always interest, especially among school children, in knowing the names of still larger numbers: quadrillions, quintillions, etc. These names are listed in on the Names for Large Numbers page. Decimal Points and Numbers: In English-speaking countries, the decimal point (decimal marker) is the period. In continental Europe and most other places, the decimal marker is the comma. The Dictionary uses the period. Since the comma often means a decimal point, the International System (SI) requires that large numbers, like the billions above, be represented as groups of three digits separated by narrow spaces, not by commas. The Dictionary observes this convention. Scientific Notation: Many authorities, including the U.S. NIST (Guide for the Use of the International System of Units, sec. 7.9), also recommend that in scientific notation (when numbers are represented using powers of ten), the exponent of the 10 should be a multiple of 3. For example, the distance from the Earth to the Sun should be stated as

approximately 149.6 x 106 km, not 1.496 x 108 km. This rule fits the structure of the prefixes used for metric units. The Dictionary follows this rule for most numbers, but not for stating the ratios between CGS and MKS units. Symbols (Abbreviations): Following the rules of the International System, the Dictionary uses no periods after abbreviations or symbols for units, and never uses an "s" on an abbreviation or symbol to indicate a plural.

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2004 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. February 14, 2000; last updated July 14, 2004.

Roman and "Arabic" Numerals The use of Roman numerals has been mathematically obsolete for more than 1100 years. Nonetheless, the Roman symbols for numbers continue to be used in a variety of ways, most of them rather stereotyped: to mark the hours on clock faces, to number pages in the prefaces of books, to express copyright dates, and to count items in a series (such as the Super Bowls of U.S. professional football). The form of Roman numeration used today was established during the Middle Ages in Western Europe. It is derived from the systems actually used in Roman times, but with certain improvements. The basic Roman numerals as used today are: I=1

V=5

X = 10

L = 50

C = 100

D = 500

M = 1000

The symbols are repeated to form larger numbers, and when different symbols are combined, the larger unit precedes the smaller. Thus VIII represents 8, CLXXX is 180, and MMDCCXXV is 2725. The Romans usually wrote IIII for 4 and XXXX for 40. The number 949 was DCCCCXXXXVIIII. To shorten the length of such numbers a "subtraction rule" was sometimes used in Roman times and was commonly used in medieval times. The

"subtraction rule" allows the use of six compound symbols in which a smaller unit precedes the larger: IV = 4

IX = 9

XL = 40

XC = 90

CD = 400

CM = 900

Using these symbols, 949 is written more compactly as CMXLIX. (Other "subtracted" symbols are not allowed. Thus 99 must written XCIX, not IC.) The use of subtracted symbols was never mandatory, so IIII and IV can be used interchangeably for 4. Actually, the symbols D (500) and M (1000) were originally written using a vertical stroke with surrounding arcs; these arcs can only be approximated on this page by using parentheses. D appeared as I ) and M as ( I ). This system allowed powers of ten larger than 1000 to be written by increasing the number of arcs: 10 000 was written (( I )) and 100 000 was written ((( I ))). The Romans had no word for 1 000 000 and rarely considered numbers of that size or larger. In late Roman and medieval times, after D and M were adopted as the symbols for 500 and 1000, a custom arose of writing a bar over a number to multiply that number by 1000. Thus 10 000 became X with a bar over it and 100 000 became C with a bar over it. These "overbarred" symbols are almost never seen today. In Roman times, only the capital letters were used for number symbols. Later, after lower case letters came into use, Roman numbers were often written in lower case. Thus "vi" means 6 and "cxxii" means 122. Sometimes cases were even mixed, as in "Mcxl" for 1140. Furthermore, the lower case letter "j" was sometimes used in place of "i". A common custom was to write "j" for the last in a series of one's, as in "xiij" for 13. Roman numerals continued in use in Europe after the fall of the Roman Empire, and they remained in general use for centuries after our modern number system became available. As we see, their use in certain applications continues even today. The modern system of numeration is based on place value, with the same symbol, such as 4, taking on different meaning (4, 40, 400, etc.) depending on its location within the representation of the number. Place value notation was used long ago in Babylonian cuneiform numerals, but our modern decimal place value system was invented by Hindu mathematicians in India, probably by the sixth century and perhaps even earlier. The modern numerals 1, 2, 3, ..., are sometimes called "Arabic" numerals in the West because they were introduced to Europeans by Arab scholars. The key figure was the great Arab mathematician Mohammed ibn-Musa al-Khowarizmi, who taught at Baghdad sometime between 800 and 850. He wrote a book on the Hindu number system known today only in a later Latin translation as De numero indorum, "On the Hindu numbers." Subsequently he wrote a longer and very influential work, Al-jabr w'al muqabalah, known in Europe as Algebra, which included all the techniques of arithmetic still taught in schools today. The author's name, Latinized as "Algorismus," is the root of the English word "algorithm".

The Hindu-Arabic numeration system was known in Europe by 1000, but at first it didn't make much of a dent in the use of Roman numerals. During the 1100's the "Arabic" numerals were a topic of great interest among European scholars, and several translations of the Algebra appeared. In 1202, Leonardo of Pisa (ca. 1180-1250) published a famous book Liber abaci explaining and popularizing the Hindu-Arabic system, the use of the zero, the horizontal fraction bar, and the various algorithms of the Algebra. (Leonardo is better known today by his patronymic Fibonacci, "son of Bonaccio.") Thereafter modern numerals and the standard operations of arithmetic were commonly used by scholars, but Roman numerals continued to be used for many purposes, including finance and bookkeeping, for many centuries to come. Incidentally, the numerals 0123456789 are more properly known as European digits. The numerals actually used in Arabic script, the true Arabic numerals, are of different forms; see Islamicity.com for a more complete discussion.

References • • •

Roman Numeral Year Dates, a Conversion Guide, by Christopher Hardy: guide to various practices that have been used in the past in writing Roman numerals. Greek Numeration, by Alan J. Cain, illustrates how Roman numeration is parallel in many ways to the Attic Greek notation. Roman Numerals, Roman Numeration System, by Gérard P. Michon, has an advanced discussion of how large numbers were represented in the Roman system.

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2004 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. March 14, 2001; latest update July 14, 2004.

Names for Large Numbers The English names for large numbers are coined from the Latin names for small numbers n by adding the ending -illion suggested by the name "million." Thus billion and trillion are coined from the Latin prefixes bi- (n = 2) and tri- (n = 3), respectively. In the American system for naming large numbers, the name coined from the Latin number n

applies to the number 103n+3. In a system traditional in many European countries, the same name applies to the number 106n. In particular, a billion is 109 = 1 000 000 000 in the American system and 1012 = 1 000 000 000 000 in the European system. For 109, Europeans say "thousand million" or "milliard." Although we describe the two systems today as American or European, both systems are actually of French origin. The French physician and mathematician Nicolas Chuquet (1445-1488) apparently coined the words byllion and tryllion and used them to represent 1012 and 1018, respectively, thus establishing what we now think of as the "European" system. However, it was also French mathematicians of the 1600's who used billion and trillion for 109 and 1012, respectively. This usage became common in France and in America, while the original Chuquet nomenclature remained in use in Britain and Germany. The French decided in 1948 to revert to the Chuquet ("European") system, leaving the U.S. as the chief standard bearer for what then became clearly an American system. In recent years, American usage has eroded the European system, particularly in Britain and to a lesser extent in other countries. This is primarily due to American finance, because Americans insist that $1 000 000 000 be called a billion dollars. In 1974, the government of Prime Minister Harold Wilson announced that henceforth "billion" would mean 109 and not 1012 in official British reports and statistics. The Times of London style guide now defines "billion" as "one thousand million, not a million million." The result of all this is widespread confusion. Anyone who uses the words "billion" and "trillion" internationally should make clear which meaning of those words is intended. On the Internet, some sites outside the U.S. use the compound designation "milliard/billion" to designate the number 1 000 000 000. In science, the names of large numbers are usually avoided completely by using the appropriate SI prefixes. Thus 109 watts is a gigawatt and 1012 joules is a terajoule. Such terms cannot be mistaken. There is no real hope of resolving the controversy in favor of either system. Americans are not likely to adopt the European nomenclature, and Europeans will always regard the American system as an imposition. However, it is possible to imagine a solution: junk both Latin-based systems and move to a Greek-based system in which, for n > 3, the Greek number n is used to generate a name for 103n. (The traditional names thousand and million are retained for n = 1 and 2 and the special name gillion, suggested by the SI prefix giga-, is proposed for n = 3.)

n=

3n

10 =

American name

European name

SI prefix

3 4

109 1012

billion trillion

milliard billion

gigatera-

Greek-based name (proposed) gillion tetrillion

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

1015 1018 1021 1024 1027 1030 1033 1036 1039 1042 1045 1048 1051 1054 1057 1060 1063 1066 1069 1072 1075 1078 1081 1084 1087 1090 1093 1096 1099

quadrillion billiard quintillion trillion sextillion trilliard septillion quadrillion octillion quadrilliard nonillion quintillion decillion quintilliard undecillion sextillion duodecillion sextilliard tredecillion septillion quattuordecillion septilliard quindecillion octillion sexdecillion octilliard septendecillion nonillion octodecillion nonilliard novemdecillion decillion vigintillion decilliard unvigintillion undecillion duovigintillion undecilliard trevigintillion duodecillion quattuorvigintillion duodecilliard quinvigintillion tredecillion sexvigintillion tredecilliard septenvigintillion quattuordecillion octovigintillion quattuordecilliard novemvigintillion quindecillion trigintillion quindecilliard untrigintillion sexdecillion duotrigintillion sexdecilliard

petaexazettayotta-

pentillion hexillion heptillion oktillion ennillion dekillion hendekillion dodekillion trisdekillion tetradekillion pentadekillion hexadekillion heptadekillion oktadekillion enneadekillion icosillion icosihenillion icosidillion icositrillion icositetrillion icosipentillion icosihexillion icosiheptillion icosioktillion icosiennillion triacontillion triacontahenillion triacontadillion triacontatrillion

This process can be continued indefinitely, but one has to stop somewhere. The name centillion (n = 100) has appeared in many dictionaries. A centillion is 10303 (1 followed by 303 zeroes) in the American system and a whopping 10600 (1 followed by 600 zeroes) in the European system. Finally, there is the googol, the number 10100 (1 followed by 100 zeroes). Invented more for fun than for use, the googol lies outside the regular naming systems. The googol equals 10 duotrigintillion in the American system, 10 sexdecilliard in the European system, and 10 triacontatrillion in the proposed Greek-based system.

The googolplex (1 followed by a googol of zeroes) is far larger than any of the numbers discussed here.

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2001 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. November 1, 2001

Using Abbreviations or Symbols In the International System of Units (SI), the units do not have "abbreviations". They have symbols. The unit symbols do not follow the grammatical rules for abbreviations, because they follow the mathematical rules for symbols instead. These rules include the following. • • •

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A symbol is never followed by a period (unless, of course, it happens to fall at the end of a sentence). The letter "s" is never added to a symbol to indicate a plural. o In other words, 2 minutes is written 2 min, not 2 min. or 2 mins. Symbols are case-sensitive and must be written as they are defined. o There is a tradition in the metric system that the first (or only) letter of an unprefixed unit symbol is capitalized if (and only if) the unit's name comes from a proper name. Thus W is the symbol for the watt and A is the symbol for the ampere, because these units are named for scientists. o It makes a big difference whether a symbol is capitalized or not, because often the same letter represents different units: t stands for the tonne and T for the tesla, for example. o There is one loophole in the rule on capitalization: it's acceptable to use the symbol L instead of l for the liter, since the letter l is so easily confused with the number 1. o The case of symbol prefixes is specified, upper and lower, and must not be changed. For example, the symbol for kilo- is k-, so kW and not KW is the symbol for the kilowatt. The superscripts 2 and 3 are always used for "square" and "cubic", respectively. o Thus the square kilometer, for example, is written km2, not sq km.

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A raised dot (also called a middle dot or half-high dot) is recommended when symbols are multiplied. It is permissible to use a space instead, but symbols should not be placed next to one another with nothing between them. o For example, A·h is the recommended symbol for the ampere hour. A h is also permitted, but not Ah or amp hr. The slash (solidus) / is used for "per". Furthermore, only one slash is allowed per symbol. o This means the SI unit of acceleration is written m/s2 rather than m/s/s, even though it is often spoken "meters per second per second". (Negative exponents can also be used: m/s2 can be written m·s-2.) Symbols are separated from the numerical quantity they follow by a space. o Thus 5 kilograms is written 5 kg, not 5kg.

In the English customary systems there are no "official" symbols or abbreviations. For many English units a variety of abbreviations are used. Sometimes these abbreviations duplicate metric symbols; for example, "A" is sometimes used in English for the acre instead of the ampere. It would be better to use the symbol "ac" for the acre. In this dictionary, the first symbol listed is either the official one or the one that should be preferred in order to minimize confusion of units. The policy of this dictionary is to define symbols for the traditional English units and to apply the SI rules to their use. This is done for both consistency and clarity. It avoids a number of outstanding problems caused by the traditional abbreviations for the English units, especially the following. •

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In the English systems, there is no general agreement as to whether abbreviations for units are capitalized or not. When English-speaking writers extend this informal practice to metric symbols, they sometimes create wild errors, such as "10 ML" used for 10 milliliters when it actually means 10 megaliters. Even standard dictionaries in English sometimes give the wrong case for metric symbols! In this dictionary, the SI convention for capitalization is applied (with a very few exceptions) to the symbols used for the English units: a letter is capitalized only if it comes from a proper name. Thus we write Btu (not BTU) for the British thermal unit. In English traditional unit abbreviations, the letter "p" is often used as an abbreviation for "per", "sq" or "s" as an abbreviation for "square", and "cu" or "c" as an abbreviation for "cubic". These are all bad ideas, despite their long usage, and they lead to confusing abbreviations. Although it is traditional to write "psi" for pounds per square inch, the symbol lb/in2 would be much clearer. (In fact, the correct symbol should really be lbf/in2, since the pounds in question are pounds of force, not pounds of mass!) A traditional abbreviation such as CFM (cubic feet per minute) is often not understood by general readers; ft3/min has a much better chance of being understood.

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2004 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. July 14, 2004

The International System of Units (SI) All systems of weights and measures, metric and non-metric, are linked through a network of international agreements supporting the International System of Units. The International System is called the SI, using the first two initials of its French name Système International d'Unités. The key agreement is the Treaty of the Meter (Convention du Mètre), signed in Paris on May 20, 1875. 48 nations have now signed this treaty, including all the major industrialized countries. The United States is a charter member of this metric club, having signed the original document back in 1875. The SI is maintained by a small agency in Paris, the International Bureau of Weights and Measures (BIPM, for Bureau International des Poids et Mesures), and it is updated every few years by an international conference, the General Conference on Weights and Measures (CGPM, for Conférence Générale des Poids et Mesures), attended by representatives of all the industrial countries and international scientific and engineering organizations. The 22nd CGPM met in October 2003; the next meeting will be in 2007. As BIPM states on its web site, "The SI is not static but evolves to match the world's increasingly demanding requirements for measurement." At the heart of the SI is a short list of base units defined in an absolute way without referring to any other units. The base units are consistent with the part of the metric system called the MKS system. In all there are seven SI base units: • • • • • • •

the meter for distance, the kilogram for mass, the second for time, the ampere for electric current, the kelvin for temperature, the mole for amount of substance, and the candela for intensity of light.

Other SI units, called SI derived units, are defined algebraically in terms of these fundamental units. For example, the SI unit of force, the newton, is defined to be the

force that accelerates a mass of one kilogram at the rate of one meter per second per second. This means the newton is equal to one kilogram meter per second squared, so the algebraic relationship is N = kg·m·s-2. Currently there are 22 SI derived units. They include: • • • • • • • • • •

the radian and steradian for plane and solid angles, respectively; the newton for force and the pascal for pressure; the joule for energy and the watt for power; the degree Celsius for everyday measurement of temperature; units for measurement of electricity: the coulomb (charge), volt (potential), farad (capacitance), ohm (resistance), and siemens (conductance); units for measurement of magnetism: the weber (flux), tesla (flux density), and henry (inductance); the lumen for flux of light and the lux for illuminance; the hertz for frequency of regular events and the becquerel for rates of radioactivity and other random events; the gray and sievert for radiation dose; and the katal, a unit of catalytic activity used in biochemistry.

Future meetings of the CGPM may make additions to this list; the katal was added by the 21st CGPM in 1999. In addition to the 29 base and derived units, the SI permits the use of certain additional units, including: • • • • •

the traditional mathematical units for measuring angles (degree, arcminute, and arcsecond); the traditional units of civil time (minute, hour, day, and year); two metric units commonly used in ordinary life: the liter for volume and the tonne (metric ton) for large masses; the logarithmic units bel and neper (and their multiples, such as the decibel); and three non-metric scientific units whose values represent important physical constants: the astronomical unit, the atomic mass unit or dalton, and the electronvolt.

The SI currently accepts the use of certain other metric and non-metric units traditional in various fields. These units are supposed to be "defined in relation to the SI in every document in which they are used," and "their use is not encouraged." These barelytolerated units might well be prohibited by future meetings of the CGPM. They include: • • • •

the nautical mile and knot, units traditionally used at sea and in meteorology; the are and hectare, common metric units of area; the bar, a pressure unit, and its commonly-used multiples such as the millibar in meteorology and the kilobar in engineering; the angstrom and the barn, units used in physics and astronomy.

The SI does not allow use of any units other than those listed above and their multiples. In particular, it does not allow use of any of the English traditional units (the horsepower, for example), nor does it allow the use of any of the algebraically-derived units of the former CGS system, such as the erg, gauss, poise, stokes, or gal. In addition, the SI does not allow use of other traditional scientific and engineering units, such as the torr, curie, calorie, or rem. Certain scientific fields have defined units more or less compatible with the SI, but not part of the SI. The use of the jansky in astronomy is a good example. There is always the chance that future meetings of the CGPM could add these units to the SI, but for the present they are not approved. For multiples of approved units, the SI includes a list of prefixes. This list has been extended several times, most recently by the 19th CGPM in 1991. Prefixes now range from yotta- at 1024 (one septillion) to yocto- at 10-24 (one septillionth). There seems to be some need for another extension, but this question was not addressed at the 1999 CGPM. The SI does not allow these prefixes to be used for binary multiples, such as the use of "kilobit" to mean 1024 bits instead of 1000. For binary multiples a new list of special prefixes has been established by the International Electrotechnical Commission. Each SI unit is represented by a symbol, not an abbreviation. The use of unit symbols is regulated by precise rules. These symbols are the same in every language of the world. However, the names of the units themselves vary in spelling according to national conventions. Therefore, it is correct for Americans to write meter and Germans to write Meter, and it is also correct for the British to write metre, Italians to write metro, and Poles to write metr. See Spelling of Metric Units for additional comments.

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2004 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. Posted July 2000; last revised May 26, 2004.

Base Units of the International System (SI) The General Conference on Weights and Measures has replaced all but one of the definitions of its base (fundamental) units based on physical objects (such as standard

meter sticks or standard kilogram bars) with physical descriptions of the units based on stable properties of the Universe. For example, the second, the base unit of time, is now defined as that period of time in which the waves of radiation emitted by cesium atoms, under specified conditions, display exactly 9 192 631 770 cycles. The meter, the base unit of distance, is defined by stating that the speed of light, a universal physical constant, is exactly 299 792 458 meters per second. These physical definitions allow scientists to reconstruct meter standards or standard clocks anywhere in the world, or even on other planets, without referring to a physical object kept in a vault somewhere. In fact, the kilogram is the only base unit still defined by a physical object. The International Bureau of Weights and Measures (BIPM) keeps the world's standard kilogram in Paris, and all other weight standards, such as those of Britain and the United States, are weighed against this standard kilogram. This one physical standard is still used because scientists can weigh objects very accurately. Weight standards in other countries can be adjusted to the Paris standard kilogram with an accuracy of one part per hundred million. So far, no one has figured out how to define the kilogram in any other way that can be reproduced with better accuracy than this. The 21st General Conference on Weights and Measures, meeting in October 1999, passed a resolution calling on national standards laboratories to press forward with research to "link the fundamental unit of mass to fundamental or atomic constants with a view to a future redefinition of the kilogram." The 22nd General Conference, in 2003, renewed this request. It is possible that the 24th General Conference, in 2007, will make a change in the definition. Following are the official definitions of the seven base units, as given by BIPM. The links in the first column are to my (possibly) less obscure definitions. meter (m) distance

"The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second."

kilogram mass (kg)

"The kilogram is equal to the mass of the international prototype of the kilogram."

second (s) time

"The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."

ampere (A)

"The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10-7 newton per metre of length."

electric current

kelvin (K) temperature

"The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water."

mole (mol)

amount of substance

"The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles."

candela (cd)

intensity of light

"The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian."

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2002 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. October 7, 2002

Derived Units of the International System (SI) In addition to the seven base units, the General Conference on Weights and Measures has approved 22 names for SI units defined as combinations of the base units. Within the SI, these units are the named derived units. Following are links to the definitions of these 22 units. The third column shows how each unit is derived from the preceding units, and the fourth column gives the formal equivalence of the unit in terms of the base units. Derived Unit hertz (Hz) newton (N) pascal (Pa) joule (J) watt (W) coulomb (C) volt (V)

Measures frequency force pressure energy or work power electric charge electric potential

Derivation /s kg·(m/s2) N/m2 N·m J/s A·s W/A

Formal Definition s-1 kg·m·s-2 kg·m-1·s-2 kg·m2·s-2 kg·m2·s-3 A·s kg·m2·s-3·A-1

farad (F) ohm (omega) siemens (S) weber (Wb) tesla (T) henry (H) degree Celsius (°C) radian (rad) steradian (sr) lumen (lm) lux (lx) becquerel (Bq) gray (Gy) sievert (Sv) katal (kat)

electric capacitance C/V electric resistance V/A electric conductance A/V magnetic flux V·s magnetic flux Wb/m2 density inductance Wb/A

kg-1·m-2·s4·A2 kg·m2·s-3·A-2 kg-1·m-2·s3·A2 kg·m2·s-2·A-1

temperature

K - 273.15

K

cd·sr lm/m2 /s J/kg Gy·(multiplier) mol/s

m·m-1 m2·m-2 cd·sr m-2·cd·sr-1 s-1 m2·s-2 m2·s-2 mol·s-1

plane angle solid angle luminous flux illuminance activity absorbed dose dose equivalent catalytic activity

kg·s-2·A-1 kg·m2·s-2·A-2

The term derived unit covers any algebraic combination of the base units, but it is only the 22 combinations listed above that have approved special names. For example, the SI derived unit of momentum (mass times velocity) has no special name; momentum is stated in kilogram meters per second (kg·m/s) or in newton seconds (N·s). A few SI derived units do have special names that have been defined but not approved. Here are some examples: Derived Unit stere (st) diopter (dpt) thermal ohm poiseuille (Pl) rayl acoustic ohm daraf talbot nit (nt) molal

Measures volume refractive power thermal resistance dynamic viscosity sound impedance sound resistance electric elastance luminous energy luminance chemical concentration

Derivation m3 m-1 K/W Pa·s Pa·s/m Pa·s/m3 F-1 lm·s cd/m2 mol/kg

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2004 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are

welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. Latest update July 14, 2004

Metric Prefixes To help the SI units apply to a wide range of phenomena, the 19th General Conference on Weights and Measures in 1991 extended the list of metric prefixes so that it reaches from yotta- at 1024 (one septillion) to yocto- at 10-24 (one septillionth). Here are the metric prefixes, with their numerical equivalents stated in the American system for naming large numbers: yotta- (Y-)

1024

1 septillion

zetta- (Z-)

1021

1 sextillion

exa- (E-)

1018

1 quintillion

peta- (P-)

1015

1 quadrillion

tera- (T-)

1012

1 trillion

giga- (G-)

109

1 billion

mega- (M-)

106

1 million

kilo- (k-)

103

1 thousand

hecto- (h-)

102

1 hundred

deka- (da-)** 10

1 ten

deci- (d-)

10-1

1 tenth

centi- (c-)

10-2

1 hundredth

milli- (m-)

10-3

1 thousandth

micro- (µ-)

10-6

1 millionth

nano- (n-)

10-9

1 billionth

pico- (p-)

10-12 1 trillionth

femto- (f-)

10-15 1 quadrillionth

atto- (a-)

10-18 1 quintillionth

zepto- (z-)

10-21 1 sextillionth

yocto- (y-)

10-24 1 septillionth

Notes: I am often asked about prefixes for other multiples, such as 104, 105, 10-4, and 10-5. The prefix myria- (my-) was formerly used for 104, but it is now considered obsolete and it is not accepted in the SI. To the best of my knowledge, no prefixes were ever accepted generally for 105, 10-4, or 10-5. There is a widespread misconception that prefixes for positive powers of ten are all capitalized, leading to the use of K- for kilo- and D- for deca-. Although this does seem like a useful idea, it is not correct. **The SI Brochure spelling of this prefix is deca-, but the U.S. National Institute of Standards and Technology (NIST) recommends deka-. National variations in spelling of the prefixes are allowed by the SI. In Italian, for example, hecto- is spelled etto- and kilois spelled chilo-. The symbols, however, are the same in all languages, so dam (not dkm) is the symbol for the dekameter and km is the symbol for the Italian chilometro. The prefixes hecto-, deka-, deci-, and centi- are widely used in everyday life but are generally avoided in scientific work. Contrary to the belief of some scientists, however, the SI does allow use of these prefixes. The last letter of a prefix is often omitted if the first letter of the unit name is a vowel, causing the combination to be hard to pronounce otherwise. Thus 100 ares is a hectare and 1 million ohms is a megohm. However, the last letter of the prefix is not omitted if pronunciation is not a problem, as in the case of the milliampere. The letter "l" is sometimes added to prefixes before the erg, so 1 million ergs is a megalerg (sounds odd, but better than "megerg"). Binary prefixes In computing, a custom arose of using the metric prefixes to specify powers of 2. For example, a kilobit is usually 210 = 1024 bits instead of 1000 bits. This practice leads to considerable confusion. In an effort to eliminate this confusion, in 1998 the International Electrotechnical Commission approved new prefixes for the powers of 2. These prefixes are as follows: kibi-

Ki- 210 = 1 024

mebi- Mi- 220 = 1 048 576 gibi-

Gi- 230 = 1 073 741 824

tebi-

Ti- 240 = 1 099 511 627 776

pebi- Pi- 250 = 1 125 899 906 842 624 exbi- Ei- 260 = 1 152 921 504 606 846 976

The Commission's ruling is that the metric prefixes should be used in computing just as they are used in other fields. Thus, 5 gigabytes (GB) should mean exactly 5 000 000 000 bytes, and 5 gibibytes (GiB) should mean exactly 5 368 709 120 bytes. The fate of this innovation is uncertain. So far, very few people are using the IEC binary prefixes. Searches for them on the Internet turn up, for the most part, complaints by people who don't want to use them. Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2005 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. April 16, 2005

English Customary Weights and Measures Distance In all traditional measuring systems, short distance units are based on the dimensions of the human body. The inch represents the width of a thumb; in fact, in many languages, the word for "inch" is also the word for "thumb." The foot (12 inches) was originally the length of a human foot, although it has evolved to be longer than most people's feet. The yard (3 feet) seems to have gotten its start in England as the name of a 3-foot measuring stick, but it is also understood to be the distance from the tip of the nose to the end of the middle finger of the outstretched hand. Finally, if you stretch your arms out to the sides as far as possible, your total "arm span," from one fingertip to the other, is a fathom (6 feet). Historically, there are many other "natural units" of the same kind, including the digit (the width of a finger, 0.75 inch), the nail (length of the last two joints of the middle finger, 3 digits or 2.25 inches), the palm (width of the palm, 3 inches), the hand (4 inches), the shaftment (width of the hand and outstretched thumb, 2 palms or 6 inches), the span (width of the outstretched hand, from the tip of the thumb to the tip of the little finger, 3 palms or 9 inches), and the cubit (length of the forearm, 18 inches). In Anglo-Saxon England (before the Norman conquest of 1066), short distances seem to have been measured in several ways. The inch (ynce) was defined to be the length of 3 barleycorns, which is very close to its modern length. The shaftment was frequently used, but it was roughly 6.5 inches long. Several foot units were in use, including a foot equal to 12 inches, a foot equal to 2 shaftments (13 inches), and the "natural foot" (pes

naturalis, an actual foot length, about 9.8 inches). The fathom was also used, but it did not have a definite relationship to the other units. When the Normans arrived, they brought back to England the Roman tradition of a 12inch foot. Although no single document on the subject can be found, it appears that during the reign of Henry I (1100-1135) the 12-inch foot became official, and the royal government took steps to make this foot length known. A 12-inch foot was inscribed on the base of a column of St. Paul's Church in London, and measurements in this unit were said to be "by the foot of St. Paul's" (de pedibus Sancti Pauli). Henry I also appears to have ordered construction of 3-foot standards, which were called "yards," thus establishing that unit for the first time in England. William of Malmsebury wrote that the yard was "the measure of his [the king's] own arm," thus launching the story that the yard was defined to be the distance from the nose to the fingertip of Henry I. In fact, both the foot and the yard were established on the basis of the Saxon ynce, the foot being 36 barleycorns and the yard 108. Meanwhile, all land in England was traditionally measured by the gyrd or rod, an old Saxon unit probably equal to 20 "natural feet." The Norman kings had no interest in changing the length of the rod, since the accuracy of deeds and other land records depended on that unit. Accordingly, the length of the rod was fixed at 5.5 yards (16.5 feet). This was not very convenient, but 5.5 yards happened to be the length of the rod as measured by the 12-inch foot, so nothing could be done about it. In the Saxon landmeasuring system, 40 rods make a furlong (fuhrlang), the length of the traditional furrow (fuhr) as plowed by ox teams on Saxon farms. These ancient Saxon units, the rod and the furlong, have come down to us today with essentially no change. The chain, a more recent invention, equals 4 rods or 1/10 furlong in order to fit nicely with the Saxon units. Longer distances in England are traditionally measured in miles. The mile is a Roman unit, originally defined to be the length of 1000 paces of a Roman legion. A "pace" here means two steps, right and left, or about 5 feet, so the mile is a unit of roughly 5000 feet. For a long time no one felt any need to be precise about this, because distances longer than a furlong did not need to be measured exactly. It just didn't make much difference whether the next town was 21 or 22 miles away. In medieval England, various mile units seem to have been used. Eventually, what made the most sense to people was that a mile should equal 8 furlongs, since the furlong was an English unit roughly equivalent to the Roman stadium and the Romans had set their mile equal to 8 stadia. This correspondence is not exact: the furlong is 660 English feet and the stadium is only 625 slightly-shorter Roman feet. In 1592, Parliament settled this question by setting the length of the mile at 8 furlongs, which works out to 1760 yards or 5280 feet. This decision completed the English distance system. Since this was just before the settling of the American colonies, British and American distance units have always been the same. Area In all the English-speaking countries, land is traditionally measured by the acre, a very

old Saxon unit that is either historic or archaic, depending on your point of view. There are references to the acre at least as early as the year 732. The word "acre" also meant "field", and as a unit an acre was originally a field of a size that a farmer could plow in a single day. In practice, this meant a field that could be plowed in a morning, since the oxen had to be rested in the afternoon. The French word for the unit is journal, which is derived from jour, meaning "day"; the corresponding unit in German is called the morgen ("morning") or tagwerk ("day's work"). Most area units were eventually defined to be the area of a square having sides equal to some simple multiple of a distance unit, like the square yard. But the acre was never visualized as a square. An acre is the area of a long and narrow Anglo-Saxon farm field, one furlong (40 rods) in length but only 4 rods (1 chain) wide. This works out, very awkwardly indeed, to be exactly 43 560 square feet . If we line up 10 of these 4 x 40 standard acres side by side, we get 10 acres in a square furlong, and since the mile is 8 furlongs there are exactly 10 x 8 x 8 = 640 acres in a square mile. Weight The basic traditional unit of weight, the pound, originated as a Roman unit and was used throughout the Roman Empire. The Roman pound was divided into 12 ounces, but many European merchants preferred to use a larger pound of 16 ounces, perhaps because a 16ounce pound is conveniently divided into halves, quarters, or eighths. During the Middle Ages there were many different pound standards in use, some of 12 ounces and some of 16. The use of these weight units naturally followed trade routes, since merchants trading along a certain route had to be familiar with the units used at both ends of the trip. In traditional English law the various pound weights are related by stating all of them as multiples of the grain, which was originally the weight of a single barleycorn. Thus barleycorns are at the origin of both weight and distance units in the English system. The oldest English weight system has been used since the time of the Saxon kings. It is based on the 12-ounce troy pound, which provided the basis on which coins were minted and gold and silver were weighed. Since Roman coins were still in circulation in Saxon times, the troy system was designed to model the Roman system directly. The troy pound weighs 5760 grains, and the ounces weigh 480 grains. Twenty pennies weighed an ounce, and therefore a pennyweight is 480/20 = 24 grains. The troy system continued to be used by jewelers and also by druggists until the nineteenth century. Even today gold and silver prices are quoted by the troy ounce in financial markets everywhere. Since the troy pound was smaller than the commercial pound units used in most of Europe, medieval English merchants often used a larger pound called the "mercantile" pound (libra mercatoria). This unit contained 15 troy ounces, so it weighed 7200 grains. This unit seemed about the right size to merchants, but its division into 15 parts, rather than 12 or 16, was very inconvenient. Around 1300 the mercantile pound was replaced in English commerce by the 16-ounce avoirdupois pound. This is the pound unit still in common use in the U.S. and Britain. Modeled on a common Italian pound unit of the late

thirteenth century, the avoirdupois pound weighs exactly 7000 grains. The avoirdupois ounce, 1/16 pound, is divided further into 16 drams. Unfortunately, the two English ounce units don't agree: the avoirdupois ounce is 7000/16 = 437.5 grains while the troy ounce is 5760/12 = 480 grains. Conversion between troy and avoirdupois units is so awkward, no one wanted to do it. The troy system quickly became highly specialized, used only for precious metals and for pharmaceuticals, while the avoirdupois pound was used for everything else. Since at least 1400 a standard weight unit in Britain has been the hundredweight, which is equal to 112 avoirdupois pounds rather than 100. There were very good reasons for the odd size of this "hundred": 112 pounds made the hundredweight equivalent for most purposes with competing units of other countries, especially the German zentner and the French quintal. Furthermore, 112 is a multiple of 16, so the British hundredweight can be divided conveniently into 4 quarters of 28 pounds, 8 stone of 14 pounds, or 16 cloves of 7 pounds each. The ton, originally a unit of wine measure, was defined to equal 20 hundredweight or 2240 pounds. During the nineteenth century, an unfortunate disagreement arose between British and Americans concerning the larger weight units. Americans, not very impressed with the history of the British units, redefined the hundredweight to equal exactly 100 pounds. The definition of the ton as 20 hundredweight made the disagreement carry over to the size of the ton: the British "long" ton remained at 2240 pounds while the American "short" ton became exactly 2000 pounds. (The American hundredweight became so popular in commerce that British merchants decided they needed a name for it; they called it the cental.) Today, most international shipments are reckoned in metric tons, which, coincidentally, are rather close in weight to the British long ton. Volume The names of the traditional volume units are the names of standard containers. Until the eighteenth century, it was very difficult to measure the capacity of a container accurately in cubic units, so the standard containers were defined by specifying the weight of a particular substance, such as wheat or beer, that they could carry. Thus the gallon, the basic English unit of volume, was originally the volume of eight pounds of wheat. This custom led to a multiplicity of units, as different commodities were carried in containers of slightly different sizes. Gallons are always divided into 4 quarts, which are further divided into 2 pints each. For larger volumes of dry commodities, there are 2 gallons in a peck and 4 pecks in a bushel. Larger volumes of liquids were carried in barrels, hogsheads, or other containers whose size in gallons tended to vary with the commodity, with wine units being different from beer and ale units or units for other liquids. The situation was still confused during the American colonial period, so the Americans were actually simplifying things by selecting just two of the many possible gallons. These two were the gallons that had become most common in British commerce by around

1700. For dry commodities, the Americans were familiar with the "Winchester bushel," defined by Parliament in 1696 to be the volume of a cylindrical container 18.5 inches in diameter and 8 inches deep. The corresponding gallon, 1/8 of this bushel, is usually called the "corn gallon" in England. This corn gallon holds 268.8 cubic inches. For liquids Americans preferred to use the traditional British wine gallon, which Parliament defined to equal exactly 231 cubic inches in 1707. As a result, the U.S. volume system includes both "dry" and "liquid" units, with the dry units being about 1/6 larger than the corresponding liquid units. In 1824, the British Parliament abolished all the traditional gallons and established a new system based on the "Imperial" gallon of 277.42 cubic inches. The Imperial gallon was designed to hold exactly 10 pounds of water under certain specified conditions. Unfortunately, Americans were not inclined to adopt this new, larger gallon, so the traditional English "system" actually includes three different volume measurement systems: U.S. liquid, U.S. dry, and British Imperial. On both sides of the Atlantic, smaller volumes of liquid are traditionally measured in fluid ounces, which are at least roughly equal to the volume of one ounce of water. To accomplish this in the different systems, the smaller U.S. pint is divided into 16 fluid ounces, and the larger British pint is divided into 20 fluid ounces. The Bottom Line Because of their many eccentricities, English customary units clearly are more cumbersome to use than metric units in trade and in science. As metrication proceeds, they are less and less in use. On the other hand, these traditional units are rich in cultural significance. We can trace their long histories in their names and relationships. We should not forget them, and it is unlikely that we will, even when Britain and America complete their slow conversion to the metric system. The American economy of the 22nd century may be completely metric, but probably Americans will still call 30 centimeters a "foot" and 1600 meters a "mile."

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2004 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. February 23, 2001

The Metric System Designed during the French Revolution of the 1790's, the metric system brought order out of the conflicting and confusing traditional systems of weights and measures then being used in Europe. Prior to the introduction of the metric system, it was common for units of length, land area, and weight to vary, not just from one country to another but from one region to another within the same country. As the modern nations were gradually assembled from smaller kingdoms and principalities, confusion simply multiplied. Merchants, scientists, and educated people throughout Europe realized that a uniform system was needed, but it was only in the climate of a complete political upheaval that such a radical change could actually be considered. The metric system replaces all the traditional units, except the units of time and of angle measure, with units satisfying three conditions: (1) One fundamental unit is defined for each quantity. These units are now defined precisely in the International System of Units. (2) Multiples and fractions of these fundamental units are created by adding prefixes to the names of the defined units. These prefixes denote powers of ten, so that metric units are always divided into tens, hundreds, thousands, etc. The original prefixes included milli- for 1/1,000, centi- for 1/100, deci- for 1/10, deka- for 10, hecto- for 100, and kilofor 1,000. (3) The fundamental units are defined rationally and are related to each other in a rational fashion. The metric units were defined in an elegant way unlike any traditional units of measure. The Earth itself was selected as the measuring stick. The meter was defined to be one tenmillionth of the distance from the Equator to the North Pole. The liter was to be the volume of one cubic decimeter, and the kilogram was to be the weight of a liter of pure water. It didn't turn out quite like this, because the scientific methods of the time were not quite up to the task of measuring these quantities precisely, but the actual metric units come very close to the design. The metric system was first proposed in 1791. It was adopted by the French revolutionary assembly in 1795, and the first metric standards (a standard meter bar and kilogram bar) were adopted in 1799. There was considerable resistence to the system at first, and its use was not made compulsory in France until 1837. The first countries to actually require use of the metric system were Belgium, the Netherlands, and Luxembourg, in 1820. Around 1850 a strong movement began among scientists, engineers, and businessmen in favor of a international system of weights and measures. The scientific and technical revolution was well underway and a global economy was developing. The need for uniformity in measurement was becoming obvious. Furthermore, the metric system was the only real choice available. The only possible competitor, the British Imperial system,

was so closely tied to the British Empire it was not even acceptable to the Americans, let alone to non-English speakers. Between 1850 and 1900 the metric system made rapid progress. It was adopted throughout continental Europe, in Latin America, and in many countries elsewhere. It became firmly established as a key part of the language of science. In the 1870s the French made a crucial decision to turn control of the system over to an international body. In 1875, most of the leading industrialized countries (including the United States, but not Britain) signed the Treaty of the Meter. The treaty established the International Bureau of Weights and Measures, which has presided ever since over what we now call the International System of Units. It also provided for distribution of copies of the metric standards throughout the world and for continuing consultation and periodic revision and improvement of the system through regular meetings of a General Conference of Weights and Measures. The 22nd General Conference met in October 2003. Since 1875 the eventual triumph of the metric system in science and international commerce has been assured, despite continuing popular opposition in Britain and the United States. In fact, the metric system has met popular opposition in every country at the time of its adoption. People don't want to change their customary units, which are part of how they see and control the world. It is naturally disturbing to do so. This opposition has been largely overcome everywhere, except in the U.S., by economic necessity: the need to participate fully in the global economic system. Even in the U.S., economic needs assure the continued creeping adoption of the system in one area and then another. Those Americans opposing adoption of metric units often argue that the metric system is abstract and intellectual or that its use would embroil us in calculations. This is not true. The metric system has been the customary measurement system in France for almost two centuries, in the rest of continental Europe for at least one century, and in the rest of the world for a least a generation or two. Most people in the world know exactly how long a kilometer is, how large a liter is, how much a kilogram weighs, and how warm 25 °C is, because they use these units every day of their lives in the same way Americans use miles, gallons, and pounds. Outside Britain and the United States there is almost no need to convert metric units into something else. In fact, the way to avoid conversion formulas is to adopt the metric system. As long as Britons and Americans continue to use traditional units, they will have to remember how these units relate to the metric units. A note: Widespread use of the metric system has not meant the complete elimination of traditional units, nor has it stopped the continuing creation of new units, many metric but some not, to meet new needs. The purpose of this dictionary is to provide information on all commonly used units, old and new. My only interest here is in preserving and

disseminating information on units, both metric and traditional, for anyone who would like to know more about them.

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2002 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. February 5, 2002; last revised May 26, 2004.

CGS and MKS Units Scientists have adopted the metric system to simplify their calculations and promote communication across national boundaries. However, there have been two ideas as to which metric units should be preferred in science. Scientists working in laboratories, dealing with small quantities and distances, preferred to measure distance in centimeters and mass in grams. Scientists and engineers working in larger contexts preferred larger units: meters for distance and kilograms for mass. Everyone agreed that units of other quantities such as force, pressure, work, power, and so on should be related in a simple way to the basic units, but which basic units should be used? The result was two clusterings of metric units in science and engineering. One cluster, based on the centimeter, the gram, and the second, is called the CGS system. The other, based on the meter, kilogram, and second, is called the MKS system. When we say, for example, that the dyne is the CGS unit of force, this determines its definition: it is the force which accelerates a mass of one gram at the rate of one centimeter per second per second. The MKS unit of force, the newton, is the force which accelerates a mass of one kilogram at the rate of one meter per second per second. The ratio between a CGS unit and the corresponding MKS unit is usually a power of 10. A newton accelerates a mass 1000 times greater than a dyne does, and it does so at a rate 100 times greater, so there are 100 000 = 105 dynes in a newton. The CGS system was introduced formally by the British Association for the Advancement of Science in 1874. It found almost immediate favor with working scientists, and it was the system most commonly used in scientific work for many years. Meanwhile, the further development of the metric system was based on meter and kilogram standards created and distributed in 1889 by the International Bureau of

Weights and Measures (BIPM). During the 20th century, metric units based on the meter and kilogram--the MKS units--were used more and more in commercial transactions, engineering, and other practical areas. By 1950 there was some discomfort among users of metric units, because the need to translate between CGS and MKS units went against the metric ideal of a universal measuring system. In other words, a choice needed to be made. In 1954, the Tenth General Conference on Weights and Measures (CGPM) adopted the meter, kilogram, second, ampere, degree Kelvin, and candela as the basic units for all international weights and measures, and in 1960 the Eleventh General Conference adopted the name International System of Units (SI) for this collection of units. (The "degree Kelvin" became the kelvin in 1967.) In effect, these decisions gave the central core of the MKS system preference over the CGS system. Although some of the CGS units remain in use for a variety of purposes, they are being replaced gradually by the SI units selected from the MKS system. Following is a table of CGS units with their SI equivalents. Note that in some cases there is more than one name for the same unit. The CGS electromagnetic and electrostatic units are not included in this table, except for those which have special names. CGS unit

measuring

SI equivalent

barye (ba)

pressure

0.1 pascal (Pa)

biot (Bi)

electric current

10 amperes (A)

calorie (cal)

heat energy

4.1868 joule (J)

darcy

permeability

0.98692 x 10-12 square meter (m2)

debye (D)

electric dipole moment

3.33564 x 10-30 coulomb meter (C·m)

dyne (dyn)

force

10-5 newton (N)

emu

magnetic dipole moment

0.001 ampere square meter (A·m2)

erg

work, energy

10-7 joule (J)

franklin (Fr)

electric charge

3.3356 x 10-10 coulomb (C)

galileo (Gal)

acceleration

0.01 meter per second squared (m·s-2)

gauss (G)

magnetic flux density 10-4 tesla (T)

gilbert (Gi)

magnetomotive force

0.795 775 ampereturns (A)

kayser (K)

wave number

100 per meter (m-1)

lambert (Lb)

luminance

3183.099 candelas per square meter (cd·m-2)

langley

heat transmission

41.84 kilojoules per square meter (kJ·m-2)

line (li)

magnetic flux

10-8 weber (Wb)

maxwell (Mx)

magnetic flux

10-8 weber (Wb)

oersted (Oe)

magnetic field strength

79.577 472 ampereturns per meter (A·m-1)

phot (ph)

illumination

104 lux (lx)

poise (P)

dynamic viscosity

0.1 pascal second (Pa·s)

stilb (sb)

luminance

104 candelas per square meter (cd·m-2)

stokes (St)

kinematic viscosity

10-4 square meters per second (m2·s-1)

unit pole

magnetic flux

1.256 637 x 10-7 weber (Wb)

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2000 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. October 26, 2003

Spelling of Metric Units Controversies arise sometimes over the spelling of metric units. In many cases, these controversies grow out of a misunderstanding as to just what is international in the International System of Units (SI). The fact is that the spellings of SI units vary from one language to another. In the case of the U.S. and Britain, spellings differ even within a language: Americans write meter and liter while the British write metre and litre.

The variation in spelling, however, goes much farther than that. Even if we disregard accent markings, the fundamental SI unit of length has numerous spellings, including: • • • • • •

meter (American English, Danish, Dutch, German, Hungarian, Norwegian, Slovak, and Swedish) metr (Czech, Polish, Russian, Ukrainian) metras (Lithuanian) metre (British, Australian, Canadian and New Zealand English; French) metri (Finnish) metro (Basque, Italian, Portuguese, Spanish)

No doubt this list could be extended quite a bit. The point is, there is no "official" spelling of the SI units. What the SI does provide includes the names, the definitions, and the symbols of the units. The words meter, metr, metre, etc. represent the same name spelled in different languages. Within the International System, Russians are welcome to call 1000 meters a kilometr, but they cannot call it a verst, because that would be a different name. The Italians call the same unit the chilometro, but they cannot make its symbol chm; they must use km.

June 4, 1999

The Metric System in the United States Article I, Section 8 of the U. S. Constitution gives Congress the power to "fix the standard of weights and measures" for the nation. The First Congress, meeting in 1789, took up the question of weights and measures, and had the metric system been available at that time it might have been adopted. What actually happened is that Thomas Jefferson, who was then serving as the first Secretary of State, submitted a report proposing a decimal-based system with a mixture of familiar and unfamiliar names for the units. Jefferson's system actually resembles the metric system in many ways. Its biggest shortcoming is that Jefferson didn't hit on the idea of using prefixes to create names for multiples of units. Consequently, his system was burdened with a long list of names. For example, he divided his basic distance unit, the foot (it was slightly shorter than the traditional foot) into 10 inches. Each inch was divided into 10 lines, and each line into 10 points. For larger distances, 10 feet equalled a decade, 100 feet was a rood, 1000 feet a furlong, and there were 10 000 feet in a mile (making the Jeffersonian mile about twice as long as the traditional mile). His basic volume unit was the cubic foot, which he proposed to call a bushel (it was about 3/4 the size of a traditional bushel). The basic weight unit was the ounce, defined so that a bushel of water weighed 1000 ounces. (This is very similar to the metric system, in which a liter of water weighs 1000 grams).

Congress gave this plan serious consideration, but because it lacked independent support from other scientists it was easy to criticize. Ultimately, Congress took no action. This left Americans with a version of the traditional English weights and measures, including: • • • •

distance measurements identical to those of the 1592 Act of Parliament, the traditional avoirdupois system of weight measurements, a system of measurement for dry volumes based on the "Winchester" bushel used in England for wheat and corn since the late Middle Ages, and a system of measurement for liquid volumes based on the English wine gallon of 1707.

It is remarkable that Congress never established this traditional system, or any other system, as the mandatory system of weights and measures for the United States. In 1832, Congress directed the Treasury Department to standardize the measures used by customs officials at U.S. ports. The Department adopted a report describing the traditional system, and Congress allowed this report to stand without taking any formal action. This is the closest the U.S. has ever come to adopting a single system of measurement. Ironically, the U.S. missed two opportunities in 1832. Americans could have adopted the metric system, which was then at an uncertain point in its history; or they could have decided to align their measurements with the British Imperial measures established by Parliament in 1824 and thus created a possible alternative to the metric system in international commerce. The metric system originated in France in the 1790's, a few years after Jefferson's proposals. During the mid-nineteenth century, as expanding trade demanded a consistent set of measurements, use of the metric system spread through continental Europe. As they imported goods from Europe or exported goods to Europe, Americans became increasingly aware of the metric system. In 1866, Congress legalized its use in an act reading: It shall be lawful throughout the United States of America to employ the weights and measures of the metric system; and no contract or dealing, or pleading in any court, shall be deemed invalid or liable to objection because the weights or measures expressed or referred to therein are weights or measures of the metric system. As a result, the U. S. has been "metric" since 1866, but only in the sense that Americans have been free since that time to use the metric system as much as they like. Although there has always been popular resistance to changing the traditional measures, the metric system has actually enjoyed strong support from American business leaders and scientists since the late nineteenth century. In 1875, the U.S. was one of the original signers of the Treaty of the Meter, which established the International Bureau of Weights and Measures (BIPM). This agency administers the International System of Units, the official version of the metric system. American scientists and engineers have always been among the leaders in improving, extending, and revising the metric system. The general public, however, has lagged far behind.

In 1893, Thomas C. Mendenhall, then Superintendent of Weights and Measures in the Treasury Department, concluded that the metric standards, the official meter and kilogram bars supplied by BIPM, should become the standards for all measurement in the U.S. With the approval of the Secretary of the Treasury, this decision was made and published; it has since been called the Mendenhall Order. The order didn't mean that metric units had to be used, but since that time the customary units have been defined officially in terms of metric standards. Currently, the foot is legally defined to be exactly 0.3048 meter and the pound is legally defined to equal exactly 453.59237 grams. In 1901, Congress established the National Bureau of Standards (NBS), now known as the National Institute of Standards and Technology (NIST), to support technical standards for American industry and commerce, including the maintenance of standards of weight and measurement. In 1964, NBS announced: Henceforth it shall be the policy of the National Bureau of Standards to use the units of the International System (SI), as adopted by the 11th General Conference of Weights and Measures, except when the use of these units would obviously impair communication or reduce the usefulness of a report. In the 1970's there was a major effort to increase the use of the metric system, and Congress passed the Metric Conversion Act of 1975 to speed this process along. However, American consumers generally rejected the use of metric units for highway distances, weather reports, and other common measurements, so little was accomplished except for the encouragement of faster metric conversion in various scientific and technical fields. In 1988, Congress passed the Omnibus Trade and Competitiveness Act, which designates "the metric system of measurement as the preferred system of weights and measures for United States trade and commerce." Among many other things, the act requires federal agencies to use metric measurements in nearly all of their activities, although there are still exceptions allowing traditional units to be used in documents intended for consumers. The real purpose of the act was to improve the competitiveness of American industry in international markets by encouraging industries to design, produce, and sell products in metric units. The debate over metric conversion continues. Although metric units have become more familiar and more widely used, the United States remains a "soft metric" country. (The phrase "soft metric" refers to designations like "1 pint (473 mL)" in which metric equivalents are simply tagged onto traditional measurements.) Proponents of the metric system in the U.S. often claim that "the United States, Liberia, and Burma (or Myanmar) are the only countries that have not adopted the metric system." This statement is not correct with respect to the U.S., and probably it isn't correct with respect to Liberia and Burma, either. The U.S. adopted the metric system in 1866. What the U.S. has failed to do is to restrict or prohibit the use of traditional units in areas touching the ordinary citizen: construction, real estate transactions, retail trade, and

education. The U.S. has not made the crucial transition from "soft metric" to "hard metric", so that "1 pint (473 mL)" becomes "500 mL (1.057 pint)", with the traditional equivalent fading into smaller type sizes and finally disappearing.

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2000 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. August 8, 2000

Country Codes The International Organization for Standardization (ISO) under its standard ISO 3166 has established two-letter (2-alpha) and three-letter (3-alpha) codes for the various countries of the world, including independent states, dependent areas, and certain areas of contested jurisdiction or special status. These codes are published and revised when needed by the ISO 3166 Maintenance Agency. The Internet Assigned Numbers Authority (IANA) assigns two-letter codes for countrycoded top-level domains in Internet addresses. These codes are the same as the ISO 2alpha codes in nearly all cases. The International Olympic Committee also assigns three-letter codes to its national organizing committees and the teams they send to the Olympic Games. These codes coincide with the ISO codes for many countries, but differ for many others. Worse: a few of the IOC codes conflict directly with ISO codes. For example, ANT is assigned by the ISO to Netherlands Antilles and by the IOC to Antigua and Barbuda. The United Nations maintains a list of Distinguishing Signs of Vehicles in International Traffic; these codes appear in oval-shaped signs displayed on the rear of vehicles. These codes were authorized by the UN's 1949 and 1968 Conventions on Road Traffic. (In the U.S., the use of the oval design is not controlled and vehicles often display similar ovals with a wide variety of non-standard codes.) Many of the vehicle codes created since the adoption of ISO 3166 coincide with either the ISO 2-alpha or 3-alpha codes, but many of the codes, especially the older European ones, do not. In Europe, the vehicle codes are often used in postal addressing, preceding the delivery code. (Complete postal addressing information is available from the Universal Postal Union.)

Three-digit numerical codes for countries are also specified by ISO 3166; these codes are actually provided by the United Nations Statistical Division. The International Telecommunications Union assigns 1-, 2-, or 3-digit country calling codes for international telephone calls. The calling code "1" is assigned to the entire North American Numbering Plan Area, which includes the U.S. and its possessions, Canada, Bermuda, the British Commonwealth nations of the Caribbean, and the Dominican Republic. Within this region the "1" is followed by a NANPA 3-digit area code. Also, code "7" is assigned to a large calling area including the Russian Federation and Kazakhstan. All other countries and territories have their own 2-digit or 3-digit code. In the following table, Internet codes are from IANA's Root-Zone Whois Index. ISO 2alpha codes are from the ISO 3166 Maintenance Agency, English country names and code elements. ISO 3-alpha codes are not posted to the Internet by ISO; the codes shown are from the United Nations, Country and Region Codes for Statistical Use, which also provided the numerical codes. Some additional 3-alpha and numerical codes are taken from the CIA Factbook Appendix D (Country Data Codes). IOC codes are from the IOC's National Olympic Committees pages. Vehicle codes are from the Transport Division of the UN Economic Commission for Europe; I have omitted several vehicle codes which appear to be obsolete because they refer to previous names of the territory rather than the present name.

Country Name AFGHANISTAN ÅLAND ISLANDS ALBANIA ALDERNEY ALGERIA (El Djazaïr) AMERICAN SAMOA ANDORRA ANGOLA ANGUILLA ANTARCTICA ANTIGUA AND BARBUDA ARGENTINA ARMENIA ARUBA ASCENSION ISLAND AUSTRALIA AUSTRIA AZERBAIJAN Country Name

ISO ISO IANA UN 2-alpha 3-alpha Internet Vehicle AF AFG .af AFG AX ALA .ax AL ALB .al AL GBA DZ DZA .dz DZ AS ASM .as AD AND .ad AND AO AGO .ao AI AIA .ai AQ ATA .aq AG ATG .ag AR ARG .ar RA AM ARM .am AM AW ABW .aw .ac AU AUS .au AUS AT AUT .at A AZ AZE .az AZ ISO ISO IANA UN 2-alpha 3-alpha Internet Vehicle

IOC UN/ISO ITU Olympic numeric calling AFG 004 93 248 ALB 008 355 ALG ASA AND ANG

ANT ARG ARM ARU

012 016 020 024 660 010 028 032 051 533

213 1-684 376 244 1-264

1-268 54 7 297 247 AUS 036 61 AUT 040 43 AZE 031 994 IOC UN/ISO ITU Olympic numeric calling

BAHAMAS BAHRAIN BANGLADESH BARBADOS BELARUS BELGIUM BELIZE BENIN BERMUDA BHUTAN BOLIVIA BOSNIA AND HERZEGOVINA BOTSWANA BOUVET ISLAND BRAZIL Country Name BRITISH INDIAN OCEAN TERRITORY BRUNEI DARUSSALAM BULGARIA BURKINA FASO BURUNDI CAMBODIA CAMEROON

BS BH BD BB BY BE BZ BJ BM BT BO BA BW BV BR ISO 2-alpha IO BN BG BF BI KH CM

BHS BHR BGD BRB BLR BEL BLZ BEN BMU BTN BOL BIH BWA BVT BRA ISO 3-alpha IOT BRN BGR BFA BDI KHM CMR

.bs .bh .bd .bb .by .be .bz .bj .bm .bt .bo .ba .bw .bv .br IANA Internet .io .bn .bg .bf .bi .kh .cm

BS BRN BD BDS BY B BH DY

BAH BRN BAN BAR BLR BEL BIZ BEN BER BHU BOL BIH BOT

044 048 050 052 112 056 084 204 060 064 BOL 068 BIH 070 BW 072 074 BR BRA 076 UN IOC UN/ISO Vehicle Olympic numeric 086 BRU BRU 096 BG BUL 100 BF BUR 854 RU BDI 108 K CAM 116 CAM CMR 120

1-242 973 880 1-246 375 32 501 229 1-441 975 591 387 267 55 ITU calling 673 359 226 257 855 237

CANADA CAPE VERDE CAYMAN ISLANDS CENTRAL AFRICAN REPUBLIC CHAD (Tchad) CHANNEL ISLANDS CHILE CHINA Country Name CHRISTMAS ISLAND COCOS (KEELING) ISLANDS COLOMBIA COMOROS CONGO, REPUBLIC OF CONGO, THE DEMOCRATIC REPUBLIC OF THE (formerly Zaire) COOK ISLANDS COSTA RICA CÔTE D'IVOIRE (Ivory Coast) CROATIA (Hrvatska) CUBA CYPRUS CZECH REPUBLIC

CA CV KY CF TD

CAN CPV CYM CAF TCD

.ca .cv .ky .cf .td

CDN

CAN CPV CAY CAF CHA

124 132 136 RCA 140 TCH 148 830 CL CHL .cl RCH CHI 152 CN CHN .cn CHN 156 ISO ISO IANA UN IOC UN/ISO 2-alpha 3-alpha Internet Vehicle Olympic numeric CX CXR .cx 162 CC CCK .cc 166 CO COL .co CO COL 170 KM COM .km COM 174

1 238 1-345 236 235

CG

COG

.cg

RCB

CGO

178

242

CD

COD

.cd

ZRE

COD

180

243

CK CR CI HR CU CY CZ

COK CRI CIV HRV CUB CYP CZE

.ck .cr .ci .hr .cu .cy .cz

CR CI HR CU CY CZ

COK CRI CIV CRO CUB CYP CZE

184 188 384 191 192 196 203

682 506 225 385 53 357 420

56 86 ITU calling

57 269

DENMARK DJIBOUTI Country Name DOMINICA DOMINICAN REPUBLIC ECUADOR EGYPT EL SALVADOR EQUATORIAL GUINEA ERITREA ESTONIA ETHIOPIA EUROPEAN UNION FAEROE ISLANDS FALKLAND ISLANDS (MALVINAS) FIJI FINLAND FRANCE Country Name FRENCH GUIANA FRENCH POLYNESIA FRENCH SOUTHERN TERRITORIES

DK DJ ISO 2-alpha DM DO EC EG SV GQ ER EE ET

DNK DJI ISO 3-alpha DMA DOM ECU EGY SLV GNQ ERI EST ETH

.dk .dj IANA Internet .dm .do .ec .eg .sv .gq .er .ee .et .eu FO FRO .fo FK FLK .fk FJ FJI .fj FI FIN .fi FR FRA .fr ISO ISO IANA 2-alpha 3-alpha Internet GF GUF .gf PF PYF .pf TF ATF .tf

DK

DEN DJI UN IOC Vehicle Olympic WD DMA DOM DOM EC ECU ET EGY ES ESA GEQ ERI EST EST ETH ETH

208 262 UN/ISO numeric 212 214 218 818 222 226 232 233 231

45 253 ITU calling 1-767 1-809 593 20 503 240 291 372 251

234 238 FJI FIJ 242 FIN FIN 246 F FRA 250 UN IOC UN/ISO Vehicle Olympic numeric 254 258 260

298 500 679 358 33 ITU calling 594 689

FR

GABON GAMBIA, THE GEORGIA GERMANY (Deutschland) GHANA GIBRALTAR GREAT BRITAIN GREECE GREENLAND GRENADA GUADELOUPE GUAM GUATEMALA Country Name

GA GM GE DE GH GI GB GR GL GD GP GU GT ISO 2-alpha GG GN GW GY HT

GUERNSEY GUINEA GUINEA-BISSAU GUYANA HAITI HEARD ISLAND AND MCDONALD HM ISLANDS HONDURAS HN HONG KONG (Special Administrative Region HK

GAB GMB GEO DEU GHA GIB GBR GRC GRL GRD GLP GUM GTM ISO 3-alpha GGY GIN GNB GUY HTI

.ga .gm .ge .de .gh .gi .uk .gr .gl .gd .gp .gu .gt IANA Internet .gg .gn .gw .gy .ht

HMD

.hm

HND HKG

.hn .hk

G WAG GE D GH GBZ GB GR

GAB GAM GEO GER GHA

266 270 268 276 288 292 GBR 826 GRE 300 304 WG GRN 308 312 GUM 316 GCA GUA 320 UN IOC UN/ISO Vehicle Olympic numeric GBG RG GUI 324 GBS 624 GUY GUY 328 RH HAI 332

241 220 49 233 350 44 30 299 1-473 590 1-671 502 ITU calling 224 245 592 509

334 HON HKG

340 344

504 852

of China) HUNGARY

HU

ICELAND INDIA INDONESIA IRAN (Islamic Republic of Iran) IRAQ IRELAND

IS IN ID IR IQ IE

Country Name ISLE OF MAN ISRAEL ITALY JAMAICA JAPAN JERSEY JORDAN (Hashemite Kingdom of Jordan) KAZAKHSTAN KENYA KIRIBATI KOREA (Democratic Peoples Republic of [North] Korea) KOREA (Republic of [South] Korea) KUWAIT

HUN

.hu

H

HUN

348

36

ISL IND IDN IRN IRQ IRL ISO ISO 2-alpha 3-alpha IM IMN IL ISR IT ITA JM JAM JP JPN JE JEY JO JOR KZ KAZ KE KEN KI KIR

.is .in .id .ir .iq .ie IANA Internet .im .il .it .jm .jp .je .jo .kz .ke .ki

IS IND RI IR IRQ IRL UN Vehicle GBM IL I JA J GBJ HKJ KZ EAK

ISL IND INA IRI IRQ IRL IOC Olympic

354 91 62 98 964 353 ITU calling

ISR ITA JAM JPN

352 356 360 364 368 372 UN/ISO numeric 833 376 380 388 392

JOR KAZ KEN KIR

400 398 404 296

962 7 254 686

KP

PRK

.kp

PRK

408

850

KR KW

KOR KWT

.kr .kw

KOR KUW

410 414

82 965

ROK KWT

972 39 1-876 81

KYRGYZSTAN KG LAO PEOPLE'S DEMOCRATIC REPUBLIC LA LATVIA LV ISO Country Name 2-alpha LEBANON LB LESOTHO LS LIBERIA LR LIBYA (Libyan Arab Jamahirya) LY LIECHTENSTEIN (Fürstentum Liechtenstein) LI LITHUANIA LT LUXEMBOURG LU MACAO (Special Administrative Region of MO China) MACEDONIA (Former Yugoslav Republic of MK Macedonia) MADAGASCAR MG MALAWI MW MALAYSIA MY MALDIVES MV MALI ML MALTA MT ISO Country Name 2-alpha

KGZ LAO LVA ISO 3-alpha LBN LSO LBR LBY LIE LTU LUX

.kg .la .lv IANA Internet .lb .ls .lr .ly .li .lt .lu

KS LAO LV UN Vehicle RL LS LB LAR FL LT L

MAC

.mo

MKD

.mk

MK

MDG MWI MYS MDV MLI MLT ISO 3-alpha

.mg .mw .my .mv .ml .mt IANA Internet

RM MW MAL

KGZ LAO LAT IOC Olympic LIB LES LBR LBA LIE LTU LUX

MKD

MAD MAW MAS MDV RMM MLI M MLT UN IOC Vehicle Olympic

417 418 428 UN/ISO numeric 422 426 430 434 438 440 442

996 856 371 ITU calling 961 266 231 218 423 370 352

446

853

807

389

450 454 458 462 466 470 UN/ISO numeric

261 265 60 960 223 356 ITU calling

MARSHALL ISLANDS MARTINIQUE MAURITANIA MAURITIUS MAYOTTE MEXICO MICRONESIA (Federated States of Micronesia) MOLDOVA MONACO MONGOLIA MONTENEGRO MONTSERRAT MOROCCO MOZAMBIQUE (Moçambique) MYANMAR (formerly Burma)

MH MQ MR MU YT MX

MHL MTQ MRT MUS MYT MEX

.mh .mq .mr .mu .yt .mx

FM

FSM

.fm

MD MC MN ME MS MA MZ MM

MDA MCO MNG MNE MSR MAR MOZ MMR

.md .mc .mn .me .ms .ma .mz .mm

NAMIBIA

NA ISO 2-alpha NR NP NL AN NC

NAM ISO 3-alpha NRU NPL NLD ANT NCL

.na IANA Internet .nr .np .nl .an .nc

Country Name NAURU NEPAL NETHERLANDS NETHERLANDS ANTILLES NEW CALEDONIA

MHL RIM MS

MTN MRI

MEX

MEX

584 474 478 480 175 484

692 596 222 230 269 52

FSM

583

691

MD MC MGL MNE

MDA MON MGL MNE

MA MOC BUR

MAR MOZ MYA

498 492 496 499 500 504 508 104

373 377 976 382 1-664 212 258 95

NAM UN Vehicle NAU NEP NL NA

NAM IOC Olympic NRU NEP NED AHO

516 UN/ISO numeric 520 524 528 530 540

264 ITU calling 674 977 31 599 687

NEW ZEALAND NICARAGUA NIGER NIGERIA NIUE NORFOLK ISLAND NORTHERN MARIANA ISLANDS NORWAY OMAN PAKISTAN Country Name PALAU PALESTINIAN TERRITORIES PANAMA PAPUA NEW GUINEA PARAGUAY PERU PHILIPPINES PITCAIRN POLAND PORTUGAL PUERTO RICO QATAR

NZ NI NE NG NU NF MP NO OM PK ISO 2-alpha PW PS PA PG PY PE PH PN PL PT PR QA

NZL NIC NER NGA NIU NFK MNP NOR OMN PAK ISO 3-alpha PLW PSE PAN PNG PRY PER PHL PCN POL PRT PRI QAT

.nz .ni .ne .ng .nu .nf .mp .no .om .pk IANA Internet .pw .ps .pa .pg .py .pe .ph .pn .pl .pt .pr .qa

NZ NIC RN WAN

NZL NCA NIG NGR

554 558 562 566 570 574 580 N NOR 578 OMA 512 PK PAK 586 UN IOC UN/ISO Vehicle Olympic numeric PLW 585 PLE 275 PA PAN 591 PNG PNG 598 PY PAR 600 PE PER 604 RP PHI 608 612 PL POL 616 P POR 620 PUR 630 Q QAT 634

64 505 227 234 683 1-670 47 968 92 ITU calling 680 970 507 675 595 51 63 48 351 1 974

RÉUNION ROMANIA RUSSIAN FEDERATION

RE RO RU ISO Country Name 2-alpha RWANDA RW SAINT BARTHÉLEMY BL SAINT HELENA SH SAINT KITTS AND NEVIS KN SAINT LUCIA LC SAINT MARTIN (French portion) MF SAINT PIERRE AND MIQUELON PM SAINT VINCENT AND THE GRENADINES VC SAMOA (formerly Western Samoa) WS SAN MARINO (Republic of) SM SAO TOME AND PRINCIPE ST SAUDI ARABIA (Kingdom of Saudi Arabia) SA SENEGAL SN SERBIA (Republic of Serbia) RS SEYCHELLES SC SIERRA LEONE SL SINGAPORE SG ISO Country Name 2-alpha

REU ROU RUS ISO 3-alpha RWA BLM SHN KNA LCA MAF SPM VCT WSM SMR STP SAU SEN SRB SYC SLE SGP ISO 3-alpha

.re .ro .ru IANA Internet .rw .bl .sh .kn .lc .mf .pm .vc .ws .sm .st .sa .sn .rs .sc .sl .sg IANA Internet

638 RO ROM 642 RUS RUS 643 UN IOC UN/ISO Vehicle Olympic numeric RWA RWA 646 652 654 SKN 659 WL LCA 662 663 666 WV VIN 670 WS SAM 882 RSM SMR 674 STP 678 SA KSA 682 SN SEN 686 SRB 688 SY SEY 690 WAL SLE 694 SGP SIN 702 UN IOC UN/ISO Vehicle Olympic numeric

262 40 7 ITU calling 250 290 1-869 1-758 508 1-784 685 378 239 966 221 381 248 232 65 ITU calling

SLOVAKIA (Slovak Republic) SLOVENIA SOLOMON ISLANDS SOMALIA SOUTH AFRICA (Zuid Afrika) SOUTH GEORGIA AND THE SOUTH SANDWICH ISLANDS SOVIET UNION (Internet code still used) SPAIN (España) SRI LANKA (formerly Ceylon) SUDAN SURINAME SVALBARD AND JAN MAYEN SWAZILAND SWEDEN SWITZERLAND (Confederation of Helvetia) SYRIAN ARAB REPUBLIC Country Name TAIWAN ("Chinese Taipei" for IOC) TAJIKISTAN TANGANYIKA TANZANIA THAILAND

SK SI SB SO ZA

SVK SVN SLB SOM ZAF

.sk .si .sb .so .za

GS

SGS

.gs

.su ES ESP .es LK LKA .lk SD SDN .sd SR SUR .sr SJ SJM .sj SZ SWZ .sz SE SWE .se CH CHE .ch SY SYR .sy ISO ISO IANA 2-alpha 3-alpha Internet TW TWN .tw TJ TJK .tj TZ TH

TZA THA

.tz .th

SK SLO SO ZA

SVK SLO SOL SOM RSA

703 705 90 706 710

421 386 677 252 27

239 E CL SUD SME

ESP SRI SUD SUR

724 144 736 740 744 SD SWZ 748 S SWE 752 CH SUI 756 SYR SYR 760 UN IOC UN/ISO Vehicle Olympic numeric TPE 158 TJ TJK 762 EAT TAN 834 T THA 764

34 94 249 597 268 46 41 963 ITU calling 886 992 255 66

TIMOR-LESTE (formerly East Timor) TOGO TOKELAU TONGA TRINIDAD AND TOBAGO TUNISIA TURKEY TURKMENISTAN TURKS AND CAICOS ISLANDS TUVALU UGANDA UKRAINE Country Name UNITED ARAB EMIRATES UNITED KINGDOM (Great Britain) UNITED STATES UNITED STATES MINOR OUTLYING ISLANDS URUGUAY UZBEKISTAN VANUATU VATICAN CITY (Holy See) VENEZUELA

TL TG TK TO TT TN TR TM TC TV UG UA ISO 2-alpha AE GB US

TLS TGO TKL TON TTO TUN TUR TKM TCA TUV UGA UKR ISO 3-alpha ARE GBR USA

.tp .tg .tk .to .tt .tn .tr .tm .tc .tv .ug .ua IANA Internet .ae .uk .us

UM

UMI

.um

UY UZ VU VA VE

URY UZB VUT VAT VEN

.uy .uz .vu .va .ve

TLS TOG

626 TG 768 772 TGA 776 TT TRI 780 TN TUN 788 TR TUR 792 TM TKM 795 796 798 EAU UGA 800 UA UKR 804 UN IOC UN/ISO Vehicle Olympic numeric UAE 784 GBR 826 USA USA 840

670 228 690 676 1-868 216 90 993 1-649 688 256 380 ITU calling 971 44 1

581 ROU UZ V YV

URU UZB VAN VAT VEN

858 860 548 336 862

598 998 678 379 58

VIET NAM VIRGIN ISLANDS, BRITISH VIRGIN ISLANDS, U.S. YUGOSLAVIA (Internet code still used) WALLIS AND FUTUNA WESTERN SAHARA (formerly Spanish Sahara) YEMEN (Yemen Arab Republic) Country Name ZAMBIA (formerly Northern Rhodesia) ZANZIBAR ZIMBABWE

VN VG VI

VNM VGB VIR

WF

WLF

.vn .vg .vi .yu .wf

EH

ESH

.eh

YE

VN BVI

VIE IVB ISV

YEM .ye YAR YEM ISO ISO IANA UN IOC 2-alpha 3-alpha Internet Vehicle Olympic ZM ZMB .zm RNR ZAM EAZ ZW ZWE .zw ZW ZIM

704 92 850

84 1-284 1-340

876

681

732 887 967 UN/ISO ITU numeric calling 894 260 716

263

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2006 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. February 19, 2004; updated June 20, 2006

Links to Related Sites Basic Sources U. S. Metric Association. The Association, founded in 1916, promotes use and understanding of the SI and the metric system in the United States. It publishes a variety of useful guides and educational aids, some of which are available online. Its Chronology of the SI Metric System is a brief outline of metric history, and its Correct SI Metric Usage is a guide to proper style in using metric units in papers and publications. NIST Metric Program. NIST is the National Institute of Standards and Technology, formerly known as the National Bureau of Standards, an agency of the U.S. Department of Commerce. NIST is concerned very broadly with establishing and maintaining technical and scientific standards for industry and research. The Metric Program is responsible for encouraging broad use of the metric system and for coordinating the plans of federal agencies to convert their measurements to metric units. Its brochure, The United States and the Metric System, provides history and background for the metrication effort. It has published a Metric Style Guide for the News Media with details on how to use metric units correctly in text. NIST Fundamental Physical Constants. From time to time the values of fundamental constants (mass of the electron, Planck's constant, etc.) are revised to reflect recent experimental measurements. Since the various constants are interrelated, it is necessary to revise all of them at once. The last general revision was in 2002; the new values differ slightly from those found in many standard textbooks and other references. Fundamental physical constants appear in this dictionary only if they are used as units of measurement. NIST Physics Laboratory Publications. At this web site you can read or download (in Adobe Acrobat format) two important official publications: •

The International System of Units (SI). (1991) This is the official English-language description of the International System.

•

Guide to the Use of the International System of Units (SI). (1995) Rules and conventions for using SI units in the United States.

Bureau International des Poids et Mésures. Home page for the international organization that maintains the SI. The same information is provided in French and in English. Here you can read or download the official specifications of the International System of Units in a document known informally as the SI Brochure. The Modern Metric System (metre.info). A concise and useful summary of the metric system by Chris Kaese. UK Metrication Association. The association promotes metrication in Britain; its site includes a useful history of the metrication effort. British Weights and Measures Association. The association opposes compulsory metrication and promotes continued use of the traditional British units.

Other Sites with Units Data A Dictionary of Units. A fine page, posted by Frank Tapson of the University of Exeter in Britain, somewhat similar in spirit and content to this site. It includes a long list of very carefully computed and precise factors for converting traditional units into SI units. ASCE Committee on Metrication. The American Society of Civil Engineers has a very complete site on metric conversion. It includes background and discussion of the issues involved. There's also a huge table of conversion factors suitable for converting almost anything into metric units. Metric prefixes. This page, by Bob Bruner of the University of California, has some excellent "sense of scale" examples. Did you know that a zettameter is approximately the radius of the Milky Way galaxy? Or that the age of the Universe is about half an exasecond? Metric Units Galore. A huge compendium, by Olle Järnefors, of metric units current and obsolete, with their symbols. A valuable reference.

Unit Converter Sites Conversion Factors. From Process Associates of America, a chemical engineering organization. Very useful modules provide conversion factors for a broad range of engineering units, with a high degree of precision. Conversion of Units. This site, posted by the Chemistry Department of the Free University of Berlin (Germany), provides fast and accurate conversion between dozens of units of all kinds.

Online Metric Converter from Science Made Simple. Handy, easy to use conversions for most of the common units. A nice feature is that you can work with only the common units, or you can expand the menus to include less-familar units as well. Convertit.com is a web-based conversion site which will perform almost any imaginable unit conversion. It is a service of Entisoft Units, a shareware program for units conversion. Site includes a huge listing of units with standard equivalents. MegaConverter. A fancy commercial site, featuring a collection of conversion modules which instantly convert between units of measurement. Seriously cool, but it doesn't cover all the categories of units (yet, anyway). Metric Typographic Units. A thorough discussion of traditional and metric units in typesetting and page layout, by Markus Kuhn.

Historic Units 15 USC Chapter 6. Posted by the Cornell University Law School, this is the law concerning weights and measures in the United States. Surveying Units and Terms. Posted by Direct Line Software, which serves surveyors and geneologists struggling with old U.S. deeds and land grants, this page includes traditional units of land measurement in British, French, and Spanish North America. Measures from Antiquity and the Bible. An interesting site posted by Jack Proot on America Online. Discusses length measurement in Egypt, Mesopotamia, Persia, Greece, and Rome. Only a handful of these units are included in this work. (Proot also has a page on Anglo-Saxon Weights and Measures, nearly all of which are also listed in this dictionary.) Old Units of Length. A good, concise discussion by J.B. Calvert of the University of Denver. Includes information on Greek and Roman measurements. Greek and Roman Weights, Measures, and Currency. This useful site is posted by Prof. John Porter of the University of Saskatchewan. Old Swedish Units. Olle Järnefors provides this description of Swedish units and how they have changed over time. Before adopting the metric system, Swedes used a decimalized version of their customary units from 1855 to 1889. Foundation metrology. Interesting research on ancient Egyptian units and their relationship to other ancient measurement systems.

Light Units The Unit of Luminous Intensity: the Candela. A nice discussion of the various light units, including the lumen and lux as well as the candela, posted by Electro Optical Industries, Inc.

Time and Calendar Units Time Zone Converter. This commercial site provides the correct local time right now in every country and most major cities of the world. Today's Calendar and Clock Page. THE site for information on all the world's calendars and how to convert between them. An invaluable resource, from Will Linden. International Standard Date and Time Notation. A thorough discussion of the ISO 8601 standard and other notations in use, from Markus Kuhn.

Animal Group Names Animal Collectives. You know, a pod of whales, a gaggle of geese, etc. These are not units of measurement (because they don't refer to a specific number), but people ask about them. This British source has the largest collection of these names I have seen.

Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2004 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. Checked October 26, 2004

Bibliography The information in the dictionary comes from many sources, but the following reference works have been particularly valuable. I recommend them to anyone interested in further research on units. They should all be available in large university libraries. R.D. Connor, The Weights and Measures of England. London: H. M. Stationery Office, 1987

A comprehensive and highly readable account of the history of weights and measures in England. Soundly disposes of some old misconceptions, based on careful examination of both documentary and archaeological evidence. Mike Darton and John O.E. Clark, The Dent Dictionary of Measurement. London: J.M. Dent, 1994. This work covers all kinds of measurement terminology, not just units. H.G. Jerrard and D.B McNeill, A Dictionary of Scientific Units. 6th edition. London: Chapman and Hall, 1992. Covers both metric and non-metric scientfic units, including many obsolete units not included in this dictionary. Ronald Edward Zupko, A Dictionary of Weights and Measures for the British Isles: The Middle Ages to the Twentieth Century. Philadelphia, American Philosophical Society (Memoir #168), 1985. This detailed and comprehensive work provides both the official definitions and a listing of all known local variations. It covers Irish, Welsh, and Scottish units as well as English. It is essential for all historical research in which knowing the size of the units is important. If you can't find it, look for Zupko's earlier work, A Dictionary of English Weights and Measures from Anglo-Saxon Times to the Nineteenth Century (Madison: University of Wisconsin, 1968), which contains much of the same information for the English units. Zupko has also published dictionaries of traditional French and Italian units. Return to the Dictionary Contents page. You are welcome to email the author ([email protected]) with comments and suggestions. All material in this folder is copyright © 2001 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time. February 20, 2001

Index of Tables and Scales • • • • •

• • •

•

Apgar scoring (newborns) Beaufort scales (wind velocity) Bushel weights (U.S.) Cotton bale weights Danjon scale (lunar eclipse brightness) Drought severity (U.S.) Fujita scale (tornados, U.S.) Glasgow coma scale

• • • • • • • •

•

Grit sizes •

Hat sizes Mercalli scale (earthquakes) Nutritional daily values (U.S.) Paper sheet sizes (ISO) Paper sheet sizes (traditional) Paper sheet sizes (U.S. basic sizes) Radiocarbon year conversion Saffir-Simpson scale (hurricanes, U.S.) Sheet metal gauges

• •

Shot pellet sizes

•

• • • •

• • •

Shotgun gauges SI units for medical data Solar flare intensity Tennis racquet gauges Torino impact hazard scale Tropical cyclone categories (Australia) Viscosity grades (ISO) Volcanic Explosivity Index Wind chill chart (U.S.) Wire gauge table (U.S./U.K.)

TABLES Apgar Scoring Sign

0 points

1 point

2 points

A

Activity (Muscle tone)

limp

limbs flexed

active movement

P

Pulse (heart rate)

absent

< 100 /min

> 100 /min

absent

grimace

cough or sneeze (nose) cry and withdrawal of

G

Grimace (response to smell or foot slap)

foot (foot slap) A

Appearance (color)

blue

body pink extremities blue

pink all over

R

Respiration (breathing)

absent

irregular weak crying

good strong cry

The total Apgar score is the sum of the scores for the five signs.

Beaufort Scales (Wind Speed) Force

Speed knots km/h mi/h

Name

Conditions at Sea

Conditions on Land

0