# International System of Units

International System of Units

The International System of Units[1] (abbreviated SI from French: Système international d'unités[2]) is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units. The SI was established in 1960, based on the metre-kilogram-second system, rather than the centimetre-gram-second system, which, in turn, had a few variants. The SI is declared as an evolving system, thus prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses, and as the precision of measurements improves.

It is the world's most widely used system of measurement, which is used both in everyday commerce and in science.[3][4][5] The system has been nearly globally adopted with the United States being the only industrialized nation that does not mainly use the metric system in its commercial and standards activities.[6] The United Kingdom has officially partially adopted metrication, with no intention of replacing customary measures entirely. Canada has adopted it for all legal purposes but imperial/US units are still in use, particularly in the buildings trade.[7]

## History

The metric system was conceived by a group of scientists (among them, Antoine-Laurent Lavoisier, who is known as the "father of modern chemistry") who had been commissioned by the Assemblée nationale and Louis XVI of France to create a unified and rational system of measures.[8] On 1 August 1793, the National Convention adopted the new decimal metre with a provisional length as well as the other decimal units with preliminary definitions and terms. On 7 April 1795 (Loi du 18 germinal, an III) the terms gramme and kilogramme replaced the former terms gravet (correctly milligrave) and grave and on 22 June 1799, after Pierre Méchain and Jean-Baptiste Delambre completed their survey, the definitive standard metre was deposited in the French National Archives. On 10 December 1799 (a month after Napoleon's coup d'état), the metric system was definitively adopted in France.

The desire for international cooperation on metrology led to the signing in 1875 of the Metre Convention, a treaty that established three international organizations to oversee the keeping of metric standards:

The history of the metric system has seen a number of variations, whose use has spread around the world, to replace many traditional measurement systems. At the end of World War II, a number of different systems of measurement were still in use throughout the world. Some of these systems were metric-system variations, whereas others were based on customary systems. It was recognised that additional steps were needed to promote a worldwide measurement system. As a result, the 9th General Conference on Weights and Measures (CGPM), in 1948, asked the International Committee for Weights and Measures (CIPM) to conduct an international study of the measurement needs of the scientific, technical, and educational communities.

Based on the findings of this study, the 10th CGPM in 1954 decided that an international system should be derived from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and electromagnetic quantities. The six base units that were recommended are the metre, kilogram, second, ampere, degree Kelvin (later renamed kelvin), and candela. In 1960, the 11th CGPM named the system the International System of Units, abbreviated SI from the French name, Le Système international d'unités. The seventh base unit, the mole, was added in 1971 by the 14th CGPM.

One of the CIPM committees, the CCU, has proposed a number of changes to the definitions of the base units used in SI.[9] The CIPM meeting of October 2010 found that the proposal was not complete,[10] and it is expected that the CGPM will consider the full proposal in 2015.

## Units and prefixes

The International System of Units consists of a set of units together with a set of prefixes. The units are divided into two classes—base units and derived units. There are seven base units, each representing, by convention, different kinds of physical quantities.

SI base units[11][12]
Unit name Unit symbol Quantity name Quantity symbol Dimension symbol
metre m length l (a lowercase L), x, r L
kilogram [note 1] kg mass m M
second s time t T
ampere A electric current I (an uppercase i) I
kelvin K thermodynamic temperature T Θ
candela cd luminous intensity Iv (an uppercase i with lowercase non-italicized v subscript) J
mole mol amount of substance n N
Note
1. ^ Despite the prefix, the kilogram is the base unit of mass. The kilogram, not the gram, is used in the definitions of derived units.

Derived units are formed from multiplication and division of the seven base units and other derived units[13] and are unlimited in number;[14] for example, the SI derived unit of speed is metre per second, m/s. Some derived units have special names; for example, the unit of resistance, the ohm, symbol Ω, is uniquely defined by the relation Ω = m2·kg·s−3·A−2, which follows from the definition of the quantity electrical resistance. The radian and steradian, once given special status, are now considered dimensionless derived units.[13]

A prefix may be added to a unit to produce a multiple of the original unit. All multiples are integer powers of ten, and beyond a hundred(th) all are integer powers of a thousand. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth; hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined: a millionth of a metre is a micrometre not a millimillimetre.

Standard prefixes for the SI units of measure
Multiples Name deca- hecto- kilo- mega- giga- tera- peta- exa- zetta- yotta-
Symbol da h k M G T P E Z Y
Factor 100 101 102 103 106 109 1012 1015 1018 1021 1024

Fractions Name deci- centi- milli- micro- nano- pico- femto- atto- zepto- yocto-
Symbol d c m μ n p f a z y
Factor 100 10−1 10−2 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24

In addition to the SI units, there is also a set of non-SI units accepted for use with SI, which includes some commonly used non-coherent units such as the litre.

## Writing unit symbols and the values of quantities

• The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit symbol; e.g., "2.21 kg", "7.3×102 m2", "22 K". This rule explicitly includes the percent sign (%). Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.[15][16]
• Symbols for derived units formed by multiplication are joined with a centre dot (·) or a non-break space, for example, "N·m" or "N m".
• Symbols for derived units formed by division are joined with a solidus (/), or given as a negative exponent. For example, the "metre per second" can be written "m/s", "m s−1", "m·s−1" or $\textstyle\frac{\mathrm{m}}{\mathrm{s}}$. Only one solidus should be used; e.g., "kg/(m·s2)" and "kg·m−1·s−2" are acceptable, but "kg/m/s2" is ambiguous and unacceptable.
• Symbols are mathematical entities, not abbreviations, and do not have an appended period/full stop (.).
• Symbols are written in upright (Roman) type (m for metres, s for seconds), so as to differentiate from the italic type used for quantities (m for mass, s for displacement). By consensus of international standards bodies, this rule is applied independent of the font used for surrounding text.[17]
• Symbols for units are written in lower case (e.g., "m", "s", "mol"), except for symbols derived from the name of a person. For example, the unit of pressure is named after Blaise Pascal, so its symbol is written "Pa", whereas the unit itself is written "pascal".[18]
• The one exception is the litre, whose original symbol "l" is unsuitably similar to the numeral "1" or the uppercase letter "i" (depending on the typeface used), at least in many English-speaking countries. The American National Institute of Standards and Technology recommends that "L" be used instead, a usage which is common in the US, Canada and Australia (but not elsewhere). This has been accepted as an alternative by the CGPM since 1979. The cursive ℓ is occasionally seen, especially in Japan and Greece, but this is not currently recommended by any standards body. For more information, see litre.
• A prefix is part of the unit, and its symbol is prepended to the unit symbol without a separator (e.g., "k" in "km", "M" in "MPa", "G" in "GHz"). Compound prefixes are not allowed.
• All symbols of prefixes larger than 103 (kilo) are uppercase.[19]
• Symbols of units are not pluralised; e.g., "25 kg", not "25 kgs".[17]
• The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the point on the line or the comma on the line." In practice, the decimal point is used in English-speaking countries and most of Asia, and the comma in most continental European languages.
• Spaces may be used as a thousands separator (1000000) in contrast to commas or periods (1,000,000 or 1.000.000) in order to reduce confusion resulting from the variation between these forms in different countries. In print, the space used for this purpose is typically narrower than that between words (commonly a thin space).
• Any line-break inside a number, inside a compound unit, or between number and unit should be avoided, but, if necessary, the last-named option should be used.
• In Chinese, Japanese, and Korean language computing (CJK), some of the commonly used units, prefix-unit combinations, or unit-exponent combinations have been allocated predefined single characters taking up a full square. Unicode includes these in its CJK Compatibility and Letterlike Symbols subranges for back compatibility, without necessarily recommending future usage.
• When writing dimensionless quantities, the terms 'ppb' (parts per billion) and 'ppt' (parts per trillion) are recognised as language-dependent terms, since the value of billion and trillion can vary from language to language. SI, therefore, recommends avoiding these terms.[15] However, no alternative is suggested by the International Bureau of Weights and Measures (BIPM).

## Writing the unit names

• Names of units follow the grammatical rules associated with common nouns - in English and in French they start with a lowercase letter (e.g., newton, hertz, pascal), even when the symbol for the unit begins with a capital letter. This also applies to 'degrees Celsius', since 'degree' is the unit. In German however, names of units, in common with all nouns, start with a capital letter.[20]
• Names of units are pluralised using the normal English grammar rules;[21][22] e.g., "henries" is the plural of "henry".[21]:31 The units lux, hertz, and siemens are exceptions from this rule: they remain the same in singular and plural form. Note that this rule applies only to the full names of units, not to their symbols.
• The official US spellings for deca, metre, and litre are deka, meter, and liter, respectively.[23]

## Realisation of units

Metrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis upon which the most accurate and reproducible measurements can be made. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. A description of how the definitions of some important units are realised in practice is given on the BIPM website.[24] However, "any method consistent with the laws of physics could be used to realise any SI unit."[25] (p. 111).

## Related systems

The definitions of the terms 'quantity', 'unit', 'dimension' etc. used in measurement, are given in the International Vocabulary of Metrology.[26]

The quantities and equations which define the SI units are now referred to as the International System of Quantities (ISQ), and are set out in the ISO/IEC 80000 Quantities and Units.

## Conversion factors

The relationship between the units used in different systems is determined by convention or from the basic definition of the units. Conversion of units from one system to another is accomplished by use of a conversion factor. There are several compilations of conversion factors; see, for example, Appendix B of NIST SP 811.[21]

## Cultural issues

Three nations have not officially adopted the International System of Units as their primary or sole system of measurement: Myanmar (Burma), Liberia, and the United States

The near-worldwide adoption of the metric system as a tool of economy and everyday commerce was based to some extent on the lack of customary systems in many countries to adequately describe some concepts, or as a result of an attempt to standardise the many regional variations in the customary system. International factors also affected the adoption of the metric system, as many countries increased their trade. For use in science, the SI prefixes simplify dealing with very large and small quantities.

Many units in everyday and scientific use are not SI units. In some cases these units have been designated by the BIPM as "non-SI units accepted for use with the SI". [27] [28] Some examples include:

• The many units of time (minute, min; hour, h; day, d) in use besides the SI second, and are specifically accepted for use according to table 6.[29]
• The year is specifically not included but has a recommended conversion factor.[30]
• The Celsius temperature scale; kelvins are rarely employed in everyday use.
• Electric energy is often billed in kilowatt-hours, instead of megajoules. Similarly, battery charge is often measured as milliampere-hours (mA·h), instead of coulombs.
• The nautical mile and knot (nautical mile per hour) used to measure travel distance and speed of ships and aircraft (1 International nautical mile = 1852 m or approximately 1 minute of latitude). In addition to these, Annex 5 of the Convention on International Civil Aviation permits the "temporary use" of the foot for altitude.
• Astronomical distances measured in astronomical units, parsecs, and light-years instead of, for example, petametres (a light-year is about 9.461 Pm or about 9461000000000000 m).
• Atomic scale units used in physics and chemistry, such as the ångström, electron volt, atomic mass unit and barn.
• Some physicists prefer the centimetre-gram-second (CGS) units, or systems based on physical constants, such as Planck units, atomic units, or geometric units.
• In some countries, the informal cup measurement has become 250 mL. Likewise, a 500 g metric pound is used in many countries. Liquids, especially alcoholic ones, are often sold in units whose origins are historical (for example, pints for beer and cider in glasses in the UK —although pint means 568 mL; Jeroboams for champagne in France).
• A metric mile of 10 km is used in Norway and Sweden. The term metric mile is also used in some countries for the 1500 m foot race.
• In the US, blood glucose measurements are recorded in milligrams per decilitre (mg/dL), which would normalise to cg/L; in Canada, Australia, New Zealand, Oceania, and Europe, the standard is millimole per litre (mmol/L) or mM (millimolar).
• Blood pressure is usually measured in mmHg(≈Torr).
• Atmospheric pressure in government weather reports is measured in inHg in the USA,[31] and in the SI unit hPa in Australia,[32] UK[33] and most other countries.

The fine-tuning that has happened to the metric base-unit definitions over the past 200 years, as experts have tried periodically to find more precise and reproducible methods, does not affect the everyday use of metric units. Since most non-SI units in common use, such as the US customary units, are defined in SI units,[34] any change in the definition of the SI units results in a change of the definition of the older units, as well.

One of the European Union's (EU) objectives is the creation of a single market for trade. In order to achieve this objective, the EU standardised on using SI as the legal units of measure. As of 2009, it has issued two units of measurement directives which catalogued the units of measure that might be used for, amongst other things, trade: the first was Directive 71/354/EEC[35] issued in 1971 which required member states to standardise on SI rather than use the variety of cgs and mks units then in use. The second was Directive 80/181/EEC[36][37][38][39][40] issued in 1979 which replaced the first and which gave the United Kingdom and the Republic of Ireland a number of derogations from the original directive.

The directives gave a derogation from using SI units in areas where other units of measure had either been agreed by international treaty or which were in universal use in worldwide trade. They also permitted the use of supplementary indicators alongside, but not in place of the units catalogued in the directive. In its original form, Directive 80/181/EEC had a cut-off date for the use of such indicators, but with each amendment this date was moved until, in 2009, supplementary indicators have been allowed indefinitely.

### Chinese characters

Chinese expressway distances road sign in eastern Beijing. Although the primary text is in Chinese, the distances use internationally recognised characters.

In Japanese: Individual Chinese characters exist for some SI units, namely metre, litre, and gram, with the prefixes from kilo- (1000) to milli- (1/1000), yielding 21 (3×7) characters. These were created in Japan in the late 19th century (Meiji period) by choosing characters for the basic units – 米 "metre", 立 "litre", and 瓦 "gram" – and for the prefixes – 千 "kilo-, 1000", 百 "hecto-, 100", 十 "deca-, 10", 分 "deci-, 1/10", 厘 "centi-, 1/100", and 毛 "milli-, 1/1000" – and then combining them to form a single character, such as 粁 (米+千) for kilometre (in the case of no prefix, the base character alone is used). The entire metre series, for example, is 粁, 粨, 籵, 米, 粉, 糎, 粍. The symbols for the metric units are internationally-recognised Latin characters.

In Chinese: The basic units are 米 mǐ "meter", 升 shēng "liter", 克 kè "gram", and 秒 mǐao "second". Some sample prefixes are 分 fēn "deci", 厘 lí "centi", 毫 háo "milli", and 微 wēi "micro". These are not combined into a single character, so for example centimeters are simply 厘米 límǐ.

 Dimensional analysis History of measurement International Vocabulary of Metrology International System of Quantities List of international common standards Long and short scales Names of large numbers Names of small numbers Non-SI units accepted for use with the SI Orders of magnitude SI base units SI derived units SI prefixes Organisations Standards and conventions ISO 80000

## References

1. ^
2. ^ Resolution of the International Bureau of Weights and Measures establishing the International System of Units
3. ^ Official BIPM definitions
4. ^ Essentials of the SI: Introduction
5. ^ An extensive presentation of the SI units is maintained on line by NIST, including a diagram of the interrelations between the derived units based upon the SI units. Definitions of the basic units can be found on this site, as well as the CODATA report listing values for special constants such as the electric constant, the magnetic constant and the speed of light, all of which have defined values as a result of the definition of the metre and ampere.

In the International System of Units (SI) (BIPM, 2006), the definition of the metre fixes the speed of light in vacuum c0, the definition of the ampere fixes the magnetic constant (also called the permeability of vacuum) μ0, and the definition of the mole fixes the molar mass of the carbon 12 atom M(12C) to have the exact values given in the table [Table 1, p.7]. Since the electric constant (also called the permittivity of vacuum) is related to μ0 by ε0 = 1/μ0c02, it too is known exactly.

– CODATA report
6. ^
7. ^
8. ^ "The name "kilogram"". Retrieved 25 July 2006.
9. ^ Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units". CCU. Retrieved 2011-01-01.
10. ^ Anon (November 2010). "BIPM Bulletin". BIPM. Retrieved 2011-01-05.
11. ^ Barry N. Taylor & Ambler Thompson Ed. (2008). The International System of Units (SI). Gaithersburg, MD: National Institute of Standards and Technology. pp. 23. Retrieved 18 June 2008.
12. ^ Quantities Units and Symbols in Physical Chemistry, IUPAC
13. ^ a b Ambler Thompson and Barry N. Taylor, (2008), Guide for the Use of the International System of Units (SI), (Special publication 811), Gaithersburg, MD: National Institute of Standards and Technology, p. 3.
14. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), p. 103, ISBN 92-822-2213-6
15. ^ a b The International System of Units (SI) (8 ed.). International Bureau of Weights and Measures (BIPM). 2006. pp. 134–135.
16. ^ Thompson, A.; Taylor, B. N. (July 2008). "NIST Guide to SI Units — Rules and Style Conventions". National Institute of Standards and Technology. Retrieved 29 December 2009.
17. ^ a b "Chapter 5. Writing unit symbols and names, and expressing the values of quantities". The International System of Units (SI) (8 ed.). International Bureau of Weights and Measures (BIPM). 2006.
18. ^ Ambler Thompson and Barry N. Taylor, (2008), Guide for the Use of the International System of Units (SI), (Special publication 811), Gaithersburg, MD: National Institute of Standards and Technology, section 6.1.2
19. ^ Ambler Thompson and Barry N. Taylor, (2008), Guide for the Use of the International System of Units (SI), (Special publication 811), Gaithersburg, MD: National Institute of Standards and Technology, section 4.3.
20. ^ Wörterbuch Englisch Dictionary German. Limassol: Eurobuch/Eurobooks. 1988.
21. ^ a b c Ambler Thompson & Barry N. Taylor (2008). NIST Special Publication 811: Guide for the Use of the International System of Units (SI). National Institute of Standards and Technology. Retrieved 18 June 2008.
22. ^ "Interpretation of the International System of Units (the Metric System of Measurement) for the United States". Federal Register (National Archives and Records Administration) 73 (96): 28432–3. 9 May 2008. FR Doc number E8-11058. Retrieved 28 October 2009.
23. ^ "The International System of Units". pp. iii. Retrieved 27 May 2008.
24. ^ SI Practical Realization brochure
25. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), p. 111, ISBN 92-822-2213-6
26. ^
27. ^ BIPM - Table 6
28. ^ BIPM - Table 8
29. ^ BIPM - Table 6
30. ^ NIST Guide to SI Units - Appendix B9. Conversion Factors
31. ^ Current Weather Conditions: DENVER INTERNATIONAL AIRPORT
32. ^ Australia Mean Sea Level Pressure Analysis
33. ^ Met Office Weather Units
34. ^ Mendenhall, T. C. (1893). "Fundamental Standards of Length and Mass". Reprinted in Barbrow, Louis E. and Judson, Lewis V. (1976). Weights and measures standards of the United States: A brief history (NBS Special Publication 447). Washington D.C.: Superintendent of Documents. Viewed 23 August 2006 at http://physics.nist.gov/Pubs/SP447/ pp. 28–29.
35. ^
36. ^ The Council of the European Communities (21 December 1979). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 7 February 2009.
37. ^ The Council of the European Communities (20 December 1984). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 7 February 2009.
38. ^ The Council of the European Communities (30 November 1989). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 7 February 2009.
39. ^ The Council of the European Communities (9 February 2000). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 7 February 2009.
40. ^ The Council of the European Communities (27 May 2009). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 14 September 2009.

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