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"SI" redirects here. For other uses, see Si (disambiguation).
File:SI Brochure Cover.jpg

Cover of brochure The International System of Units

The International System of Units[1] (abbreviated SI from Template:Lang-fr[2]) is the modern form of the metric system. It comprises a system of units of measurement devised around seven base units and the convenience of the number ten. The SI was established in 1960, based on the metre-kilogram-second system, rather than the centimetre-gram-second system, which, in turn, had several variants. The SI has been declared to be 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.

SI is the world's most widely used system of measurement, used in both everyday commerce and science.[3][4][5] The system has been nearly globally adopted with Burma, Liberia and the United States not having adopted SI units as their official system of weights and measures. While only the US does not commonly use metric units outside of science, medicine, and the government,[6] the United Kingdom has officially adopted a partial metrication policy, with no intention of replacing imperial units entirely. Canada has adopted it for most purposes but Imperial units, which are used in the United States, are still legally permitted and remain in common use throughout a few sectors of Canadian society, particularly in the buildings trades and railways sectors.[7][8]


Main article: History of the metric system

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.[9] 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 organisations to oversee the keeping of metric standards:

  • General Conference on Weights and Measures (Conférence générale des poids et mesures or CGPM) – a meeting every four to six years of delegates from all member states;
  • International Bureau of Weights and Measures (Bureau international des poids et mesures or BIPM) – an international metrology centre at Sèvres in France; and
  • International Committee for Weights and Measures (Comité international des poids et mesures or CIPM)—an administrative committee that meets annually at the BIPM.

The history of the metric system has seen a number of variations, and 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 BIPM has also described SI as "the modern metric system".[10]

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.[11] The CIPM meeting of October 2010 found that the proposal was not complete,[12] and it is expected that the CGPM will consider the full proposal in 2015.

Units and prefixes

Main article: SI base unit

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[13][14]
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
  1. Despite the prefix "kilo-", the kilogram is the base unit of mass. The kilogram, not the gram, is used in the definitions of derived units. Nonetheless, units of mass are named as if the gram were the base unit.

Derived units are formed from multiplication and division of the seven base units and other derived units[15] and are unlimited in number;[16] 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.[15]

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, and multiples of the kilogram are named as if the gram was the base unit. Thus a millionth of a metre is a micrometre, not a millimillimetre, and a millionth of a kilogram is a milligram, not a microkilogram.


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.Template:Val/delimitnum/fraction×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.[17][18]
  • Symbols for derived units formed by multiplication are joined with a centre dot (·) or a non-break space; e.g., N·m or N m.
  • Symbols for derived units formed by division are joined with a solidus (/), or given as a negative exponent. E.g., the "metre per second" can be written m/s, m s−1, m·s−1, or . 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.[19]
  • 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".[20]
    • 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 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. The litre is not an SI unit per se and is expressed in SI terms as a cubic decimetre, i.e., dm3.
  • 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.[21]
  • Symbols of units are not pluralised; e.g., "25 kg", not "25 kgs".[19]
  • 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 of Latin America and in continental European languages.[22]
  • Spaces may be used as a thousands separator (Template:Gaps) 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. These are summarised in Unicode symbols.
  • 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.[17] 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.[23]
  • Names of units are pluralised using the normal English grammar rules,[24][25] e.g. "henries" is the plural of "henry".[24]: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.
  • When unit names are combined by multiplication, they are separated with a hyphen or a space (e.g. newton-metre or newton metre). The plural is formed by pluralising the last unit name as above (e.g. ten newton-metres).
  • The official US spellings for deca, metre, and litre are deka, meter, and liter, respectively.[26]

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 on 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.[27] However, "any method consistent with the laws of physics could be used to realise any SI unit."[28] (p. 111).

Related systems

Main article: Metric system

The definitions of the terms 'quantity', 'unit', 'dimension' etc. used in measurement, are given in the International Vocabulary of Metrology.[29]

The quantities and equations that 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.

"New SI"

Main article: New SI definitions
File:Relations between new SI units definitions.png

Relations between proposed SI units definitions (in colour) and seven physical constants (in grey) with fixed numerical values in the proposed system.

When the metre was redefined in 1960, the kilogram was the only SI base unit that relied on a specific artefact. Moreover, after the 1996–1998 recalibration a clear divergence between the various prototype kilograms was observed.

At its 23rd meeting (2007), the CGPM mandated the CIPM to investigate the use of natural constants as the basis for all units of measure rather than the artifacts that were then in use. At a meeting of the CCU held in Reading, United Kingdom in September 2010, a resolution[30] and draft changes to the SI brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed to in principle.[11] The proposals that the CCU put forward were:

  • In addition to the speed of light, four constants of nature—Planck's constant, an elementary charge, Boltzmann constant and Avogadro's number—be defined to have exact values.
  • The international prototype kilogram be retired
  • The current definitions of the kilogram, ampere, kelvin and mole be revised.
  • The wording of the definitions of all the base units be tightened up

The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meeting have not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time".[31] The CIPM did however sponsor a resolution at the 24th CGPM in which the changes were agreed in principle and which were expected to be finalised at the CGPM's next meeting in 2014.[32]

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.[24]

Cultural issues

File:Non-Metric User.svg

The CIA claims that three nations have not adopted the International System of Units as their official system of measurement: Myanmar (Burma), Liberia, and the United States[6]

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". [33] [34] Some examples include:

  • The units of time (minute, min; hour, h; day, d) in use besides the SI second, are specifically accepted for use according to table 6.[35]
  • The year is specifically not included but has a recommended conversion factor.[36]
  • 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 = Template:Gaps 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 Template:Gaps 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 normalises 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,[37] and in the SI unit hPa in Australia,[38] UK[39] 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,[40] any change in the definition of the SI units results in a change of the definition of the older units, as well.

International trade

Main article: Metrication in the United States

One of the European Union's (EU) objectives is the creation of a single market for trade. 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[41] 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[42][43][44][45][46] issued in 1979, which replaced the first and 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 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

File:PRC Expressway RoadSign Distances.jpg

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", 升 "litre", and 克 "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 "metre", 升 shēng "litre", 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 centimetres are simply 厘米 límǐ.

See also

  • 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
  • List of scientific units named after people
  • Institute for Reference Materials and Measurements (IRMM)
Standards and conventions
  • Coordinated Universal Time (UTC)
  • ISO 80000
  • UCUM


  1. Template:SIbrochure8th
  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 on SI units is maintained on-line by NIST, including a diagram of the relations between the derived units based on the SI units. Definitions of the basic units can be found on this site, as well as the CODATA report, which lists 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. 6.0 6.1 Appendix G : Weights and Measures. The World Factbook. Central Intelligence Agency. URL accessed on 3 September 2011.
  7. Weights and Measures Act
  8. Weights and Measures Act, accessed January 2012, Act current to 18 January 2012. Canadian units (5) The Canadian units of measurement are as set out and defined in Schedule II, and the symbols and abbreviations therefore are as added pursuant to subparagraph 6(1)(b)(ii).
  9. The name "kilogram". URL accessed on 25 July 2006.
  10. Template:SIbrochure8th]]
  11. 11.0 11.1 Ian Mills. Draft Chapter 2 for SI Brochure, following redefinitions of the base units. CCU. URL accessed on 1 January 2011.
  12. Anon. BIPM Bulletin. BIPM. URL accessed on 5 January 2011.
  13. Barry N. Taylor & Ambler Thompson Ed. (2008). The International System of Units (SI), 23, Gaithersburg, MD: National Institute of Standards and Technology. URL accessed 18 June 2008.
  14. Quantities Units and Symbols in Physical Chemistry, IUPAC
  15. 15.0 15.1 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.
  16. Template:SIBrochure8th
  17. 17.0 17.1 (2006) The International System of Units (SI), 8, 134–135, International Bureau of Weights and Measures (BIPM).
  18. NIST Guide to SI Units — Rules and Style Conventions. National Institute of Standards and Technology. URL accessed on 29 December 2009.
  19. 19.0 19.1 (2006) "Chapter 5. Writing unit symbols and names, and expressing the values of quantities" The International System of Units (SI), 8, International Bureau of Weights and Measures (BIPM).
  20. 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
  21. 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.
  22. (March – April 2008)Period or Comma? Decimal Styles over Time and Place. Science Editor 31.
  23. (1988) Wörterbuch Englisch Dictionary German, Limassol: Eurobuch/Eurobooks.
  24. 24.0 24.1 24.2 Ambler Thompson & Barry N. Taylor (2008). NIST Special Publication 811: Guide for the Use of the International System of Units (SI).
  25. (9 May 2008)Interpretation of the International System of Units (the Metric System of Measurement) for the United States. Federal Register 73 (96): 28432–3. FR Doc number E8-11058.
  26. The International System of Units. URL accessed on 27 May 2008.
  27. SI Practical Realization brochure
  28. Template:SIbrochure8th
  29. The International Vocabulary of Metrology (VIM).
  30. Ian Mills. On the possible future revision of the International System of Units, the SI. CCU. URL accessed on 1 January 2011.
  31. Towards the "new SI". International Bureau of Weights and Measures (BIPM). URL accessed on 20 February 2011.
  32. (17–21 October 2011) "Resolution 1 - On the possible future revision of the International System of Units, the SI" in 24th meeting of the General Conference on Weights and Measures. {{{booktitle}}}. Retrieved on 25 October 2011. 
  33. BIPM - Table 6
  34. BIPM - Table 8
  35. BIPM - Table 6
  36. NIST Guide to SI Units - Appendix B9. Conversion Factors
  37. Current Weather Conditions: DENVER INTERNATIONAL AIRPORT
  38. Australia Mean Sea Level Pressure Analysis
  39. Met Office Weather Units
  40. 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 pp. 28–29.
  41. Council Directive of 18 October 1971 on the approximation of laws of the member states relating to units of measurement, (71/354/EEC). URL accessed on 7 February 2009.
  42. The Council of the European Communities. 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. URL accessed on 7 February 2009.
  43. The Council of the European Communities. 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. URL accessed on 7 February 2009.
  44. The Council of the European Communities. 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. URL accessed on 7 February 2009.
  45. The Council of the European Communities. 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. URL accessed on 7 February 2009.
  46. The Council of the European Communities. 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. URL accessed on 14 September 2009.

Further reading

External links

Pro-metric advocacy groups
Pro-customary measures pressure groups

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