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Encyclopedia > SI units
For other uses, see SI (disambiguation).

The International System of Units (symbol: SI) (for the French phrase Systme International d'Units) is the most widely used system of units. It is used for everyday commerce in virtually every country of the world except the United States, Liberia and Myanmar, and it is almost globally used in scientific and engineering work. In 1960, SI was selected as a specific subset of the existing Metre-Kilogram-Second systems of units (MKS), rather than the older Centimetre-Gram-Second system of units (CGS). Various new units were added with the introduction of the SI and at later times. SI is sometimes referred to as the metric system (especially in the United States, which has not widely adopted it, although it has been used more commonly in recent years, and in the UK, where conversion is incomplete). The International System of Units refers to a specific canon of measurements derived and extended from the Metric system; however, not all metric units of measurement are accepted as SI units.

There are seven base units and several derived units, together with a set of prefixes. Non-SI units can be converted to SI units (or vice versa) according to the conversion of units. Virtually all non-SI units have been redefined in terms of SI units.



The units of the SI are decided by a series of international conferences organised by the standards organization Bureau International des Poids et Mesures (International Bureau of Weights and Measures). The SI was first given its name in 1960, and last added to in 1971.

The true origins of the SI or metric system date back to approximately 1640. It was invented by French scientists, and was given a huge boost in popularity by the French Revolution of 1789. The metric system tried to choose units which were non-arbitrary, merging well with the revolution's official ideology of "Pure Reason".

The most important unit is that of length: one metre was intended to be equal to 1/10,000,000th of the distance from the pole to the equator along the meridian through Paris. This is approximately 10% longer than one yard. Later on, a platinum rod with a rigid, X-shaped cross section was produced to serve as the easy-to-check standard for one metre's length. However, due to the difficulty of actually measuring the length of a meridian quadrant in the 18th century, the first platinum prototype was short by 0.2 millimetres. Then a multiple of a specific radiation wavelength was introduced to abstractly define the (unchanged) length of the metre unit, and finally the metre was defined as the distance travelled by light in a vacuum in a specific period of time.

The original base unit of mass in the metric system was the gram, but was quickly changed to the kilogram, which was defined as the mass of distilled pure water at its densest (+3.98 degrees Celsius) contained inside a cube having sides equal to 1/10th of a metre. One kilogram is about 2.2 pounds. This cubic space was also called one litre so volumes of different liquids could easily be compared. By 1799, a platinum cylinder was manufactured to serve as the standard for a kilogram, so no water-based standard ever served as the primary standard when the metric system was actually used anywhere. In 1890, this was replaced by a cylinder of a 90% platinum, 10% iridium alloy which as served as the standard ever since.

The unit of temperature became the centigrade or inverted Celsius grade, which means the mercury scale is divided into 100 equal length parts between the water-ice mixture and the boiling point of pure, distilled water. Boiling water thus becomes one hundred degrees Celsius and freezing is zero degrees Celsius. This is the metric unit of temperature in everyday use. A hundred years later, scientists discovered absolute zero. This prompted the establishment of a new temperature scale, called the absolute scale or Kelvin scale, which relocates the zero place but still uses 100 kelvins between the freezing point and boiling point of water.

The metric unit of time became the second, originally defined as 1/86,400 of a mean solar day. The formal definition of the second has been changed several times for enhanced scientific requirements (astronomic observations, tuning fork clock, quartz clock and then caesium atomic clock) but wristwatch users remain relatively unaffected.

The swift worldwide adoption of the metric system as a tool of economy and everday commerce was based mainly on the lack of customary systems in many countries to adequately describe some concepts, or as a result of an attempt to standardize the many regional variations in the customary system. International factors also affected the adoption of the metric system, as many countries increased their trade. Scientifically, it provides ease when dealing with very large and small quantities because it lines up so well with our decimal numeral system.

Cultural differences can be represented in the local everyday uses of metric units. For example, bread is sold in one-half, one or two kilogram sizes in many countries, but you buy them by multiples of one hundred grams in the former USSR. In some countries, the informal cup measurement has become 250 mL, and prices for items are sometimes given per 100 g rather than per kilogram.

Non-scientific people should not be put off by the fine-tuning that has happened to the metric base units over the past two hundred years, as experts regularly tried to refine the metric system to fit the best scientific researcher (e.g. CGS to MKS to SI system changes or the invention of Kelvin scale). These changes seldom affect the everyday use of metric units. The presence of these adjustments has been one reason advocates of the U.S. customary units have used against metrication.


SI is built on seven SI base units, the kilogram, metre, second, ampere, kelvin, mole, and candela. These are used to define various SI derived units.

SI also defines a number of SI prefixes to be used with the units: these combine with any unit name to give subdivisions and multiples. For example, the prefix kilo denotes a multiple of a thousand, so the kilometre is 1 000 metres, the kilogram 1 000 grams, and so on. Note that a millionth of a kilogram is a milligram, not a microkilogram.

SI writing style

  • Symbols are written in lower case, except the symbols that are derived from the name of a person. This means that the symbol for the SI unit for pressure, named after Blaise Pascal, is Pa, whereas the unit itself is written pascal. The official SI brochure lists the symbol for the litre as an allowed exception to the capitalization rules: either capital or lowercase L is acceptable.
  • Symbols are written in singular, e.g. 25 kg (not "25 kgs").
  • Symbols, unlike abbreviations, do not have a period (.) at the end.
  • It is preferable to keep the symbol in upright Roman type (for example, m for metres, L for litres), so as to differentiate from mathematical and physical variables (for example, m for mass, l for length).
  • A space is left between the numbers and the symbols: 2.21 kg, 7.3102 m2. There is an exception to this rule. The symbols for plane angular degrees, minutes and seconds (, ′ and ″) are placed immediately after the number, with no intervening space.
  • SI uses spaces to separate decimal digits in sets of three. e.g. 1 000 000 or 342 142 (in contrast to the commas or dots used in other systems, e.g. 1,000,000 or 1.000.000).
  • SI used only a comma as the separator for decimal fractions until 1997. The number "twenty four and fifty one hundredths" would be written as "24,51". In 1997 the CIPM decided that the British full stop (the "dot on the line", or period) would be the decimal separator in text whose main language is English ("24.51"); the comma remains the decimal separator in all other languages.
  • Symbols for derived units formed from multiple units by multiplication are joined with a space or centre dot (), e.g. N m or Nm.
  • Symbols formed by division of two units are joined with a solidus (/), or given as a negative exponent, e.g. m/s, m s-1, ms-1 or . A solidus should not be used if the result is ambiguous, e.g. kgm-1s-2, not "kg/m/s2".

With a few exceptions (such as draught beer sales in the United Kingdom) the system can legally be used in every country in the world and many countries do not maintain definitions of other units. Those countries that still give official recognition to non-SI units (e.g. the US and UK) have defined the modern in terms of SI units; for example, the common inch is defined to be exactly 0.0254 metres. In the US, survey distances have, however, not been redefined due to the accumulation of error it would entail and the survey foot and survey inch remain as separate units. (This was not a problem for the United Kingdom, as the Ordnance Survey has been metric since before World War II.) (See weights and measures for a history of the development of units of measurement.)


Base units

The following are the fundamental units from which all others are derived, they are dimensionally independent. The definitions stated below are widely accepted.

SI Base units

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Name Symbol Quantity Definition
metre m Length The unit of length is equal to the length of the path traveled by light in a vacuum during the time interval of 1/299 792 458 of a second (17th CGPM (1983) Resolution 1, CR 97). This number is exact; the metre is defined this way.
kilogram kg Mass The unit of mass is equal to the mass of the international prototype kilogram (a platinum-iridium cylinder) kept at the Bureau International des Poids et Mesures (BIPM), Svres, Paris (1st CGPM (1889), CR 34-38). Note that the kilogram is the only base unit with a prefix; the gram is defined as a derived unit, equal to 1/1000 of a kilogram; prefixes such as mega are applied to the gram, not the kg; e.g. Gg, not Mkg. It is also the only unit still defined by a physical prototype instead of a measurable natural phenomenon (see the kilogram article for an alternate definition).
second s Time The unit of time is the duration of exactly 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium-133 atom at a temperature of 0 K (13th CGPM (1967-1968) Resolution 1, CR 103).
ampere A Electrical Current The unit of electrical current is the constant current which, if maintained in two straight parallel conductors, of infinite length and negligible cross-section, placed 1 metre apart in a vacuum, would produce a force between these conductors equal to 210 −7 newton per metre of length (9th CGPM (1948) Resolution 7, CR 70).
kelvin K Thermodynamic Temperature The unit of thermodynamic temperature (or absolute temperature) is the fraction 1/273.16 (exactly) of the thermodynamic temperature at the triple point of water (13th CGPM (1967) Resolution 4, CR 104).
mole mol Amount of substance The unit of amount of substance is the amount of substance which contains as many elementary entities as there are atoms in 0.012 kilograms of pure carbon-12 (14th CGPM (1971) Resolution 3, CR 78). (Elementary entities may be atoms, molecules, ions, electrons, or particles.) It is approximately equal to 6.022141991023 units.
candela cd Luminous intensity The unit of luminous intensity is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5401012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian (16th CGPM (1979) Resolution 3, CR 100).

Dimensionless derived units

The following SI units are derived from the base units and are dimensionless.

SI Dimensionless derived units

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Name Symbol Quantity Definition
radian rad Angle The unit of angle is the angle subtended at the centre of a circle by an arc of the circumference equal in length to the radius of the circle. There are radians in a circle.
steradian sr Solid angle The unit of solid angle is the solid angle subtended at the centre of a sphere of radius r by a portion of the surface of the sphere having an area r2. There are steradians in a sphere.

Derived units with special names

Base units can be put together to derive units of measurement for other quantities. Some have been given names.

SI derived units with special names

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Name Symbol Quantity Expressed in base units
hertz Hz Frequency s-1
newton N Force kg m s -2
joule J Energy N m = kg m2 s-2
watt W Power J/s = kg m2 s-3
pascal Pa Pressure N/m2 = kg m -1 s-2
lumen lm Luminous flux cd
lux lx Illuminance cd m-2
coulomb C Electric Charge A s
volt V Electrical potential difference J/C = kg m2 A-1 s-3
ohm Ω Electric resistance V/A = kg m2 A-2 s-3
farad F Electric capacitance Ω-1 s = A2 s4 kg-1 m-2
weber Wb Magnetic flux kg m2 s-2 A-1
tesla T Magnetic flux density Wb/m2 = kg s-2 A-1
henry H Inductance Ω s = kg m2 A-2 s-2
siemens S Electric conductance Ω-1 = kg-1 m-2 A2 s3
becquerel Bq Radioactivity (decays per unit time) s-1
gray Gy Absorbed dose (of ionising radiation) J/kg = m2 s-2
sievert Sv Equivalent dose (of ionising radiation) J/kg = m2 s-2
katal kat Catalytic activity mol/s = mol s-1
degree Celsius C thermodynamic temperature K - 273.15

Non-SI units accepted for use with SI

The following units are not SI units but are "accepted for use with the International System."

Non-SI units accepted for use with SI

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Name Symbol Quantity Equivalent SI unit
minute min time 1 min = 60 s
hour h time 1 h = 60 min = 3600 s
day d time 1 d = 24 h = 1440 min = 86400 s
degree of arc angle 1 = (π/180) rad
minute of arc angle 1′ = (1/60) = (π/10800) rad
second of arc angle 1″ = (1/60)′ = (1/3600) = (π/648000) rad
litre l or L volume 0.001 m3
tonne t mass 1 t = 103 kg

Non-SI units not formally adopted by the CGPM

neper, field quantity Np ratio (dimensionless) LF = ln(F/F0) Np
neper, power quantity Np ratio (dimensionless) LP = ln(P/P0) Np
bel, field quantity B ratio (dimensionless) LF = 2 log10(F/F0) B
bel, power quantity B ratio (dimensionless) LP = log10(P/P0) B

Empirical non-SI units accepted for use with SI

electronvolt eV energy 1eV = 1.60217733 (49) 10-19 J
atomic mass unit u mass 1u = 1.6605402 (10) 10-27 kg
astronomical unit au length 1au = 1.49597870691 (30) 1011 m

Other Non-SI units currently accepted for use with SI

nautical mile nautical mile length 1 nautical mile = 1852 m
knot knot speed 1 knot = 1 nautical mile per hour = (1852/3600) m/s
are a area 1a = 1dam2 = 100 m2
hectare ha area 1ha = 100a = 10000 m2
bar bar pressure 1 bar = 105Pa
ngstrm, angstrom length 1 = 0.1 nm = 10-10 m
barn b area 1b = 10-28 m2

SI prefixes

The following SI prefixes can be used to prefix any of the above units to produce a multiple or submultiple of the original unit.

SI prefixes
10n Prefix Symbol Short scale Long scale Name Decimal Equivalent
1024 yotta Y Septillion Quadrillion 1 000 000 000 000 000 000 000 000
1021 zetta Z Sextillion Trilliard (thousand trillion) 1 000 000 000 000 000 000 000
1018 exa E Quintillion Trillion 1 000 000 000 000 000 000
1015 peta P Quadrillion Billiard (thousand billion) 1 000 000 000 000 000
1012 tera T Trillion Billion 1 000 000 000 000
109 giga G Billion Milliard (thousand million) 1 000 000 000
106 mega M Million 1 000 000
103 kilo k Thousand 1 000
102 hecto h Hundred 100
101 deca, deka da Ten 10
10−1 deci d Tenth 0.1
10−2 centi c Hundredth 0.01
10−3 milli m Thousandth 0.001
10−6 micro Millionth 0.000 001
10−9 nano n Billionth Milliardth 0.000 000 001
10−12 pico p Trillionth Billionth 0.000 000 000 001
10−15 femto f Quadrillionth Billiardth 0.000 000 000 000 001
10−18 atto a Quintillionth Trillionth 0.000 000 000 000 000 001
10−21 zepto z Sextillionth Trilliardth 0.000 000 000 000 000 000 001
10−24 yocto y Septillionth Quadrillionth 0.000 000 000 000 000 000 000 001
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Obsolete SI prefixes

The following SI prefixes are no longer in use.

Obsolete SI prefixes
10n Prefix Symbol Number name Decimal equivalent
104 myria ma Myriad (ten thousand) 10 000
10−4 myrio mo Myriadth (ten thousandth) 0.000 1
Also obsolete are double prefixes, such as those formerly used in micromicrofarads, hectokilometres, micromillimetres, etc.
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Spelling variations

Several nations, notably the United States, typically use the spellings 'meter' and 'liter' instead of 'metre' and 'litre'. This is in keeping with standard American English spelling (for example, Americans also use 'center' rather than 'centre,' using the latter only rarely for its stylistic implications; see also American and British English differences). In addition, the official US spelling for the SI prefix 'deca' is 'deka'.

The US government has approved these spellings for official use, but the BIPM only recognizes the British English spellings as official names for the units. In scientific contexts only the symbols are used; since these are universally the same, the differences do not arise in practice in scientific use.

The unit 'gram' is also sometimes spelled 'gramme' in English-speaking countries other than the United States, though that is an older spelling and use is declining.

See also

External links


  • BIPM (SI maintenance agency) (http://www.bipm.fr/en/si/) (home page)
  • BIPM reference (http://www.bipm.org/en/publications/brochure/) (SI reference)


Pro-metric pressure groups

Further reading

  • I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC: Quantities, Units and Symbols in Physical Chemistry, 2nd ed., Blackwell Science Inc 1993, ISBN 0632035838.

  Results from FactBites:
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SI is sometimes referred to as the metric system (especially in the United States, which has not widely adopted it, and the UK, where conversion is incomplete).
The unit of time is the duration of exactly 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of caesium-133 atom.
The unit of angle is the angle subtended at the centre of a circle by an arc of the circumference equal in length to the radius of the circle.
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