International System of Units

The International System of Units, (symbol: SI) (for the French phrase Système International d'Unités), 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. SI was selected from the existing Metre-Kilogram-Second system of units (MKS), with the addition of extra units, rather than the older Centimetre-Gram-Second system of units (CGS). 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). However, not all metric units of measurement are accepted as SI units. It is perhaps most accurately referred to as French Units, since that nation was the first to originate it.

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.

Origin

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

Basis

SI is built on seven SI base units, such as the kilogram, metre, and second. 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 for in symbols where the unit is the same as the name of a person, or 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")

It is preferable to keep the symbol in upright roman type (for example, kg for kilograms, m for metres), 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, 7.3·10² m²

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.

The symbol (or prefix) can be used in place of the decimal separator. 2.3k would be 2k3, 4.7A (Amps) would be 4A7, and 0.0047F would be 4m7F.

The system can legally be used in every country in the world, and in many countries its use is obligatory. Those countries that still give official recognition to non-SI units (e.g. the US and UK) define them in terms of SI units; for example, the inch is defined to be exactly 0.0254 metres. It was adopted by the 11th General Conference on Weights and Measures (CGPM) in 1960. (See weights and measures for a history of the development of units of measurement.)

Units

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.

Name	Unit Symbol	Measure Of	Definition
metre	m	Length	The unit of length is equal to the length of the path travelled by light in a vacuum during the time interval of 1/299 792 458 of a second. 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), Sèvres, Paris. Note that the kilogram is the only base unit with a prefix; the gram is defined as a derived unit, equal to 1/1 000 of a kilogram.
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 caesium-133 atom.
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 2×10 ⁻⁷ newton per metre of length.
kelvin	K	Absolute 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.
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 kilogram of pure carbon-12. (Elementary entities may be atoms, molecules, ions, electrons, or particles.) It is approximately equal to 6.02214199×10²³ 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 540×10¹² hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

Dimensionless derived units

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

Name	Unit Symbol	Measure Of	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 $2\pi$ 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 $4\pi$ 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.

Name	Unit Symbol	Measure of	Expressed in base units
hertz	Hz	Frequency	s^-1
newton	N	Force	kg m/s ²
joule	J	Energy	N m = kg m²/s²
watt	W	Power	J/s = kg m²/s³
pascal	Pa	Pressure	N/m² = kg/m s²
lumen	lm	Luminous flux	cd sr
lux	lx	Illuminance	cd sr/m²
coulomb	C	Electric Charge	A s
volt	V	Electric 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	A² s⁴ kg^-1 m^-2 = $\Omega$ ^-1 s
weber	Wb	Magnetic flux	kg m²/s² A
tesla	T	Magnetic flux density	Wb/m² = kg/s² A
henry	H	Inductance	kg m² A^-2 s^-2 = $\Omega$ s
siemens	S	Electric conductance	$\Omega$ ^-1 = kg^-1 m^-2 A² s³
degree Celsius	°C	Celsius temperature	K
becquerel	Bq	Radioactivity (decays per unit time)	s^-1
gray	Gy	Absorbed dose (of ionising radiation)	J/kg
sievert	Sv	Dose equivalent (of ionising radiation)	J/kg
katal	kat	Catalytic activity	mol/s

The unit of volume litre, abbreviated L or l and being equal to 0.001 m³, is not an SI unit but is "accepted for use with the International System."

Spelling variations

Several nations, notably the United States, typically use the spellings 'meter' and 'liter' instead of 'metre' and 'litre', in keeping with standard American English spelling (for example, Americans also use 'center' rather than 'centre'; see also American and British English differences). In addition, the official US spelling for the SI prefix 'deca' is 'deka' (again, a variation not recognized by the BIPM).

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 abbreviations 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 is falling out of use.

External links

Official

SI maintenance agency (home page)
BIPM reference (SI reference)

Information

US NIST reference on SI
SI -- Its History and Use in Science and Industry
Nelson, Robert A., "The International System of Units Its History and Use in Science and Industry". Via Satellite, February 2000.
A Dictionary of Units of Measurement by Russ Rowlett
Calculation of many metric and American Units