International System of Units

The International System of Units, known by the international abbreviation SI[lower-alpha 1] in all languages[1]:125[2]:iii[3] and sometimes pleonastically as the SI system,[lower-alpha 2] is the modern form[1]:117[6][7] of the metric system[lower-alpha 4] and based on the metre[lower-alpha 5] as the unit of length and either the kilogram[lower-alpha 6] as the unit of mass or the kilogram-force[lower-alpha 7] as the unit of force.</ref> and the world's most widely used system of measurement.[1]:123[8][9] Established and maintained[10] by the General Conference on Weights and Measures[lower-alpha 10] (CGPM[lower-alpha 11]), it is the only system of measurement with an official status[lower-alpha 13] in nearly every country in the world,[lower-alpha 14] employed in science, technology, industry, and everyday commerce.

SI defining constants
Symbol Defining constant Exact value
ΔνCs hyperfine transition frequency of Cs9192631770 Hz
c speed of light299792458 m/s
h Planck constant6.62607015×10−34 Js
e elementary charge1.602176634×10−19 C
k Boltzmann constant1.380649×10−23 J/K
NA Avogadro constant6.02214076×1023 mol−1
Kcd luminous efficacy of 540 THz radiation683 lm/W
SI base units
Symbol Name Quantity
s secondtime
m metrelength
kg kilogrammass
A ampereelectric current
K kelvinthermodynamic temperature
mol moleamount of substance
cd candelaluminous intensity

The SI comprises a coherent[lower-alpha 15] system of units of measurement starting with seven base units, which are the second (symbol s, the unit of time), metre (m, length), kilogram (kg, mass), ampere (A, electric current), kelvin (K, thermodynamic temperature), mole (mol, amount of substance), and candela (cd, luminous intensity). The system can accommodate coherent units for an unlimited number of additional quantities. These are called coherent derived units, which can always be represented as products of powers of the base units.[lower-alpha 16] Twenty-two coherent derived units have been provided with special names and symbols.[lower-alpha 17]

The seven base units and the 22 coherent derived units with special names and symbols may be used in combination to express other coherent derived units.[lower-alpha 18] Since the sizes of coherent units will be convenient for only some applications and not for others, the SI provides twenty-four prefixes which, when added to the name and symbol of a coherent unit[lower-alpha 19] produce twenty-four additional (non-coherent) SI units for the same quantity; these non-coherent units are always decimal (i.e. power-of-ten) multiples and sub-multiples of the coherent unit.[lower-alpha 20][lower-alpha 21] The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves.

Since 2019, the magnitudes of all SI units have been defined by declaring that seven defining constants have certain exact numerical values when expressed in terms of their SI units. These defining constants are the speed of light in vacuum c, the hyperfine transition frequency of caesium ΔνCs, the Planck constant h, the elementary charge e, the Boltzmann constant k, the Avogadro constant NA, and the luminous efficacy Kcd. The nature of the defining constants ranges from fundamental constants of nature such as c to the purely technical constant Kcd. Prior to 2019, h, e, k, and NA were not defined a priori but were rather very precisely measured quantities. In 2019, their values were fixed by definition to their best estimates at the time, ensuring continuity with previous definitions of the base units.

The current way of defining the SI is a result of a decades-long move towards increasingly abstract and idealised formulation in which the realisations of the units are separated conceptually from the definitions. A consequence is that as science and technologies develop, new and superior realisations may be introduced without the need to redefine the unit. One problem with artefacts is that they can be lost, damaged, or changed; another is that they introduce uncertainties that cannot be reduced by advancements in science and technology. The last artefact used by the SI was the International Prototype of the Kilogram, a cylinder of platinum–iridium.

The original motivation for the development of the SI was the diversity of units that had sprung up within the centimetre–gram–second (CGS) systems (specifically the inconsistency between the systems of electrostatic units and electromagnetic units) and the lack of coordination between the various disciplines that used them. The General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM), which was established by the Metre Convention of 1875, brought together many international organisations to establish the definitions and standards of a new system and to standardise the rules for writing and presenting measurements. The system was published in 1960 as a result of an initiative that began in 1948, so it is based on the metre–kilogram–second system of units (MKS) rather than any variant of the CGS.

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