International System of Units

The International System of Units, internationally known by the abbreviation SI (from its official French name, Système international d'unités), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce. The International Bureau of Weights and Measures (abbreviated BIPM from French: Bureau international des poids et mesures) coordinates the SI.

The SI comprises a coherent 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. Twenty-two coherent derived units have been provided with special names and symbols. The 7 base units and the 22 coherent derived units with special names and symbols may be used in combination to express other coherent derived units. Since the sizes of coherent units will be convenient for only some applications and not for others, the SI provides 24 prefixes which, when added to the name and symbol of a coherent unit produce 24 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. The current way of defining the SI is a result of a decades-long move towards definitions of the units that do not depend on artefacts made as physical realisations. A consequence is that as science and technologies develop, new and potentially 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 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, and is based on the metre–kilogram–second system of units (MKS) combined with ideas from the development of the CGS system.

Definition The International System of Units consists of a set of seven defining constants with seven corresponding base units, derived units, and a set of decimal-based multipliers that are used as prefixes.

SI defining constants

The seven defining constants are the most fundamental feature of the definition of the system of units. Each defining constant consists of an exact numerical value and units. The 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. The values assigned to these constants were fixed to ensure continuity with previous definitions of the base units.

SI base units

The SI selects seven units to serve as base units, corresponding to seven base physical quantities. They are the second for time, metre for length, kilogram for mass, ampere for electric current, kelvin for thermodynamic temperature, mole for amount of substance, and candela for luminous intensity. The base units are defined in terms of the defining constants. For example, the kilogram is defined by taking the Planck constant h to be 6.62607015×10−34 J⋅s, giving the expression in terms of the defining constants

1 kg = ⁠(299792458)2/(6.62607015×10−34)(9192631770)⁠⁠h ΔνCs/c2⁠. All units in the SI can be expressed in terms of the base units, and the base units serve as a preferred set for expressing or analysing the relationships between units. The choice of which and even how many quantities to use as base quantities is not fundamental or even unique – it is a matter of convention.

Derived units

The system allows for an unlimited number of additional units, called derived units, which can always be represented as products of powers of the base units, possibly with a nontrivial numeric multiplier. When that multiplier is one, the unit is called a coherent derived unit. For example, the coherent derived SI unit of velocity is the metre per second, with the symbol m/s. The base and coherent derived units of the SI together form a coherent system of units (the set of coherent SI units). A useful property of a coherent system is that when the numerical values of physical quantities are expressed in terms of the units of the system, then the equations between the numerical values have exactly the same form, including numerical factors, as the corresponding equations between the physical quantities. Twenty-two coherent derived units have been provided with special names and symbols as shown in the table below. The radian and steradian have no base units but are treated as derived units for historical reasons.

The derived units in the SI are formed by powers, products, or quotients of the base units and are unlimited in number.

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