International System of Units

The International System of Units, abbreviated as SI from its French name *Système international d'unités*, is the modern version of the metric system and the most widely used measurement system globally. It holds official status in nearly every country and is applied in science, technology, industry, and daily commerce. The system is overseen by the International Bureau of Weights and Measures (BIPM).

The SI is built around seven base units: the second (s) for time, the metre (m) for length, the kilogram (kg) for mass, the ampere (A) for electric current, the kelvin (K) for thermodynamic temperature, the mole (mol) for amount of substance, and the candela (cd) for luminous intensity. From these, an unlimited number of additional units—called coherent derived units—can be formed as products of powers of the base units. Twenty-two of these coherent derived units have been given special names and symbols. These base and derived units can be combined to express other coherent derived units. Because coherent units are not always convenient in size, the SI also provides 24 prefixes that, when added to a unit’s name or symbol, create non-coherent decimal multiples or submultiples of that unit.

The current definition of the SI is the result of a long effort to move away from definitions relying on physical artefacts. Artefacts can be lost, damaged, or changed, and they introduce uncertainties that cannot be reduced by scientific progress. By defining units through constants, new and better realisations can be introduced without redefining the unit itself.

The SI was developed to address the diversity of units in the centimetre–gram–second (CGS) systems, particularly the inconsistency between electrostatic and electromagnetic units, and the lack of coordination across disciplines. The General Conference on Weights and Measures (CGPM), established by the Metre Convention of 1875, brought together international organisations to define and standardise the system. Published in 1960, the SI grew from an initiative starting in 1948 and is based on the metre–kilogram–second (MKS) system, combined with ideas from the CGS system.

The system’s definition rests on seven defining constants: 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). These constants range from fundamental natural constants to the technical constant Kcd. Their assigned values were chosen to ensure continuity with earlier definitions of the base units.

The seven base units correspond to seven base physical quantities. Each base unit is defined in terms of these constants. For instance, the kilogram is defined by fixing the Planck constant h to 6.62607015×10⁻³⁴ J·s, leading to an expression like 1 kg = (299792458)² / (6.62607015×10⁻³⁴)(9192631770) · h ΔνCs / c². All SI units can be expressed in terms of the base units, which serve as a preferred set for analysing relationships between units. The choice of base quantities is a matter of convention, not fundamental or unique.

Derived units can always be represented as products of powers of base units, possibly with a nontrivial numeric multiplier. When that multiplier is one, the unit is coherent. For example, the coherent derived SI unit for velocity is the metre per second (m/s). The base and coherent derived units together form a coherent system, meaning that equations between numerical values in these units match the form of the physical equations. Twenty-two coherent derived units have special names and symbols; the radian and steradian are treated as derived units for historical reasons, though they have no base units. Derived units are formed by powers, products, or quotients of the base units.