International System of Units

The International System of Units, abbreviated SI from its French name Système international d’unités, is the internationally agreed system for expressing measurements of physical quantities. It provides a common framework for physics, chemistry, engineering, and trade. SI combines seven base units, units derived from them, and prefixes denoting decimal multiples and submultiples. Since May 20, 2019, its definitions have rested on exact numerical values assigned to seven defining constants, rather than on a material reference artifact. (nist.gov)

Historical development and governance

SI developed from the metric system introduced in France in the late eighteenth century. International cooperation acquired a permanent institutional framework through the Metre Convention, signed in Paris on May 20, 1875. The treaty established the International Bureau of Weights and Measures (BIPM) and an international structure for coordinating measurement standards. The General Conference on Weights and Measures (CGPM) formally adopted the name International System of Units in 1960; the mole became its seventh base unit in 1971. (bipm.org)

Definitions progressively moved from artifacts and astronomical references toward reproducible physical phenomena. The metre’s platinum–iridium prototype was replaced by a krypton-86 radiation definition in 1960, then by a definition based on light propagation in 1983. On November 16, 2018, the CGPM approved revised definitions of the kilogram, ampere, kelvin, and mole, effective May 20, 2019. The BIPM publishes the authoritative SI Brochure. (bipm.org)

Base quantities and units

The seven base quantities and corresponding units remain the conventional foundation for organizing SI quantities and their dimensions. Although the modern system is defined through constants, the distinction between base and derived units remains useful. (bipm.org)

Other SI units are constructed by multiplying powers of these base units. Base quantities are regarded as dimensionally independent by convention; this does not mean that their unit definitions are independent of one another. For example, the metre’s definition uses the second, while the kilogram’s definition involves the metre and second through the dimensions of the Planck constant. (bipm.org)

Definition through constants

SI assigns exact numerical values to the following constants when expressed in the indicated units:

Together, these values determine the scale of all SI units. Thus, one mole contains exactly 6.022 140 76 × 10²³ specified elementary entities. Fixing the constants defines units; it does not eliminate uncertainty from experiments that realize or measure those units. (bipm.org)

Derived units and coherence

Derived units express quantities such as velocity, force, pressure, and energy. Velocity has the unit metre per second, m/s; acceleration has m/s². Some derived units have special names: the newton is kg m s⁻², the pascal is kg m⁻¹ s⁻², and the joule is kg m² s⁻². These names simplify expressions without creating additional base units. (nist.gov)

SI is coherent: coherent derived units are products of powers of base units with no additional numerical factor. Consequently, a physical equation retains its form when quantities are expressed in coherent SI units. Prefix-bearing units belong to SI but generally are not coherent units. The degree Celsius is a special name for the kelvin when expressing Celsius temperature: its unit magnitude equals one kelvin, while the temperature scales differ by an exact offset of 273.15. (nist.gov)

Decimal prefixes and notation

SI prefixes denote powers of ten, including kilo (k, 10³), milli (m, 10⁻³), micro (µ, 10⁻⁶), and nano (n, 10⁻⁹). In November 2022, the CGPM added ronna (R, 10²⁷), quetta (Q, 10³⁰), ronto (r, 10⁻²⁷), and quecto (q, 10⁻³⁰), bringing the total to 24. Prefixes attach directly to unit symbols, as in km and µs. For mass, prefixes attach to gram rather than kilogram: mg, not µkg. (nist.gov)

Unit symbols are upright, case-sensitive mathematical symbols, not ordinary abbreviations. They do not take plural endings or abbreviation periods. A space normally separates a numerical value from its unit, including “25 °C”; plane-angle symbols are exceptions, as in “90°”. Multiplication and division require unambiguous notation, such as N m or m/s. (nist.gov)

Practical realization and traceability

Metrology, the science of measurement, distinguishes a unit’s definition from its practical realization. A Kibble balance, for example, realizes mass by relating mechanical and electrical measurements to the fixed Planck constant. Improved experimental methods can therefore implement the same definition without changing the unit itself. (nist.gov)

Metrological traceability connects a measurement result to a reference through a documented, unbroken chain of calibrations, each contributing to measurement uncertainty. National measurement institutes maintain realizations and reference standards that support this chain. Exact defining constants do not make instruments exact: calibration, environmental effects, and experimental limitations still contribute uncertainty to reported results. (nist.gov)