International System of Units

SI provides a coherent framework in which units are related by exact mathematical definitions. The seven base units are the second, metre, kilogram, ampere, kelvin, mole, and candela; other units are derived from them, such as the square metre, pascal, and joule.¹ The system is maintained through international metrology, the science of measurement, under arrangements coordinated by the International Bureau of Weights and Measures and the General Conference on Weights and Measures. SI is decimal, so prefixes such as milli-, kilo-, micro-, and giga- scale units by powers of ten. Although the base-and-derived structure is fundamental, SI also permits certain non-SI units for use with it, including the minute, hour, litre, and tonne.²

The 2019 revision replaced definitions tied to physical objects or idealized experimental procedures with definitions based on seven exact constants of nature.¹ The kilogram is now defined by fixing the numerical value of the Planck constant; the ampere by the elementary charge; the kelvin by the Boltzmann constant; and the mole by the Avogadro constant. The second, metre, and candela retain their established conceptual roles, with the second based on a cesium-133 atomic transition and the metre based on the speed of light in vacuum. The change took effect on 20 May 2019, World Metrology Day, and did not alter the size of the units in ordinary practice. It instead made their definitions more stable, universal, and adaptable to improved experiments.³

Derived SI units express relationships among base units and may receive special names and symbols. The newton is kilogram metre per second squared, the joule is a newton metre, and the pascal is a newton per square metre.² Special names simplify technical writing but do not create independent dimensions: a joule can also be written as a kilogram metre squared per second squared. SI symbols are written in upright type, are not followed by full stops, and do not take plural forms; prefixes attach directly to unit symbols, as in km and μs. The degree Celsius is an SI-derived unit with a special name, while the kelvin is the SI base unit for thermodynamic temperature. Dimensionless quantities include the radian and steradian, which have special names retained for clarity in geometry and physics.

SI contains several conventions and edge cases that are easy to overlook. The kilogram is the only base-unit name whose prefix is built into the unit; multiples and submultiples are formed from gram, such as milligram and megagram, rather than by attaching a prefix to kilogram.¹ The 2022 addition of the prefixes ronna-, quetta-, ronto-, and quecto- extended the official range to 10³⁰ and 10⁻³⁰, responding partly to data-intensive science and extremely small measurements.⁴ SI also distinguishes mass from weight: mass is measured in kilograms, whereas weight is a force measured in newtons. Electrical units preserve the names of contributors including ampere, volt, ohm, and weber, linking modern notation to the history of experimental physics. National institutes such as the National Institute of Standards and Technology disseminate practical guidance for applying these rules.⁵

Base unit

One of the seven units from which the SI system derives other units.

Derived unit

A unit formed algebraically from SI base units, sometimes with a special name and symbol.

Metrology

The science of measurement, including units, standards, calibration, and measurement uncertainty.

SI prefix

A decimal multiplier placed before a unit name or symbol, such as kilo- for 10³.

Defining constant

A physical constant assigned an exact numerical value in the modern SI definitions.