Overview
An SI derived unit is a unit of measurement in the International System of Units (SI) that can be written as a product of powers of the seven SI base units, or that is dimensionless. Derived units appear throughout science and engineering because most physical quantities (force, pressure, energy, electric potential, etc.) are not described directly by the base units. A number of derived units have been given conventional names and symbols for convenience.

Base units and expression

The SI base units are metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol) and candela (cd). Any derived unit can be expressed algebraically in terms of these. For example, the newton (N), a unit of force, is kg·m·s^-2, and the joule (J), a unit of energy, is N·m or kg·m^2·s^-2. The hertz (hertz) is defined as one cycle per second (s^-1) and is the SI unit of frequency. Some derived units are dimensionless: the radian (rad) and steradian (sr) describe plane and solid angles respectively.

Named derived units

  • Radian (rad) — plane angle, dimensionless
  • Steradian (sr) — solid angle, dimensionless
  • Hertz (Hz) — frequency, s^-1
  • Newton (N) — force, kg·m·s^-2
  • Pascal (Pa) — pressure, N·m^-2
  • Joule (J) — energy, N·m
  • Watt (W) — power, J·s^-1
  • Coulomb (C) — electric charge
  • Volt (V) — electric potential
  • Farad (F) — capacitance
  • Ohm (Ω) — electrical resistance
  • Siemens (S) — electrical conductance
  • Weber (Wb) — magnetic flux
  • Tesla (T) — magnetic flux density
  • Henry (H) — inductance
  • Degree Celsius (°C) — temperature interval (offset relative to K)
  • Lumen (lm) — luminous flux
  • Lux (lx) — illuminance
  • Becquerel (Bq) — radioactivity (decays per second)
  • Gray (Gy) — absorbed dose of ionizing radiation
  • Sievert (Sv) — dose equivalent for biological effect
  • Katal (kat) — catalytic activity

History and standardization

The SI system and its named derived units were progressively standardized in the 20th century and are maintained by the Bureau International des Poids et Mesures (BIPM). The set of seven base units was chosen so that most other practical units can be derived in a coherent way, meaning a derived unit is directly equal to a product of base units without extra numerical factors.

Uses, conventions and notable points

Named derived units simplify notation and communication across disciplines: saying "pascal" is often clearer than writing "kg·m^-1·s^-2." Most derived units accept SI prefixes (milli-, kilo-, mega-, etc.) where it is sensible to do so. Dimensionless derived units such as the radian are treated specially in some contexts because they represent ratios rather than independent physical dimensions. Degree Celsius has a special name but differs from kelvin by an additive offset, so care is needed when converting thermodynamic quantities. These units form the backbone of quantitative measurement in science, industry and commerce worldwide.

For further authoritative definitions and official tables of SI units, refer to international metrology resources.