SI derived units are

units of measurement A unit of measurement, or unit of measure, is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other qua ...

derived from the seven

SI base unit The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which al ...

s specified by the

International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), 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 s ...

(SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are

dimensionless Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another sy ...

, as when the units cancel out in ratios of like quantities. SI coherent derived units involve only a trivial proportionality factor, not requiring conversion factors. The SI has special names for 22 of these coherent derived units (for example,

hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in ter ...

, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the

square metre The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter ( American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square ...

(m²), the SI derived unit of area; and the

kilogram per cubic metre The kilogram per cubic metre (symbol: kg·m−3, or kg/m3) is the unit of density in the International System of Units (SI). It is defined by dividing the SI unit of mass, the kilogram, by the SI unit of volume, the cubic metre. Conversions *1 k ...

(kg/m³ or kg⋅m⁻³), the SI derived unit of

density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

. The names of SI coherent derived units, when written in full, are always in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz", while the symbol for

metre The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...

is "m".

Special names

The International System of Units assigns special names to 22 derived units, which includes two dimensionless derived units, the

radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at ...

(rad) and the

steradian The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. A solid angle in the fo ...

(sr).

By field of application

Kinematics

Mechanics

Chemistry

Electromagnetics

Photometry

Thermodynamics

Other units used with SI

Some other units such as the

hour An hour (symbol: h; also abbreviated hr) is a unit of time historically reckoned as of a day and defined contemporarily as exactly 3,600 seconds ( SI). There are 60 minutes in an hour, and 24 hours in a day. The hour was initially establis ...

litre The litre ( Commonwealth spelling) or liter ( American spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metres (m3). A ...

tonne The tonne ( or ; symbol: t) is a unit of mass equal to 1,000 kilograms. It is a non-SI unit accepted for use with SI. It is also referred to as a metric ton in the United States to distinguish it from the non-metric units of the s ...

, bar, and

electronvolt In physics, an electronvolt (symbol eV), also written electron-volt and electron volt, is the measure of an amount of kinetic energy gained by a single electron accelerating through an Voltage, electric potential difference of one volt in vacuum ...

are not SI units, but are widely used in conjunction with SI units.

Supplementary units

Until 1995, the SI classified the

and the

as ''supplementary units'', but this designation was abandoned and the units were grouped as derived units.

References

Bibliography

External links

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