SI derived units are units of measurement derived from the seven

base units A base unit (also referred to as a fundamental unit) is a unit adopted for measurement of a '' base quantity''. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in ter ...

specified by the International System of Units (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 In engineering, applied mathematics, and physics, the Buckingham theorem is a key theorem in dimensional analysis. It is a formalization of Rayleigh's method of dimensional analysis. Loosely, the theorem states that if there is a physically me ...

). Some are

dimensionless A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

, as when the units cancel out in ratios of like quantities. The SI has special names for 22 of these derived units (for example,

hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that o ...

, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (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), defined by mass in kilograms divided by volume in cubic metres. Conversions *1 kg/m3 = 1 g/ L (exactly) *1 kg/m3 = 0 ...

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

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

. The names of SI 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 (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefi ...

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. The unit was formerly an SI supplementary unit (before tha ...

(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. Whereas an angle in radian ...

(sr).

Examples of derived quantities and units

Other units used with SI

Some other units such as the hour,

litre The litre (international spelling) or liter (American English 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 metre (m3 ...

tonne The tonne ( or ; symbol: t) is a unit of mass equal to 1000 kilograms. It is a non-SI unit accepted for use with SI. It is also referred to as a metric ton to distinguish it from the non-metric units of the short ton ( United State ...

, 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 from rest through an 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

* {{Portal bar, Physics Derived sv:SI-enhet#Härledda enheter