SI derived units are units of
measurement derived from the
seven
base units 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). 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 one her ...
, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the
square metre (m
2), the SI derived unit of area; and the
kilogram per cubic metre (kg/m
3 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. Mathematicall ...
.
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 p ...
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 radi ...
(sr).
Examples of derived quantities and units
Other units used with SI
Some other units such as the
hour
An hour (symbol: h; also abbreviated hr) is a unit of time conventionally reckoned as of a day and scientifically reckoned between 3,599 and 3,601 seconds, depending on the speed of Earth's rotation. There are 60 minutes in an hour, and 24 ho ...
,
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
Bar or BAR may refer to:
Food and drink
* Bar (establishment), selling alcoholic beverages
* Candy bar
* Chocolate bar
Science and technology
* Bar (river morphology), a deposit of sediment
* Bar (tropical cyclone), a layer of cloud
* Bar (un ...
, 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 vacu ...
are
not SI units, but are widely used in conjunction with SI units.
Supplementary units
Until 1995, the SI classified 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 ...
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 radi ...
as ''supplementary units'', but this designation was abandoned and the units were grouped as derived units.
See also
*
List of physical quantities
This article consists of tables outlining a number of physical quantities.
The first table lists the base quantities used in the International System of Units to define the physical dimension of physical quantities for dimensional analysis. The ...
*
International System of Quantities
The International System of Quantities (ISQ) consists of the quantities used in physics and in modern science in general, starting with basic quantities such as length and mass, and the relationships between those quantities. This system underl ...
(ISQ)
*
International Vocabulary of Metrology
*
Metric prefix
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pr ...
*
Metric system
The metric system is a system of measurement that succeeded the decimalised system based on the metre that had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the Intern ...
References
Bibliography
*
External links
*
{{Portal bar, Physics
Derived
sv:SI-enhet#Härledda enheter