SI derived unit

Short description: Measurement unit derived from base metric units

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

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 is "m".[1]

## Contents

* 1 Special names
* 2 Examples of derived quantities and units
* 3 Other units used with SI
* 4 Supplementary units
* 5 See also
* 6 References
* 7 Bibliography
* 8 External links

## Special names

The International System of Units assigns special names to 22 derived units, which includes two dimensionless derived units, the radian (rad) and the steradian (sr).

Named units derived from SI base units[2] Name  | Symbol | Quantity | Equivalents  | SI base unit
Equivalents

|
|
|
|

hertz | Hz  | frequency | 1/s  | s−1
radian | rad  | angle | m/m  | 1
steradian | sr  | solid angle | m2/m2 | 1
newton | N  | force, weight | kg⋅m/s2 | kg⋅m⋅s−2
pascal | Pa  | pressure, stress | N/m2 | kg⋅m−1⋅s−2
joule | J  | energy, work, heat | m⋅N, C⋅V, W⋅s  | kg⋅m2⋅s−2
watt | W  | power, radiant flux | J/s, V⋅A  | kg⋅m2⋅s−3
coulomb | C  | electric charge or quantity of electricity  | s⋅A, F⋅V  | s⋅A
volt | V  | voltage, electrical potential difference, electromotive force | W/A, J/C  | kg⋅m2⋅s−3⋅A−1
farad | F  | electrical capacitance | C/V, s/Ω  | kg−1⋅m−2⋅s4⋅A2
ohm  | Ω  | electrical resistance, impedance, reactance | 1/S, V/A  | kg⋅m2⋅s−3⋅A−2
siemens | S  | electrical conductance | 1/Ω, A/V  | kg−1⋅m−2⋅s3⋅A2
weber | Wb  | magnetic flux | J/A, T⋅m2,V⋅s  | kg⋅m2⋅s−2⋅A−1
tesla | T  | magnetic induction, magnetic flux density | V⋅s/m2, Wb/m2, N/(A⋅m)  | kg⋅s−2⋅A−1
henry | H  | electrical inductance | V⋅s/A, Ω⋅s, Wb/A  | kg⋅m2⋅s−2⋅A−2
degree Celsius | °C  | temperature relative to 273.15 K | K  | K
lumen | lm  | luminous flux | cd⋅sr  | cd
lux | lx  | illuminance | lm/m2 | cd⋅m−2
becquerel | Bq  | radioactivity (decays per unit time)  | 1/s  | s−1
gray | Gy  | absorbed dose (of ionizing radiation)  | J/kg  | m2⋅s−2
sievert | Sv  | equivalent dose (of ionizing radiation)  | J/kg  | m2⋅s−2
katal | kat  | catalytic activity  | mol/s  | s−1⋅mol.

## Examples of derived quantities and units

## Other units used with SI

Some other units such as the hour, litre, tonne, bar, and electronvolt are not SI units, but are widely used in conjunction with SI units.

## Supplementary units

Until 1995, the SI classified the radian and the steradian as supplementary units, but this designation was abandoned and the units were grouped as derived units.[3]

## See also

* List of physical quantities
* International System of Quantities (ISQ)
* International Vocabulary of Metrology
* Metric prefix
* Metric system

## References

1. ↑ Suplee, Curt (2 July 2009). "Special Publication 811". http://physics.nist.gov/Pubs/SP811/sec06.html.
2. ↑ International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), ISBN 92-822-2213-6, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf
3. ↑ "Resolution 8 of the CGPM at its 20th Meeting (1995)". Bureau International des Poids et Mesures. http://www.bipm.org/en/CGPM/db/20/8/.

## Bibliography

* I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC (June 1993). Quantities, Units and Symbols in Physical Chemistry (2nd ed.). Blackwell Science Inc. p. 72.

## External links

* v
* t
* e

SI units

Base units|

* ampere
* candela
* kelvin
* kilogram
* {{{sp}}}}}|us|er|re}}
* mole
* second

Derived units
with special names|

* becquerel
* coulomb
* degree Celsius
* farad
* gray
* henry
* hertz
* joule
* katal
* lumen
* lux
* newton
* ohm
* pascal
* radian
* siemens
* sievert
* steradian
* tesla
* volt
* watt
* weber

Other accepted units|

* astronomical unit
* dalton
* day
* decibel
* degree of arc
* electronvolt
* hectare
* hour
* {{{sp}}}}}|us|er|re}}
* minute
* minute and second of arc
* neper
* tonne

See also|

* Conversion of units
* Metric prefixes
* 2005–2019 definition
* 2019 redefinition
* Systems of measurement

* Book
* Category

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