Definition:SI Units

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Definition

The SI Units are the elements of the International System of Units.


SI Base Units

SI Base Units
Name Unit symbol Dimension Symbol
metre $\mathrm m$ $\mathsf L$: Length $l$
kilogram $\mathrm {kg}$ $\mathsf M$: Mass $m$
second $\mathrm s$ $\mathsf T$: Time $t$
ampere $\mathrm A$ $\mathsf I$: Electric Current $I$
kelvin $\mathrm K$ $\Theta$: Temperature $T$
candela $\mathrm {cd}$ $\mathsf J$: Luminous Intensity $I_v$
mole $\mathrm {mol}$ $\mathsf N$: Amount of Substance $n$


SI Supplementary Units

The supplementary SI units are as follows:

SI Supplementary Units
Name Unit symbol Dimension Used for Symbol
radian $\mathrm {rad}$ $\text {none}$ plane angle $\theta$
steradian $\mathrm {sr}$ $\text {none}$ solid angle


SI Derived Units

The units derived from the SI base units include the following:

Derived SI Units
Name of Unit Unit symbol Quantity measured Dimension Base units Derivation
Square metre $\mathrm m^2$ Area $\mathsf L^2$ $\mathrm m^2$
Cubic metre $\mathrm m^3$ Volume $\mathsf L^3$ $\mathrm m^3$
Mechanics
Newton $\mathrm N$ Force $\mathsf M \mathsf L \mathsf T^{-2}$ $\mathrm {kg} \, \mathrm m \, \mathrm s^{-2}$ Mass times acceleration
Joule $\mathrm J$ Energy and work $\mathsf M \mathsf L^2 \mathsf T^{-2}$ $\mathrm {kg} \, \mathrm m^2 \, \mathrm s^{-2}$ $\mathrm N \, \mathrm m$
Watt $\mathrm W$ Power $\mathsf M \mathsf L^2 \mathsf T^{-3}$ $\mathrm {kg} \, \mathrm m^2 \, \mathrm s^{-3}$ $\mathrm J \, \mathrm s^{-1}$ or $\mathrm C \, \mathrm V$
Electricity
Coulomb $\mathrm C$ Electric Charge $\mathsf I \mathsf T$ $\mathrm A \, \mathrm s$ Current times time
Volt $\mathrm V$ Electric Potential $\mathsf M \mathsf L^2 \mathsf T^{−3} \mathsf I^{−1}$ $\mathrm {kg} \, \mathrm m^2 \mathrm s^{-3} \mathrm A^{-1}$ $\mathrm J \, \mathrm C^{-1}$ or $\mathrm W \, \mathrm A^{-1}$
Ohm $\Omega$ Resistance $\mathsf {M L}^2 \mathsf T^{−3} \mathsf I^{−2}$ $\mathrm {kg} \, \mathrm m^2 \mathrm s^{-3} \mathrm A^{-2}$ $\mathrm V \, \mathrm A^{-1}$
Farad $\mathrm F$ Capacitance $\mathsf M^{-1} \mathsf L^{-2} \mathsf T^4 \mathsf I^2$ $\mathrm {kg}^{-1} \, \mathrm m^{-2} \, \mathrm s^4 \mathrm A^2$ $\mathrm C \, \mathrm V^{-1}$
$\mathrm V / \mathrm m$ Electric Field Strength $\mathsf {M L T}^{-3} \mathsf I^{-1}$ $\mathrm {kg} \, \mathrm m \, \mathrm s^{-3} \mathrm A^{-1}$ $\mathrm V \, \mathrm m^{-1}$ or $\mathrm N \, \mathrm C^{-1}$
$\mathrm C / \mathrm m^2$ Electric Flux Density $\mathsf I \mathsf T \mathsf L^{-2}$ $\mathrm A \, \mathrm s \, \mathrm m^{-2}$ $\mathrm C \, \mathrm m^{-2}$
Magnetism
Tesla $\mathrm T$ Magnetic Flux Density $\mathsf {M T}^{-2} \mathsf I^{-1}$ $\mathrm {kg} \, \mathrm s^{-2} \mathrm A^{-1}$ $\mathrm N \, \mathrm m^{-1} \mathrm A^{-1}$ or $\mathrm {Wb} \, \mathrm m^{-2}$
Weber $\mathrm {Wb}$ Magnetic Flux $\mathsf M \mathsf L^2 \mathsf T^{-2} \mathsf I^{-1}$ $\mathrm {kg} \, \mathrm m^2 \, \mathrm s^{-2} \mathrm A^{-1}$ $\mathrm T \, \mathrm m^2$ or $\mathrm V \, \mathrm s$
Henry $\mathrm H$ Inductance $\mathsf {M L}^2 \mathsf T^{-2} \mathsf I^{-2}$ $\mathrm {kg} \, \mathrm m^2 \, \mathrm s^{-2} \mathrm A^{-2}$ $\mathrm {Wb} \, \mathrm A^{-1}$ or $\mathrm V \, \mathrm s \, \mathrm A^{-1}$
$\mathrm A / \mathrm m$ Magnetic Field Strength $\mathsf {I L}^{-1}$ $\mathrm A \, \mathrm m^{-1}$ $\mathrm A \, \mathrm m^{-1}$ or $\mathrm H / \mu$
$\mathrm A / \mathrm m$ Intensity of Magnetization $\mathsf {I L}^{-1}$ $\mathrm A \, \mathrm m^{-1}$ $\mathrm A \, \mathrm m^{-1}$ or $\mathrm H / \mu$


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Also see


Historical Note

The SI units originated in the work done by Joseph Louis Lagrange to establish a decimal system for weights and measures.


Linguistic Note

The abbreviation SI in the term SI units is from the French Le Système International d'Unités (the International System of Units).


Sources

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