Definition:SI Units/Derived
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Definition
The units derived from the SI base units include the following:
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 $\mathrm V \, \mathrm s \, \mathrm A^{-1}$ |
$\mathrm A / \mathrm m^{-1}$ | Magnetic Field Strength | $\mathsf {I L}^{-1}$ | $\mathrm A \, \mathrm m^{-1}$ | $\mathrm A \, \mathrm m^{-1}$ or $\mathrm H / \mu$ | |
$\mathrm A / \mathrm m^{-1}$ | 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
- 1969: J.C. Anderson, D.M. Hum, B.G. Neal and J.H. Whitelaw: Data and Formulae for Engineering Students (2nd ed.) ... (previous) ... (next): $1.$ Units and Abbreviations: $1.2$ SI units $(2)$ Derived units