PlanetPhysics/SI Units and Derivations

The seven SI base units are given in the table below. These units are assumed to be independent of each other.

base quantity	SI base unit	symbol
length, [[../Position/|position]]	meter	$\mathrm{m}$
[[../CosmologicalConstant/|mass]]	kilogram	$\mathrm{k}\mathrm{g}$
time	second	$\mathrm{s}$
current	ampere	$\mathrm{A}$
[[../BoltzmannConstant/|temperature]]	Kelvin	$\mathrm{K}$
amount of substance	mole	$\mathrm{m}\mathrm{o}\mathrm{l}$
intensity	candela	$\mathrm{c}\mathrm{d}$

There are many quantities that can be measured using units that are derived from the base units. Some of these are written in terms of the base units. Some examples are given in the table below.

quantity	SI derived unit	symbol
area	[[../PiecewiseLinear/|square]] meter	${\mathrm{m}}^{\mathrm{2}}$
[[../Volume/|volume]]	cubic meter	${\mathrm{m}}^{\mathrm{3}}$
[[../Velocity/|speed]], [[../Velocity/|velocity]]	meter per second	$\mathrm{m}/\mathrm{s}$
[[../Acceleration/|acceleration]]	meter per second squared	$\mathrm{m}/{\mathrm{s}}^{\mathrm{2}}$
density	kilogram per cubic meter	$\mathrm{k}\mathrm{g}/{\mathrm{m}}^{\mathrm{3}}$
specific volume	cubic meter per kilogram	${\mathrm{m}}^{\mathrm{3}}/\mathrm{k}\mathrm{g}$
concentration	mole per cubic meter	$\mathrm{m}\mathrm{o}\mathrm{l}/{\mathrm{m}}^{\mathrm{3}}$
[[../CosmologicalConstant2/|wave]] number	reciprocal meter	${\mathrm{m}}^{\mathrm{-}\mathrm{1}}$
current density	ampere per square meter	$\mathrm{A}/{\mathrm{m}}^{\mathrm{2}}$
[[../MagneticInductionVector/|magnetic field strength]]	ampere per cubic meter	$\mathrm{A}/{\mathrm{m}}^{\mathrm{3}}$
luminance	candela per square meter	$\mathrm{c}\mathrm{d}/{\mathrm{m}}^{\mathrm{2}}$

Other derived units have their own names. Some examples are given in the table below.

quantity	SI unit	symbol	derivation from other SI units
volume	liter	$\mathrm{L}$ or $\mathrm{\ell }$	$\mathrm{1}{\mathrm{0}}^{\mathrm{-}\mathrm{3}}{\mathrm{m}}^{\mathrm{3}}$
plane angle	radian	$\mathrm{r}\mathrm{a}\mathrm{d}$
[[../CoIntersections/|solid]] angle	steradian	$\mathrm{s}\mathrm{r}$
frequency	hertz	$\mathrm{H}\mathrm{z}$	${\mathrm{s}}^{\mathrm{-}\mathrm{1}}$
[[../Thrust/|force]]	newton	$\mathrm{N}$	$\mathrm{k}\mathrm{g}\mathrm{\cdot }\mathrm{m}/{\mathrm{s}}^{\mathrm{2}}$
pressure, stress	[[../LQG2/|Pascal]]	$\mathrm{P}\mathrm{a}$	$\mathrm{N}/{\mathrm{m}}^{\mathrm{2}}$
[[../CosmologicalConstant/|energy]], [[../Work/|work]]	joule	$\mathrm{J}$	$\mathrm{N}\mathrm{\cdot }\mathrm{m}$
[[../Power/|power]]	watt	$\mathrm{W}$	$\mathrm{J}/\mathrm{s}$
[[../Charge/|charge]]	coulomb	$\mathrm{C}$	$\mathrm{A}\mathrm{\cdot }\mathrm{s}$
potential difference	volt	$\mathrm{V}$	$\mathrm{W}/\mathrm{A}$
[[../Conduction/|resistance]]	ohm	$\mathrm{\Omega }$	$\mathrm{V}/\mathrm{A}$
temperature	degree Celsius	${}^{\mathrm{\circ }}\mathrm{C}$	$\mathrm{K}+273.15$

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\noindent Reference: National Institute of Standards and Technology, http://physics.nist.gov/cuu/Units/