In certain fields, for example, chemistry and physics, it is often useful to convert between various energy units.  Common examples are the conversions among frequency (MHz), wavenumber (1/cm), energy (hartrees), molar energy (kJ/mol), and temperature (kelvin).

Energy conversions are performed by using the 'energy'=true option with the functions convert/units and convert/dimensions.

Energy conversions may be seen as applying the following transformations on the dimensions of the units:

where c is the absolute value of the speed of light in meters per second, by definition $299792458$, h is the absolute value of the Planck constant in joule seconds, approximately $6.6260755\times {10}^{\mathrm{-34}}$, and k is the absolute value of the Boltzmann constant in joules per kelvin, approximately $1.380658\times {10}^{\mathrm{-23}}$.

$\mathrm{convert}\left(\frac{1}{'\mathrm{centimeter}'}\,'\mathrm{dimensions}'\,'\mathrm{energy}'=\mathrm{true}\right)$

$\frac{1}{\mathrm{length}}$

$\mathrm{convert}\left(83.59347279\,'\mathrm{units}'\,\frac{1}{'\mathrm{centimeter}'}\,'\mathrm{megahertz}'\,'\mathrm{energy}'=\mathrm{true}\right)$

$2.506069268\times {10}^6$

$\mathrm{convert}\left(83.59347279\,'\mathrm{units}'\,\frac{1}{'\mathrm{centimeter}'}\,'\mathrm{attojoules}'\,'\mathrm{energy}'=\mathrm{true}\right)$

$0.001660539049$

$\mathrm{convert}\left(83.59347279\,'\mathrm{units}'\,\frac{1}{'\mathrm{centimeter}'}\,\frac{'\mathrm{kilojoules}'}{'\mathrm{mole}'}\,'\mathrm{energy}'=\mathrm{true}\right)$

$1.000000006$

$\mathrm{convert}\left(83.59347279\,'\mathrm{units}'\,\frac{1}{'\mathrm{centimeter}'}\,'\mathrm{kelvin}'\,'\mathrm{energy}'=\mathrm{true}\right)$

$120.2723964$

$\mathrm{convert}\left('C'\,'\mathrm{dimensions}'\,'\mathrm{energy}'=\mathrm{true}\right)$

$1$

$\mathrm{convert}\left(1.6021917\times {10}^{\mathrm{-19}}\,'\mathrm{units}'\,'C'\,\mathrm{sqrt}\left('\mathrm{centimeters}''\mathrm{gram}'\right)\,'\mathrm{energy}'=\mathrm{true}\right)$

$1.602191700\times {10}^{\mathrm{-20}}$

$\mathrm{convert}\left(1.6021917\times {10}^{\mathrm{-19}}\,'\mathrm{units}'\,'C'\,\frac{{'\mathrm{centimeters}'}^{\frac{3}{2}}{'\mathrm{gram}'}^{\frac{1}{2}}}{'\mathrm{second}'}\,'\mathrm{energy}'=\mathrm{true}\right)$

$4.803249879\times {10}^{\mathrm{-10}}$

$\mathrm{convert}\left(\frac{'m'}{'s'}\,'\mathrm{dimensions}'\,'\mathrm{energy}'=\mathrm{true}\right)$

$1$

$\mathrm{convert}\left(2.99792458\times {10}^8\,'\mathrm{units}'\,\frac{'m'}{'s'}\,'\mathrm{planck}'\,'\mathrm{energy}'=\mathrm{true}\right)$

$6.626070041\times {10}^{\mathrm{-34}}$

$\mathrm{convert}\left('W'\,'\mathrm{dimensions}'\,'\mathrm{energy}'=\mathrm{true}\right)$

$\frac{1}{{\mathrm{length}}^2}$

$\mathrm{convert}\left(299.7924580\,'\mathrm{units}'\,'\mathrm{newtons}'\,'\mathrm{watts}'\,'\mathrm{energy}'=\mathrm{true}\right)$

$8.987551787\times {10}^{10}$

$\mathrm{convert}\left(299.7924580\,'\mathrm{units}'\,'\mathrm{joule}'\,\mathrm{sqrt}\left('\mathrm{watts}'\right)\,'\mathrm{energy}'=\mathrm{true}\right)$

$1.164642654\times {10}^{19}$

Lide, David, R., ed. Handbook of Chemistry and Physics. CRC Press, 1996.