In radiometry, radiant energy density is the measure of the amount of radiant energy per unit volume at a given location and time.[1] Its SI unit is joule per cubic metre (J/m3).

It is defined by

${\displaystyle w={\frac {\mathrm {d} W}{\mathrm {d} V}},}$[2]

where

${\displaystyle w}$ is the radiant energy density,
${\displaystyle W}$ is the amount of radiant energy in some volume,
${\displaystyle V}$ is the volume.

## Relation to other radiometric quantities

Because radiation always transmits the energy,[2] it is useful to wonder what the speed of the transmission is. If all the radiation at given location propagates in the same direction, then the radiant flux through a unit area perpendicular to the propagation direction is expressed by radiant flux density, whose value is

${\displaystyle I_{\mathrm {e} }=cw,}$[2]

where

${\displaystyle I_{\mathrm {e} }}$ is the radiant flux density (i.e. radiant flux per unit area),
${\displaystyle c}$ is the speed of light (generally radiation propagation speed),
${\displaystyle w}$ is the radiant energy density.

Contrarily if the radiation intensity is equal in all directions, like in a cavity in a thermodynamic equilibrium, then the energy transmition is best described by radiance (i.e. radiant flux per unit area and unit solid angle), whose value is

${\displaystyle L_{\mathrm {e} }={\frac {c}{4\pi }}w.}$[3]

Radiant exitance through a small opening from such cavity is ${\displaystyle M_{\mathrm {e} }=\pi L_{\mathrm {e} }}$.[4] These relations can be used for example in the black body radiation equations derivation.

## References

1. IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Radiant energy density. Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.R05040. Last update: 2012-08-19; version: 2.3.2. Visited 2013-10-07.
2. Karel Rusňák. Přenos energie elektromagnetickým vlněním. Department of Physics, Faculty of Applied Sciences, University of West Bohemia. 2005-11. Visited 2013-10-06
3. Max Plack. The Theory of Heat Radiation. Equation 21. 1914.
4. Max Plack. The Theory of Heat Radiation. Equation 7. 1914.

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Quantity Unit Dimension Notes
Name Symbol[nb 1] Name Symbol Symbol
Radiant energy Qe[nb 2] joule J ML2T−2 energy
Radiant flux Φe[nb 2] watt W or J/s ML2T−3 radiant energy per unit time, also called radiant power.
Spectral power Φ[nb 2][nb 3] watt per metre W⋅m−1 MLT−3 radiant power per wavelength.
Radiant intensity Ie watt per steradian W⋅sr−1 ML2T−3 power per unit solid angle.
Spectral intensity I[nb 3] watt per steradian per metre W⋅sr−1⋅m−1 MLT−3 radiant intensity per wavelength.
Radiance Le watt per steradian per square metre W⋅sr−1m−2 MT−3 power per unit solid angle per unit projected source area.

confusingly called "intensity" in some other fields of study.

or
L[nb 4]
or

metre per hertz

W⋅sr−1m−3
or
W⋅sr−1⋅m−2Hz−1
ML−1T−3
or
MT−2
commonly measured in W⋅sr−1⋅m−2⋅nm−1 with surface area and either wavelength or frequency.

Irradiance Ee[nb 2] watt per square metre W⋅m−2 MT−3 power incident on a surface, also called radiant flux density.

sometimes confusingly called "intensity" as well.

or
E[nb 4]
watt per metre3
or
watt per square metre per hertz
W⋅m−3
or
W⋅m−2⋅Hz−1
ML−1T−3
or
MT−2
commonly measured in W⋅m−2nm−1
or 10−22 W⋅m−2⋅Hz−1, known as solar flux unit.[nb 5]

Me[nb 2] watt per square metre W⋅m−2 MT−3 power emitted from a surface.
M[nb 3]
or
M[nb 4]
watt per metre3
or

watt per square
metre per hertz

W⋅m−3
or
W⋅m−2⋅Hz−1
ML−1T−3
or
MT−2
power emitted from a surface per unit wavelength or frequency.

Radiosity Je watt per square metre W⋅m−2 MT−3 emitted plus reflected power leaving a surface.
Spectral radiosity J[nb 3] watt per metre3 W⋅m−3 ML−1T−3 emitted plus reflected power leaving a surface per unit wavelength
Radiant exposure He joule per square metre J⋅m−2 MT−2 also referred to as fluence
Radiant energy density ωe joule per metre3 J⋅m−3 ML−1T−2