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Radiant energy density

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Title: Radiant energy density  
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Radiant energy density

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

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


w is the radiant energy density,
W is the amount of radiant energy in some volume,
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

I_\mathrm{e} = c w,[2]


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

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

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


  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. ^ a b c 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.
SI radiometry units
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.

Spectral radiance L[nb 3]
L[nb 4]
watt per steradian per metre3

watt per steradian per square
metre per hertz

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.

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

Radiant exitance /
Radiant emittance
Me[nb 2] watt per square metre W⋅m−2 MT−3 power emitted from a surface.
Spectral radiant exitance /
Spectral radiant emittance
M[nb 3]
M[nb 4]
watt per metre3

watt per square
metre per hertz

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
See also: SI · Radiometry · Photometry
  1. ^ quantities should be denoted with a suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
  2. ^ a b c d e Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant emittance.
  3. ^ a b c d e f Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek) to indicate a spectral concentration. Spectral functions of wavelength are indicated by "(λ)" in parentheses instead, for example in spectral transmittance, reflectance and responsivity.
  4. ^ a b c Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with the suffix "v" (for "visual") indicating a photometric quantity.
  5. ^ NOAA / Space Weather Prediction Center includes a definition of the solar flux unit (SFU).
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