Wolfram Alpha:

```Planck Radiation Law
--------------------
From the assumption that the electromagnetic modes in a cavity were quantized in energy
with the quantum energy equal to Planck's constant times the frequency, Planck derived
a radiation formula. The average energy per "mode" or "quantum" is the energy of the
quantum times the probability that it will be occupied (the Einstein-Bose distribution
function):

E = hν/(ehν/kT - 1)

This average energy times the density of such states, expressed in terms of either
frequency or wavelength

ρ(ν) = dns/dν = (8π/c3)ν2
ρ(λ) = dns/dλ = 8π/λ4

gives the energy density, the Planck radiation formula.

Sν = (8πh/c3)(ν3/ehν/kT - 1)

Sλ = (8πhc/λ5)(1/ehν/λkT - 1)

The Planck radiation formula is an example of the distribution of energy according to
Bose-Einstein statistics.  The above expressions are obtained by multiplying the density
of states in terms of frequency or wavelength times the photon energy times the
Bose-Einstein distribution function with normalization constant A = 1.

To find the radiated power per unit area from a surface at this temperature, multiply
the energy density by c/4. The density above is for thermal equilibrium, so setting
inward = outward gives a factor of 1/2 for the radiated power outward. Then one must
average over all angles, which gives another factor of 1/2 for the angular dependence
which is the square of the cosine. ```