The total energy density U can be similarly calculated, except the integration is over the whole sphere and there is no cosine, and the energy flux (U c) should be divided by the velocity c to give the energy density U : U = 1 c ∫ ∫ 0 ∞ ∞ I ( ν ν , T ) d ν ν ∫ ∫ d Ω Ω Thus ∫ ∫ 0 π π / 2 cos ⁡ ⁡ θ θ sin ⁡ ⁡ θ θ d θ θ is replaced by ∫ ∫ 0 π π sin ⁡ ⁡ θ θ d θ θ , giving an extra factor of 4.