The infinitesimal solid angle can be expressed in spherical polar coordinates : d Ω Ω = sin ⁡ ⁡ ( θ θ ) d θ θ d ϕ ϕ . So that: P = ∫ ∫ 0 ∞ ∞ d ν ν ∫ ∫ 0 π π 2 d θ θ ∫ ∫ 0 2 π π d ϕ ϕ B ν ν ( T ) cos ⁡ ⁡ ( θ θ ) sin ⁡ ⁡ ( θ θ ) = σ σ T 4 where σ σ = 2 k B 4 π π 5 15 c 2 h 3 ≈ ≈ 5.670400 × × 10 − − 8 J s − − 1 m − − 2 K − − 4 is known as the Stefan–Boltzmann constant.