# Why normalise Lambertian BRDF by 1/pi?

Why is a Lambertian BRDF normalised by dividing by $\pi$? Since the area of a unit sphere is $4 \pi$, and the area of the half sphere above the surface is $2 \pi$, shouldn't it rather be $1/(2\pi)$?

Because $cos(\theta)$ integrates to $\pi$ over the hemisphere (and not $2\pi$). And the incoming light is multiplied by $cos(\theta)$ (and the BRDF).