Lighting Design Glossary

Solid Angle

(Term of mathematics/geometry)

The angle that, seen from the center of a sphere, includes a given area on the surface of that sphere. The value of the solid angle is numerically equal to the size of that area divided by the square of the radius of the sphere.

W = A / r²

Other than the diagram might suggest, the shape of the area doesn't matter at all. Any shape on the surface of the sphere that holds the same area will define a solid angle of the same size.

Also, the diagram only shows the elements that define a solid angle, not the solid angle itself. The solid angle is the quantitative aspect of the conical slice of space, that has the center of the sphere as its peak, the area on the surface of the sphere as one of its spherical cross sections, and extends to infinity.

The maximum solid angle is ~12.57, corresponding to the full area of the unit sphere, which is 4*Pi.

Standard unit of a solid angle is the Steradian (sr).
(Mathematically, the solid angle is unitless, but for practical reasons, the steradian is assigned.)