It is used in three dimensional geometry, and is analogous to the radian, which quantifies planar angles.

The magnitude of the solid angle expressed in steradians is defined as the quotient of the surface area of the spherical cap and the square of the sphere's radius.

A solid angle of one steradian subtends a cone aperture of approximately 1.144 radians or 65.54 degrees.

For a general sphere of radius r, any portion of its surface with area A = r2 subtends one steradian at its centre.

By the same argument, the maximum solid angle that can be subtended at any point is 4π sr.

From this, one can compute the cone aperture (a plane angle) 2θ of the cross-section of a simple spherical cone whose solid angle equals one steradian: giving θ ≈ 0.572 rad = 32.77° and aperture 2θ ≈ 1.144 rad = 65.54°.

≈ 3282.80635 square degrees, and to the spherical area of a polygon having an angle excess of 1 radian.

[clarification needed] Millisteradians (msr) and microsteradians (μsr) are occasionally used to describe light and particle beams.