Solid Angle

Defined as the Surface Area $\Omega$ of a Unit Sphere which is subtended by a given object $S$. Writing the Spherical Coordinates as $\phi$ for the Colatitude (angle from the pole) and $\theta$ for the Longitude (azimuth),

$$\Omega\equiv A_{\rm projected} = \int\!\!\!\int _S \sin\phi\,d\theta\,d\phi.$$

Solid angle is measured in Steradians, and the solid angle corresponding to all of space being subtended is $4\pi$ Steradians.

See also Sphere, Steradian