Square degree

A square degree (deg²) is a non-SI unit measure of solid angle. Other denotations include sq. deg. and (°)². Just as degrees are used to measure parts of a circle, square degrees are used to measure parts of a sphere.

Analogous to one degree being equal to ⁠π/180⁠ radians, a square degree is equal to (⁠π/180⁠)² steradians (sr), or about ⁠1/3283⁠ sr or about 3.046×10⁻⁴ sr. The whole sphere has a solid angle of 4πsr which is approximately 41253 deg²:

${\displaystyle 4\pi \left({\frac {180}{\pi }}\right)^{2}\,{\deg }^{2}={\frac {360^{2}}{\pi }}~{\deg }^{2}={\frac {129\,600}{\pi }}~{\deg }^{2}\approx 41\,252.96~{\deg }^{2}.}$