Square degree

square degree
Unit of	solid angle
Symbol	deg2
Conversions
1 deg2 in ...	... is equal to ...
SI units	≈ 3.04617×10−4 sr
arcsec2	12960000 arcsec2

An illustration of a solid angle formed by a rectangular pyramid, whose apex angles are both 10 degrees. The resulting solid angle is about 99.747369 square degrees. The size of Moon, as seen from Earth, is shown in yellow for comparison.

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 0.3046 msr (millisteradian). The whole sphere has a solid angle of 4π sr, which is approximately 41253 deg²:

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