# Square degree

Square degree
Unit ofSolid angle
Symboldeg2
Conversions
1 deg2 in ...... is equal to ...
SI units   3.04617×10−4 sr

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:

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

## Examples

• The full moon covers only about 0.2 deg2 of the sky when viewed from the surface of the Earth. The Moon is only a half degree across (i.e. a circular diameter of roughly 0.5°), so the moon's disk covers a circular area of: π(0.5°/2)2, or 0.2 square degrees. The moon varies from 0.188 to 0.244 deg2 depending on its distance to the Earth.
• Viewed from Earth, the Sun is roughly half a degree across (the same as the full moon) and covers only 0.2 deg2 as well.
• It would take 210100 times the full moon (or the Sun) to cover the entire celestial sphere.
• Conversely, an average full moon (or the Sun) covers a 2 / 210100 fraction, or less than 1/1000 of a percent (0.00000952381) of the celestial hemisphere, or above-the-horizon sky.
• Assuming the Earth to be a sphere with a surface area of 510 million km2, the area of Northern Ireland (14130 km2) and Connecticut (14357 km2) represent a solid angle of 1.14 deg2 and 1.16 deg2, respectively.
• The largest constellation, Hydra, covers a solid angle of 1303 deg2, whereas the smallest, Crux, covers only 68 deg2.[1]