# Square degree

A square degree (deg2) is a non-SI-compliant 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, or about 1/3283 = 3.0462×10−4 steradians (0.30462 msr).

The number of square degrees in a whole sphere is approximately 41253 deg2. This is the total area of the 88 modern constellations in the sky.

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

## Examples

• A whole sphere has approximately 41253 deg2.
• 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 deg), so the moon's disk covers a circular area of: π × (0.5°/2)2, or 0.2 square degrees.
• 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.
• 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 1.1 deg2 and 1.2 deg2, respectively.
• The largest constellation, Hydra, covers a solid angle of 1303 deg2, whereas the smallest, Crux, covers only 68 deg2.[1]