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.

Square degree
Unit of	Solid angle
Symbol	deg2
Conversions
1 deg2 in ...	... is equal to ...
SI units	≈ 3.04617×10−4 sr

The whole sphere has a solid angle of 4πsr which is approximately 41253 deg²:

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

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 from 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) represents a solid angle of 1.14 deg², Connecticut (14357 km²) represents a solid angle of 1.16 deg², Equatorial Guinea (28050 km²) represents a solid angle of 2 deg².
• The largest constellation, Hydra, covers a solid angle of 1303 deg², whereas the smallest, Crux, covers only 68 deg².

See also

• Steradian
• Spat (angular unit)
• Minute and second of arc
• List of constellations by area

External links

• "Square Degrees - the Area of something on the sky". The RASC Calgary Centre. 2018-11-05. Retrieved 2022-01-21.