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

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

Subdivisions

Each square degree is equal to 3600 square arcminutes, and each square arcminute is equal to 3600 square arcseconds. So, each square degree is equal to 12960000 square arcseconds. The whole sphere contains about 148.51 million square arcminutes and about 534.64 billion square arcseconds.

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 deg². 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 the fraction 2 / 210100, 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 square kilometres, 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, and 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

References

External links

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