Square degree

Asquare degree(deg²) is a non-SIunitmeasure ofsolid angle.Other denotations includesq. deg.and (°)².Just asdegreesare used to measure parts of a circle, square degrees are used to measure parts of asphere.Analogous to one degree being equal to⁠π/180⁠radians, a square degree is equal to (⁠π/180⁠)²steradians(sr), or about⁠1/3283⁠sr or about3.046×10⁻⁴sr.

Square degree
Unit of	Solid angle
Symbol	deg2
Conversions
1 deg2in...	... is equal to...
SI units	≈3.04617×10−4sr

Thewhole spherehas a solid angle of4πsrwhich is approximately41253deg²:

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

Examples

• Thefull mooncovers only about0.2 deg²of the sky when viewed from the surface of the Earth. The Moon is only a half degree across (i.e. a circular diameter of roughly0.5°), 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 to0.244 deg²depending on its distance from the Earth.
• Viewed from Earth, theSunis roughly half a degree across (the same as the full moon) and covers only0.2 deg²as well.
• It would take210100times the full moon (or the Sun) to cover the entire celestial sphere.
• Conversely, an average full moon (or the Sun) covers a 2 /210100fraction, 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 ofNorthern Ireland(14130km²) represents a solid angle of1.14 deg²,Connecticut(14357km²) represents a solid angle of1.16 deg²,Equatorial Guinea(28050km²) represents a solid angle of2 deg².
• The largest constellation,Hydra,covers a solid angle of1303 deg²,whereas the smallest,Crux,covers only68 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.Retrieved2022-01-21.