An illustration of a solid angle formed by a rectangular pyramid, whose apex angles are both 10 degrees. The resulting solid angle is about 99.747369 square degrees. The size of Moon, as seen from Earth, is shown in yellow for comparison.

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/180⁠radians, a square degree is equal to (⁠π/180⁠)2 steradians (sr), or about ⁠1/3283⁠sr or about 0.3046msr (millisteradian). The whole sphere has a solid angle of 4πsr, which is approximately 41253deg2:

4 π ( 180 π ) 2 deg 2 = 360 2 π deg 2 = 129 600 π deg 2 ≈ 41 252.96 deg 2 . {\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 0.2deg2 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 0.2deg2. The moon varies from 0.188 to 0.244deg2 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 0.2deg2 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 (14130km2) represents a solid angle of 1.14deg2, Connecticut (14357km2) represents a solid angle of 1.16deg2, and Equatorial Guinea (28050km2) represents a solid angle of 2deg2.
  • The largest constellation, Hydra, covers a solid angle of 1303deg2, whereas the smallest, Crux, covers only 68deg2.

See also

External links

  • . The RASC Calgary Centre. 2018-11-05.