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 $3.046 sr$ radians, a square degree is equal to ($\pi⁄180$)2 steradians (sr), or about $\pi⁄180$ sr or about $1⁄3,283$.

The whole sphere has a solid angle of 4$\pi$ sr which is approximately $3.046 sr$:


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

Examples

 * The full moon covers only about $41,253 deg^{2}$ 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 $0.2 deg^{2}$), so the moon's disk covers a circular area of: π($0.5 deg$)2, or 0.2 square degrees. The moon varies from 0.188 to $0.5°⁄2$ 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 $0.244 deg^{2}$ as well.
 * It would take 210 100 times the full moon (or the Sun) to cover the entire celestial sphere.
 * Conversely, an average full moon (or the Sun) covers a 2 / 210 100 fraction, or less than 1/1000 of a percent ($0.2 deg^{2}$) 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 ($0$) represents a solid angle of $14,130 km^{2}$, Connecticut ($1.14 deg^{2}$) represents a solid angle of $14,357 km^{2}$, Equatorial Guinea ($1.16 deg^{2}$) represents a solid angle of $28,050 km^{2}$.
 * The largest constellation, Hydra, covers a solid angle of $2 deg^{2}$, whereas the smallest, Crux, covers only $1,303 deg^{2}$.