# Square degree

A square degree is a non-SI unit measure of solid angle. It is denoted in various ways, including deg2, sq.deg., (°)², and ☐°. 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, or about 1/3283 or 3.0462×10−4 steradian (0.30462 msr). The number of square degrees in a whole sphere is

$4 \pi \left(\frac{180}{\pi}\right)^2 = \frac{129\,600}{\pi},$

or approximately 41 253 deg2. This is the total area of the 88 constellations in the list of constellations by area. The largest constellation, Hydra covers a solid angle of 1303 deg2, whereas the smallest, Crux covers 68 deg2.[1]

For example, observed from the surface of the Earth, the sun or the full moon has a diameter of approximately 0.5°, so it covers a solid angle of approximately 0.2 deg2 (≈ π (0.5/2)2 deg2), which is 4.8 × 10−6 of the total sky sphere.

Assuming the Earth to be a sphere with a surface area of 510 000 000 km2, the area of Northern Ireland, 13 600 km2 represents a solid angle of 1.10 deg2.[2] Similarly, the area of Connecticut, 14 356 km2 represents a solid angle of 1.16 deg2.[3]