Square degree

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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 3.0462×104 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 and the full moon both have a diameter of approximately 0.5°, so each of them 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]

See also[edit]


  1. ^ RASC Calgary Centre - The Constellations
  2. ^ Country Profiles: Key Statistics - Northern Ireland, August 2012
  3. ^ The 50 States | Embassies & Consulates Directory

External links[edit]