Square degree

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A square degree (deg2) is a non SI-compliant 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 / 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 approximately 41253 deg2. This is the total area of the 88 modern constellations in the sky.

4 \pi \left(\frac{180}{\pi}\right)^2 \, \mathrm{deg^2} = \frac{360^2}{\pi}\,\, \mathrm{deg^2} = \frac{129\,600}{\pi} \,\, \mathrm{deg^2} = 41\,253 \,\, \mathrm{deg^2}


  • A whole sphere has 41253 deg2
  • The full moon covers only about 0.2 deg2 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 deg), so the moon's disk covers a circular area of: π (0.5 deg/2)2, or 0.2 square degrees.
  • Viewed from Earth, the Sun is roughly half a degree across (the same as the full moon) and covers only 0.2 deg2 as well.
  • It would take about 200000 times the full moon (or the Sun) to cover the entire celestial sphere.
  • Assuming the Earth to be a sphere with a surface area of 510 million km2, the area of Northern Ireland (14130 km2) and Connecticut (14357 km2) represent a solid angle of 1.1 deg2 and 1.2 deg2, respectively.
  • The largest constellation, Hydra, covers a solid angle of 1303 deg2, whereas the smallest, Crux, covers only 68 deg2.[1]

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