solid angle

A solid angle (or angular area) is a size measurement for a region of possible directions from a point, which is equivalent to regions on the surface of a sphere. The concept is applicable regardless of the shape of such a region on the sphere's surface (circle, rectangle-like, etc.). For example, a solid angle quantifies the size of a region of the celestial sphere. A unit of a solid angle is the steradian (for square radian, which is adopted as a SI unit): the area on the surface of a sphere of its radius squared. 4π (roughly 12.6) steradians cover a whole sphere. Another unit, the square degree (deg²) is similarly defined for a degree: a degree has a length along a circle of π/180 radii and a square degree is that value squared. A square-like shape on the surface of a sphere (four equal angles), where each edge is a degree in length following a great circle, is actually slightly more than a square degree in size because of the curvature of the surface, but the difference is small. A solid angle of 4π(180/π)² (roughly 41253) square degrees covers a whole sphere and (180/π)² (roughly 3283) square degrees covers a steradian. For example, the area of USA on the surface of the Earth is roughly 0.28 steradians or 922 square degrees. A square arcminute is 1/3600 square degree.

Solid angles are used in the definition of some electromagnetic radiation measurements, and in equations modeling spherical objects such as stars. They are also cited to describe the apparent size of astronomical objects (galaxies or nebulae), fields of view, and the areas covered by surveys. Square degrees are often used for the latter, but steradians are as well.