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From Citizendium, the Citizens' Compendium

The steradian, abbreviated sr, is a measure of solid angle, and is the SI derived unit of solid angle. The unit of solid angle is the solid angle subtended at the centre of a sphere of radius r by a portion of the surface of the sphere having an area r². There are 4π steradians on a sphere.

A steradian is also equal to the spherical area of a polygon having an angle excess of 1 radian, to 1/4π of a complete sphere, or to (180/π)² or 3282.80635 square degrees. The central angle of a cone which subtends one steradian is approximately 1.144 rad or 65.54°.