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# Calculate Solid Angles in Steradian

Calculator for a solid angle as part of a spherical surface. The solid angle is the three-dimensional equivalent of the two-dimensional angle. In a sphere, a cone with the tip at the sphere's center is raised. The ratio between the area cut off by the cone, a calotte, and the square of the radiuses is the solid angle in steradian.

Ω = A / r²

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## Solid Angle and Plane Angle

The solid angle results from the plane angle of the cone α. The formulas are:

Ω = 2π * ( 1 - cos( α / 2) )

α = 2 * arccos( 1 - Ω / (2π) )

## Solid Angle in Square Degrees

Square degree, °², is a less common, much smaller unit as steradian. 1°² = (π/180)² sr = 0.0003046174 sr

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