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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 Calotte area A: z.B. cm² Sphere radius r: z.B. cm Solid angle Ω: sr
Round to    decimal places.

Please enter two values, the third will be calculated.

The solid cut out of the sphere by the cone is a spherical cap. A complete sphere has a solid angle of 4π sr, a hemisphere has 2π sr.

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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) )

 Plane angle α: ° Solid angle Ω: sr Solid angle Ω in pi: π sr
Round to    decimal places.

Please enter one value, the other two will be calculated.

## 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

 Solid angle Ω in steradian: sr Solid angle Ω in pi: π sr Solid angle Ω in square degrees: °²
Round to    decimal places.

Please enter one value, the other two will be calculated.

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