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
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
The solid angle is a much more complicated quantity than the normal angle and is also used much less frequently. It is hardly used in everyday life and is unknown to many people. Solid angles, in contrast to normal angles, are probably not part of common knowledge and one can usually get through life just fine without them. However, solid angles are used in some physical and mathematical, particularly geometric, applications. Examples include the photometric quantities luminous intensity and luminance, as well as Gauss's law for electric flux through a closed surface. Some nuclear physics effects can also be described using solid angles, including the relatively well-known Rutherford scattering. In experiments between 1909 and 1913, Ernest Rutherford was able to measure the size of atomic nuclei relative to the atoms using this scattering of alpha particles on an extremely thin gold foil.