Steradian

steradian
A graphical representation of two different steradians. The sphere has radius r, and in this case the area A of the highlighted spherical cap is r2. The solid angle Ω equals [A/r2] sr which is 1 sr in this example. The entire sphere has a solid angle of 4π sr.
General information
Unit system	SI
Unit of	solid angle
Symbol	sr
Conversions
1 sr in ...	... is equal to ...
SI base units	1 m2/m2
square degrees	⁠1802/π2⁠ deg2 ≈ 3282.8 deg2

The steradian (symbol: sr) or square radian^[1][2] is the unit of solid angle in the International System of Units (SI). It is used in three dimensional geometry, and is analogous to the radian, which quantifies planar angles. A solid angle in the form of a right circular cone can be projected onto a sphere, defining a spherical cap where the cone intersects the sphere. The magnitude of the solid angle expressed in steradians is defined as the quotient of the surface area of the spherical cap and the square of the sphere's radius. This is analagous to the way a plane angle projected onto a circle defines a circular arc on the circumference, whose length is proportional to the angle. Steradians can be used to measure a solid angle of any shape. The solid angle subtended is the same as that of a cone with the same projected area.

In the SI system, the steradian is considered to be a dimensionless unit, the quotient of the area projected onto a surrounding sphere and the square of the sphere's radius. Both the numerator and denominator of this ratio have dimension length squared (i.e. L²/L² = 1, dimensionless). The SI "solid angle" is therefore the number of steradians in the physical solid angle. In other words, the SI steradian is the number of physical steradians in one physical steradian. It is useful to distinguish between dimensionless quantities of a different kind, such as the radian (in the SI, a ratio of quantities of dimension length), so the symbol sr is used to indicate a physical solid angle. For example, radiant intensity can be measured in watts per steradian (W⋅sr⁻¹). The steradian was formerly an SI supplementary unit, but this category was abolished in 1995 and the steradian is now considered an SI derived unit.

The name steradian is derived from the Greek στερεός stereos 'solid' + radian.