steradian | |
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![]() 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 steradians, projected onto a sphere, gives the area of a spherical cap on the surface, whereas an angle in radians, projected onto a circle, gives a length of a circular arc on the circumference. The name is derived from the Greek στερεός stereos 'solid' + radian.
The steradian is a dimensionless unit, the quotient of the area subtended and the square of its distance from the centre. Both the numerator and denominator of this ratio have dimension length squared (i.e. L2/L2 = 1, dimensionless). It is useful, however, to distinguish between dimensionless quantities of a different kind, such as the radian (a ratio of quantities of dimension length), so the symbol "sr" is used to indicate a 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.