The watt per steradian (W · sr -1 ) is the standard unit of radiant intensity. Reduced to base units in the International System of Units ( SI ), it is the equivalent of a kilogram meter squared per second cubed per steradian (kg · m 2 · s -3 · sr -1 ).
A point source of electromagnetic (EM) power that radiates equally well in all directions, and whose output is 1 W · sr -1 , has a total output power of 4 p (approximately 12.5664) watt s (W). This is because there are 4 p steradians in three-dimensional space with respect to a point of reference. The watt per steradian can be used to define the radiant intensity at any EM wavelength , from low-frequency radio waves through the gamma-ray spectrum. For visible light, in the wavelength range of approximately 390 to 770 nanometers (nm), the lumen is the preferred unit.
Suppose an electromagnetic field having P watts of total power is radiated from an isotropic emitter (that is, a point source that radiates equally well in all directions). Then the radiant intensity, P' , in watts per steradian is given by the following formula:
P' = P / (4 p )