A steradian is used to measure "solid" angles

A steradian is related to the surface area of a sphere
in the same way a radian is related to the circumference of a circle:

 A Radian "cuts out" a length of a circle's circumference equal to the radius. A Steradian "cuts out" an area of a sphere equal to (radius)2.

The name steradian is made up from the Greek stereos for "solid" and radian. The SI Unit abbreviation is "sr".

• The surface area of a sphere is 4πr2,
• The surface area of a steradian is just r2.

And because you are measuring an angle, it doesn't matter what size the sphere is, it will always measure 4π steradians.

### Example: a sphere with a radius of 1 (called the "unit sphere"):

• has a surface area of 4π,
• and a steradian "cuts out" an area of 1.

Radiant intensity (how brightly something shines) can be measured in watts per steradian (W/sr).

Example: You measure the light coming from a powerful globe. Your sensor is 50mm × 50mm in size, and if you hold it 2m away it measures 0.1 Watts. What is the radiant intensity in W/sr ?

Answer: At 2m, one steradian cuts through 2×2 = 4 m2 of the sphere.

And because the sensor is relatively small, its flat surface area is approximately the area of sphere that it occupies. So 0.05 × 0.05 = 0.0025m2.