SI unit of solid angle

The steradian (symbol: sr) or square radian is an SI unit. It is like a radian, but for smooth 3D objects, for example, a sphere. A steradian is about one twelfth the surface area of a sphere, regardless of how big the sphere is.[1]

• The surface area of a sphere is ${\displaystyle 4\pi r^{2}}$
• The surface area of a steradian is just ${\displaystyle r^{2}}$

So a sphere measures 4π steradians, or about 12.57 steradians. Likewise a steradian is 1/12.57, or about 8% of a sphere. And because we measure an angle, it doesn't matter what size the sphere is, it will always measure 4π steradians.[2]

References

1. Weisstein, Eric W. "Steradian". mathworld.wolfram.com. Retrieved 2020-03-27.