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# Steradian

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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]

A steradian on a sphere

## Sphere vs Steradian

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

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" (in en).