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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 [math]4\pi r^2[/math]
  • The surface area of a steradian is just [math]r^2[/math]

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). https://mathworld.wolfram.com/Steradian.html. 
  2. "Steradian". https://www.mathsisfun.com/geometry/steradian.html.