Steradian

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.

A steradian on a sphere

Sphere vs Steradian

• The surface area of a sphere is [math]\displaystyle{ 4\pi r^2 }[/math]
• The surface area of a steradian is just [math]\displaystyle{ 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.

Steradian Media

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  Solid angle of countries and other entities relative to the Earth.

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  Section of cone (1) and spherical cap (2) that subtend a solid angle of one steradian inside a sphere