Solid Angles on a Sphere

solid angle

1

sphere's radius

1

A solid angle is related to the surface area of a sphere in the same way an ordinary angle is related to the circumference of a circle. The intersection of the cone with a sphere of radius 1 defines a surface whose area is equal to the solid angle subtended by the cone. The SI unit for solid angles is the steradian. While there are

2π

radians in a circle, there are

4π

steradians in a sphere.