Solid angle

A solid angle is the three dimensional analog of the ordinary angle. Instead of two lines meeting at a vertex, though, one needs a three dimensional figure that meets at a point. Good examples of objects that do this are a cone or a pyramid. To find the solid angle that the object covers, imagine a sphere centered at the point of the object. Now, take the surface area of the part of the sphere that is contained within the object, and divide that by the total area of the sphere.

Solid angle is measured in either radians² or degrees². To obtain the solid angle in radians squared, multiply the fractional area by 4π. To obtain the solid angle in degrees squared, multiply the fractional area by 180²/π which is equal to 129600/π. The SI unit of solid angle is the steradian (symbol sr), which is equal to radian².

Solid angle is useful for...

• defining luminosity