Area of a Spherical Triangle

A spherical triangle is a triangle traced out on the surface of a sphere. Each side is a portion of a circular arc instead of a straight line in two dimensions, because it goes along the curvature of that sphere.

The area of a spherical triangle with points $A$, $B$, and $C$ can be calculated as follows:

$$Area = r^2(\angle{A} + \angle{B} +\angle{C} - \pi)$$

Where $r$ equals the radius of the sphere and the angles are measured in radians (if you don't remember how to convert between degrees and radians, check out this topic).

Be careful when calculating the angles – you'll want to use spherical trigonometry, not the planar geometry you're probably most familiar with. There is a spherical version of the law of sines that might help you find these angles.