# Dictionary:Spherical excess

The amount by which the sum of the angles of a triangle on the surface of a sphere exceeds 180 degrees. For a sphere, this excess is the area of the triangle. For a spherical triangle on an ellipsoid, such as the Earth approximates, the spherical excess is approximately:

where *b* and *c* are two adjacent sides of the triangle which intersect at the angle , m = latitude function=, =number of seconds of arc/radian=206 264.8, *R*=radius of curvature in the meridian, and *N*=radius of curvature in the prime vertical. Values of *m* for various ellipsoids are obtained from tables; the value for the center of the triangle to the nearest half degree is usually used. For greater precision a correction factor is often applied in iterative fashion.