Computing the area of a spherical polygon of arbitrary shape

An algorithm for determining the area of a spherical polygon of arbitrary shape is presented. The kernel of the problem is to compute the interior angle at each vertex of the spherical polygon; a well-known relationship between the area of a spherical polygon and the sum of its interior angles then may be exploited. The algorithm has been implemented as a FORTRAN subroutine and a listing is provided. Both algorithm and subroutine are general in their capabilities and can be used, for example, to determine the area of a spherical polygon containing one or more holes.