Vincenty

Vincenty refers to a pair of geodetic formulae developed by Thaddeus Vincenty in 1975 for calculating geodesic distances on the Earth's ellipsoid. The Vincenty formulae solve two related problems on an oblate spheroid: the inverse problem, which returns the distance and bearing between two given points, and the direct problem, which determines the destination point given a start point, initial bearing, and distance.

The method uses the parameters of a reference ellipsoid, typically the semi-major axis a and the flattening f (for example, the WGS-84 ellipsoid). It computes reduced latitudes, iterates to solve for an angular quantity along the geodesic, and then derives the distance and the forward and backward azimuths. The approach provides higher accuracy than spherical approximations such as the great-circle distance, especially over long ranges.

Limitations include potential non-convergence of the iterative solution for nearly antipodal points, and sensitivity to the chosen ellipsoid parameters. In such cases, alternative algorithms or more robust geodesic solvers, such as Karney’s methods, may be used. Despite these caveats, Vincenty’s formulae remain widely implemented in geographic information systems, navigation software, and geodetic calculations because of their balance of precision and computational efficiency.

See also: geodesic, ellipsoid, direct problem, inverse problem, haversine formula, great-circle distance.