haversinedistance

Haversine distance is the great-circle distance between two points on a sphere computed from their latitudes and longitudes. In the haversine formula, treat φ1 and φ2 as latitudes and λ1 and λ2 as longitudes in radians. Let Δφ = φ2 − φ1 and Δλ = λ2 − λ1. Then a = sin²(Δφ/2) + cosφ1 cosφ2 sin²(Δλ/2). The central angle between the points is c = 2 arcsin(√a). The distance on a sphere of radius R is d = R·c. For Earth, R is typically taken as mean radius about 6,371 kilometers (3,959 miles).

Uses and practical aspects: The haversine distance is widely used in navigation, mapping, and geographic information systems as a simple, fast method to estimate distance between two coordinates. It requires only basic trigonometry and is well supported in most programming environments. It is most reliable for short to moderate distances where a spherical model is a reasonable approximation.

Limitations and alternatives: The calculation assumes a perfect sphere, whereas Earth is an oblate spheroid, so the result is an approximation. For higher accuracy over long distances, ellipsoidal formulas such as Vincenty’s or other algorithms that model the Earth's shape more precisely are preferred. Numerical cautions include ensuring inputs are in radians, guarding against rounding that yields a negative value under the square root, and optionally clipping a to [0,1] before taking the square root.