haversinekaavaa

Haversinekaavaa refers to the haversine formula, a mathematical method used to calculate the great-circle distance between two points on the surface of a sphere given their latitudes and longitudes. It is widely used in navigation, aviation, and geographic information systems because it is simple to implement and performs well for many practical purposes.

Formula: if φ1 and λ1 are the latitude and longitude of the first point and φ2 and λ2 those of the second, all in radians, then Δφ = φ2 − φ1 and Δλ = λ2 − λ1. The haversine of the central angle is a = sin^2(Δφ/2) + cos φ1 cos φ2 sin^2(Δλ/2). The central angle is c = 2 atan2(√a, √(1−a)). The distance on a sphere of radius R is d = R c. The mean Earth radius is commonly taken as about 6,371 km, yielding distances in kilometers when R is that value.

History and naming: the formula is named after the haversine function hav(θ) = sin^2(θ/2). It entered widespread use in navigation in the 19th and 20th centuries and remains popular because it avoids some numerical issues of other trigonometric forms.

Limitations and alternatives: the haversine formula assumes a perfect sphere; the Earth is closer to an ellipsoid. For high precision over long distances, ellipsoidal models such as WGS84 and methods like Vincenty are preferred. In some implementations, the formula can be computed with radians to avoid degree conversion errors.

See also: great-circle distance, Vincenty formula, spherical law of cosines.

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