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Learn how to calculate the distance between two points on the Earth's surface using different approximations and formulae. Compare flat, spherical and ellipsoidal models and their errors and limitations.
Learn how to calculate the great-circle distance between two points on a sphere using the haversine formula, a special case of the law of haversines. The formula uses the haversine function, which is half a versine of the central angle, and depends on the latitude and longitude of the points.
Vincenty's formulae are methods to calculate the distance and azimuth between two points on a spheroid. They are based on Legendre, Bessel and Helmert's formulas and are accurate to within 0.5 mm on the Earth ellipsoid.
Learn about the process and history of triangulation, a surveying method that uses angles and trigonometry to locate points. Find out how to calculate the coordinates of an unknown point using triangulation formulae and examples.
Euclidean distance is the length of the line segment between two points in Euclidean space. It can be calculated from the Cartesian coordinates using the Pythagorean theorem, and has various properties and applications in mathematics and statistics.
Learn how to calculate the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. See different formulas, proofs and examples for lines defined by equations, points or normals.
The haversine formula is a computational formula for calculating the great-circle distance between two points on a sphere, using the chord length relation. It is numerically better-conditioned for small distances than the spherical law of cosines formula, but less accurate for antipodal points.
A milepost equation is a place where mileposts on a linear feature, such as a highway or rail line, fail to increase normally. Learn how milepost equations are caused by realignment or changes in planned alignment, and how they affect mileage calculation.
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