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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.
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.
Learn how to navigate a vessel along a great circle, the shortest distance between two points on the globe, using spherical trigonometry. Find formulas, examples, and details for finding way-points and position angles.
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.
Learn about the definition, formulas, properties and applications of Euclidean distance, the length of the line segment between two points in Euclidean space. Euclidean distance is a metric space that obeys the Pythagorean theorem and Ptolemy's inequality.
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.
Learn how to calculate the distance between two parallel lines in the plane using linear systems and vector products. See the formula, the proof, and examples of non-vertical parallel lines.
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