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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 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 perpendicular distance from a point to a line in Euclidean geometry using different methods and formulas. See examples, diagrams and proofs for various cases of lines defined by equations or 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.
Sagitta is the distance from the midpoint of a circular arc to the midpoint of its chord. It is used in architecture, optics, physics and other fields. Learn the formulas, approximations and applications of sagitta.
The midpoint of a line segment is the middle point that is equidistant from both endpoints. Learn how to find the midpoint using a formula, a compass and straightedge construction, and explore its geometric properties in various shapes and spaces.
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.
Vincenty's formulae are iterative methods to calculate the distance and azimuth between two points on a spheroid. They are based on Legendre, Bessel and Helmert's series and are accurate to within 0.5 mm on the Earth ellipsoid.
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