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Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path between the two points on the surface of the sphere. (By comparison, the shortest path passing through the sphere's interior is the chord between ...
Distance from a point to a line. The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be ...
Mercator 1569 world map (Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata) showing latitudes 66°S to 80°N. The Mercator projection (/ mərˈkeɪtər /) is a conformal cylindrical map projection first presented by Flemish mapmaker Gerardus Mercator in 1569. In the 18th century, it became the standard map ...
The Euclidean distance is the length of the displacement vector. The displacement in classical physics measures the change in position of an object during an interval of time. While distance is a scalar quantity, or a magnitude, displacement is a vector quantity with both magnitude and direction. In general, the vector measuring the difference ...
The distance along the great circle will then be s 12 = Rσ 12, where R is the assumed radius of the Earth and σ 12 is expressed in radians. Using the mean Earth radius, R = R 1 ≈ 6,371 km (3,959 mi) yields results for the distance s 12 which are within 1% of the geodesic length for the WGS84 ellipsoid; see Geodesics on an ellipsoid for details.
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