Geographical distance

Geographical distance is the distance measured along the surface of the earth. 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 problem.

Calculating the distance between geographical coordinates is based on some level of abstraction; it does not provide an exact distance, which is unattainable if one attempted to account for every irregularity in the surface of the earth. Common abstractions for the surface between two geographic points are:

All abstractions above ignore changes in elevation. Calculation of distances which account for changes in elevation relative to the idealized surface are not discussed in this article.

Distance, ${\displaystyle D,\,\!}$ is calculated between two points, ${\displaystyle P_{1}\,\!}$ and ${\displaystyle P_{2}\,\!}$. The geographical coordinates of the two points, as (latitude, longitude) pairs, are ${\displaystyle (\phi _{1},\lambda _{1})\,\!}$ and ${\displaystyle (\phi _{2},\lambda _{2}),\,\!}$ respectively. Which of the two points is designated as ${\displaystyle P_{1}\,\!}$ is not important for the calculation of distance.

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