Geographical distance

Geographical distance or geodetic 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: Flat surface; Spherical surface; Ellipsoidal surface. 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, is calculated between two points, and . The geographical coordinates of the two points, as (latitude, longitude) pairs, are and respectively. Which of the two points is designated as is not important for the calculation of distance. Latitude and longitude coordinates on maps are usually expressed in degrees. In the given forms of the formulae below, one or more values must be expressed in the specified units to obtain the correct result. Where geographic coordinates are used as the argument of a trigonometric function, the values may be expressed in any angular units compatible with the method used to determine the value of the trigonometric function. Many electronic calculators allow calculations of trigonometric functions in either degrees or radians. The calculator mode must be compatible with the units used for geometric coordinates. Differences in latitude and longitude are labeled and calculated as follows: It is not important whether the result is positive or negative when used in the formulae below. "Mean latitude" is labeled and calculated as follows: Colatitude is labeled and calculated as follows: For latitudes expressed in radians: For latitudes expressed in degrees: Unless specified otherwise, the radius of the earth for the calculations below is: = 6,371.