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The formulas involved can be complex and in some cases, such as in the ECEF to geodetic conversion above, the conversion has no closed-form solution and approximate methods must be used. References such as the DMA Technical Manual 8358.1 [15] and the USGS paper Map Projections: A Working Manual [16] contain formulas for conversion of map ...
The reverse conversion is harder: given X-Y-Z can immediately get longitude, but no closed formula for latitude and height exists. See "Geodetic system." Using Bowring's formula in 1976 Survey Review the first iteration gives latitude correct within 10-11 degree as long as the point is within 10,000 meters above or 5,000 meters below the ellipsoid.
To convert Transverse Mercator coordinates to lat-lon, first calculate ′, the footprint latitude— i.e. the latitude of the point on the central meridian that has the same N as the point to be converted; i.e. the latitude that has a meridian distance on the spheroid equal to N/. Bowring's formulas below seem quickest, but traditional ...
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 ...
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such ...
Alternatively, use formula BASE(Degrees from South or West * power(20, 4) , 20) in any Spreadsheet or Calculator to compute the OLC Code. For the coordinates 1°17′12″N 103°51′16″E / 1.286785°N 103.854503°E / 1.286785; 103.854503 from the previous example
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Let's take a point of latitude and of longitude and compute its UTM coordinates as well as point scale factor and meridian convergence using a reference meridian of longitude . By convention, in the northern hemisphere N 0 = 0 {\displaystyle N_{0}=0} km and in the southern hemisphere N 0 = 10000 {\displaystyle N_{0}=10000} km.