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TransverseMercatorProj -- perform transverse Mercator projection


TransverseMercatorProj [ -s | -t ] [ -l lon0 ] [ -k k0 ] [ -r ] [ -e a f ] [ -w ] [ -p prec ] [ --comment-delimiter commentdelim ] [ --version | -h | --help ] [ --input-file infile | --input-string instring ] [ --line-separator linesep ] [ --output-file outfile ]


Perform the transverse Mercator projections. Convert geodetic coordinates to transverse Mercator coordinates. The central meridian is given by lon0. The longitude of origin is the equator. The scale on the central meridian is k0. By default an implementation of the exact transverse Mercator projection is used.

Geodetic coordinates are provided on standard input as a set of lines containing (blank separated) latitude and longitude (decimal degrees or degrees, minutes, seconds); for detils on the allowed formats for latitude and longitude, see the "GEOGRAPHIC COORDINATES" section of GeoConvert(1). For each set of geodetic coordinates, the corresponding projected easting, x, and northing, y, (meters) are printed on standard output together with the meridian convergence gamma (degrees) and scale k. The meridian convergence is the bearing of grid north (the y axis) measured clockwise from true north.


use the sixth-order Krueger series approximation to the transverse Mercator projection instead of the exact projection.
use the exact algorithm with the "EXTENDED DOMAIN".
specify the longitude of origin lon0 (degrees, default 0).
specify the scale k0 on the central meridian (default 0.9996).
perform the reverse projection. x and y are given on standard input and each line of standard output gives latitude, longitude, gamma, and k.
specify the ellipsoid via the equatorial radius, a and the flattening, f. Setting f = 0 results in a sphere. Specify f < 0 for a prolate ellipsoid. A simple fraction, e.g., 1/297, is allowed for f. By default, the WGS84 ellipsoid is used, a = 6378137 m, f = 1/298.257223563. If the exact algorithm is used, f must be positive.
on input and output, longitude precedes latitude (except that on input this can be overridden by a hemisphere designator, N, S, E, W).
set the output precision to prec (default 6). prec is the number of digits after the decimal point for lengths (in meters). For latitudes and longitudes (in degrees), the number of digits after the decimal point is prec + 5. For the convergence (in degrees) and scale, the number of digits after the decimal point is prec + 6.
set the comment delimiter to commentdelim (e.g., "#" or "//"). If set, the input lines will be scanned for this delimiter and, if found, the delimiter and the rest of the line will be removed prior to processing and subsequently appended to the output line (separated by a space).
print version and exit.
print usage and exit.
print full documentation and exit.
read input from the file infile instead of from standard input; a file name of "-" stands for standard input.
read input from the string instring instead of from standard input. All occurrences of the line separator character (default is a semicolon) in instring are converted to newlines before the reading begins.
set the line separator character to linesep. By default this is a semicolon.
write output to the file outfile instead of to standard output; a file name of "-" stands for standard output.


The exact transverse Mercator projection has a branch point on the equator at longitudes (relative to lon0) of +/- (1 - e) 90 = 82.636..., where e is the eccentricity of the ellipsoid. The standard convention for handling this branch point is to map positive (negative) latitudes into positive (negative) northings y; i.e., a branch cut is placed on the equator. With the extended domain, the northern sheet of the projection is extended into the south hemisphere by pushing the branch cut south from the branch points. See the reference below for details.


   echo 0 90 | TransverseMercatorProj
   => 25953592.84 9997964.94 90 18.40
   echo 260e5 100e5 | TransverseMercatorProj -r
   => -0.02 90.00 90.01 18.48


An illegal line of input will print an error message to standard output beginning with "ERROR:" and causes TransverseMercatorProj to return an exit code of 1. However, an error does not cause TransverseMercatorProj to terminate; following lines will be converted.


TransverseMercatorProj was written by Charles Karney.


The algorithms for the transverse Mercator projection are described in C. F. F. Karney, Transverse Mercator with an accuracy of a few nanometers, J. Geodesy 85(8), 475-485 (Aug. 2011); DOI <>; preprint <>. The explanation of the extended domain of the projection with the -t option is given in Section 5 of this paper.


TransverseMercatorProj was added to GeographicLib, <>, in 2009-01. Prior to version 1.9 it was called TransverseMercatorTest (and its interface was slightly different).

2024-07-14 GeographicLib 2.4