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Geo::Ellipsoid - longitude and latitude calculations using an ellipsoid model


Version 1.15.


  use Geo::Ellipsoid;

  my $geo = Geo::Ellipsoid->new(ellipsoid  => 'NAD27',
                                angle_unit => 'degrees');

  my @origin = ( 37.619002, -122.374843 );      # SFO
  my @dest   = ( 33.942536, -118.408074 );      # LAX

  # range and bearing from one location to another

  my ( $range, $bearing ) = $geo->to( @origin, @dest );
  $range = $geo->range( @origin, @dest );
  $bearing = $geo->bearing( @origin, @dest );

  # destination given start point, range, and bearing

  my ( $lat, $lon ) = $geo->at( @origin, 2000, 45.0 );

  # approximate displacement given one location and a destination

  my ( $x, $y ) = $geo->displacement( @origin, @dest );

  # approximate location given one location and displacement

  my @pos = $geo->location( $lat, $lon, $x, $y );


Accurate latitude/longitude calculations.


Geo::Ellipsoid performs geometrical calculations on the surface of an ellipsoid. An ellipsoid is a three-dimension object formed from the rotation of an ellipse about one of its axes. The approximate shape of the earth is an ellipsoid, so Geo::Ellipsoid can accurately calculate distance and bearing between two widely-separated locations on the earth's surface.

The shape of an ellipsoid is defined by the lengths of its semi-major and semi-minor axes. The shape may also be specified by the flattening ratio f as:

    f = ( semi-major - semi-minor ) / semi-major

which, since f is a small number, is normally given as the reciprocal of the flattening 1/f.

The shape of the earth has been surveyed and estimated differently at different times over the years. The two most common sets of values used to describe the size and shape of the earth in the United States are 'NAD27', dating from 1927, and 'WGS84', from 1984. United States Geological Survey topographical maps, for example, use one or the other of these values, and commonly-available Global Positioning System (GPS) units can be set to use one or the other. See "DEFINED ELLIPSOIDS" below for the ellipsoid survey values that may be selected for use by Geo::Ellipsoid.



The new() constructor may be called with a hash list to set the value of the ellipsoid to be used, the value of the units to be used for angles and distances, and whether or not the output range of longitudes and bearing angles should be symmetric around zero or always greater than zero. The initial default constructor is equivalent to the following:

    my $geo = Geo::Ellipsoid->new(
      ellipsoid           => 'WGS84',
      angle_unit          => 'radians' ,
      distance_unit       => 'meter',
      longitude_symmetric => 0,
      bearing_symmetric   => 0,

The constructor arguments may be of any case and, with the exception of the ellipsoid value, abbreviated to their first three characters. Thus, ( UNI => 'DEG', DIS => 'FEE', Lon => 1, ell => 'NAD27', bEA => 0 ) is valid.



Returns a list with the names all known ellipsoids.




Set the angle unit used by the Geo::Ellipsoid object. The unit may also be set in the constructor of the object. The allowable values are 'degrees' or 'radians'. The default is 'radians'. The unit value is not case sensitive and may be abbreviated to 3 letters. The unit of angle apply to both input and output latitude, longitude, and bearing values.


Set the distance unit used by the Geo::Ellipsoid object. The unit of distance may also be set in the constructor of the object. The recognized values are 'meter', 'kilometer', 'mile', 'nm' (nautical mile), or 'foot'. The default is 'meter'. The value is not case sensitive and may be abbreviated to 3 letters.


For any other unit of distance not recognized by this method, pass a numerical argument representing the length of the distance unit in meters. For example, to use units of furlongs, call


The distance conversion factors used by this module are as follows:

  Unit          Units per meter
  --------      ---------------
  foot             0.3048
  kilometer     1000.0
  mile          1609.344
  nm            1852.0

Set the ellipsoid to be used by the Geo::Ellipsoid object. See "DEFINED ELLIPSOIDS" below for the allowable values. The value may also be set by the constructor. The default value is 'WGS84'.


Sets the ellipsoid parameters to the specified semi-major axis (given in meters) and reciprocal flattening. A zero value for the reciprocal flattening will result in a sphere for the ellipsoid, and a warning message will be issued.

    $geo->set_custom_ellipsoid( 'sphere', 6378137, 0 );

If called with no argument or a true argument, sets the range of output values for longitude to be symmetric around zero, i.e., in the range [-pi,+pi) radians, [-180,180) degrees etc. depending on the angle unit.

If called with a false or undefined argument, sets the output angle range to be non-negative, i.e., [0,2*pi) radians, [0, 360) degrees etc. depending on the angle unit.


If called with no argument or a true argument, sets the range of output values for bearing to be symmetric around zero, i.e., in the range [-pi,+pi) radians, [-180,180) degrees etc. depending on the angle unit.

If called with a false or undefined argument, sets the output angle range to be non-negative, i.e., [0,2*pi) radians, [0,360) degrees etc. depending on the angle unit.


Sets the defaults for the new() constructor method. Call with key, value pairs similar to new.

      ellipsoid           => 'GRS80',
      angle_unit          => 'degrees',
      distance_unit       => 'kilometer',
      longitude_symmetric => 1,
      bearing_symmetric   => 0

Keys and string values (except for the ellipsoid identifier) may be shortened to their first three letters and are case-insensitive:

      uni => 'deg',
      ell => 'GRS80',
      dis => 'kil',
      lon => 1,
      bea => 0



Returns the name of the ellipsoid.


Returns the equatorial radius in meters.


Returns the polar radius in meters.

get_geocentric_radius ANGLE

Returns the geocentric radius in meters, given a geocentric latitude. The geocentric latitude is the angle between the equatorial plane and the radius from centre to the point on the surface.


Returns the flattening.


Returns the eccentricity.


Returns true if the longitude is symmetric around zero, and false otherwise.


Returns true if the bearing is symmetric around zero, and false otherwise.


Returns the angle unit, i.e., the unit for latitude, longitude, and bearing.


Returns the distance unit.



Returns a list consisting of the distance unit per angle of latitude and longitude (degrees or radians) at the specified latitude. These values may be used for fast approximations of distance calculations in the vicinity of some location.

    ( $lat_scale, $lon_scale ) = $geo->scales($lat0);
    $x = $lon_scale * ($lon - $lon0);
    $y = $lat_scale * ($lat - $lat0);

Returns the range in distance units between two specified locations given as latitude, longitude pairs.

    my $dist = $geo->range( $lat1, $lon1, $lat2, $lon2 );
    my $dist = $geo->range( @origin, @destination );

Returns the bearing in degrees or radians from the first location to the second. Zero bearing is true north.

    my $bearing = $geo->bearing( $lat1, $lon1, $lat2, $lon2 );

Returns the list (latitude,longitude) in degrees or radians that is a specified range and bearing from a given location.

    my( $lat2, $lon2 ) = $geo->at( $lat1, $lon1, $range, $bearing );

In list context, returns (range, bearing) between two specified locations. In scalar context, returns just the range.

    my( $dist, $theta ) = $geo->to( $lat1, $lon1, $lat2, $lon2 );
    my $dist = $geo->to( $lat1, $lon1, $lat2, $lon2 );

Returns the (x,y) displacement in distance units between the two specified locations.

    my( $x, $y ) = $geo->displacement( $lat1, $lon1, $lat2, $lon2 );

NOTE: The x and y displacements are only approximations and only valid between two locations that are fairly near to each other. Beyond 10 kilometers or more, the concept of X and Y on a curved surface loses its meaning.


Returns the list (latitude,longitude) of a location at a given (x,y) displacement from a given location.

        my @loc = $geo->location( $lat, $lon, $x, $y );


The following ellipsoids are defined in Geo::Ellipsoid, with the semi-major axis in meters and the reciprocal flattening as shown. The default ellipsoid is WGS84.

    Ellipsoid        Semi-Major Axis (m.)     1/Flattening
    ---------        -------------------     ---------------
    AIRY                 6377563.396         299.3249646
    AIRY-MODIFIED        6377340.189         299.3249646
    AUSTRALIAN           6378160.0           298.25
    BESSEL-1841          6377397.155         299.1528128
    CLARKE-1880          6378249.145         293.465
    EVEREST-1830         6377276.345         290.8017
    EVEREST-MODIFIED     6377304.063         290.8017
    FISHER-1960          6378166.0           298.3
    FISHER-1968          6378150.0           298.3
    GRS80                6378137.0           298.25722210088
    HOUGH-1956           6378270.0           297.0
    HAYFORD              6378388.0           297.0
    IAU76                6378140.0           298.257
    KRASSOVSKY-1938      6378245.0           298.3
    NAD27                6378206.4           294.9786982138
    NWL-9D               6378145.0           298.25
    SOUTHAMERICAN-1969   6378160.0           298.25
    SOVIET-1985          6378136.0           298.257
    WGS72                6378135.0           298.26
    WGS84                6378137.0           298.257223563


The methods should not be used on points which are too near the poles (above or below 89 degrees), and should not be used on points which are antipodal, i.e., exactly on opposite sides of the ellipsoid. The methods will not return valid results in these cases.


The conversion algorithms used here are Perl translations of Fortran routines written by LCDR L. Pfeifer NGS Rockville MD that implement T. Vincenty's Modified Rainsford's method with Helmert's elliptical terms as published in "Direct and Inverse Solutions of Ellipsoid on the Ellipsoid with Application of Nested Equations", T. Vincenty, Survey Review, April 1975.

The Fortran source code files inverse.for and forward.for may be obtained from


Peter John Acklam, <> (current maintainer)

Jim Gibson, <> (original author)



There are currently no known bugs.

Please report any bugs or feature requests via

Old bug reports and feature requests can be found at


You can find documentation for this module with the perldoc command.

    perldoc Geo::Ellipsoid

You can also look for information at:


Copyright 2016-2021 Peter John Acklam, current maintainer.

Copyright 2005-2008 Jim Gibson, all rights reserved.

This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.


Geo::Distance, Geo::Ellipsoids