Cartographic projection

The foundation of PROJ is the large number of projections available in the library. This section is devoted to the generic parameters that can be used on any projection in the PROJ library.

Below is a list of PROJ parameters which can be applied to most coordinate system definitions. This table does not attempt to describe the parameters particular to particular projection types. These can be found on the pages documenting the individual projections.




Semimajor radius of the ellipsoid axis (always in meters)


Axis orientation


Semiminor radius of the ellipsoid axis (always in meters)


Ellipsoid name (see proj -le)


Scaling factor (deprecated)


Scaling factor


Latitude of origin (in degree if no angular unit specified)


Central meridian (in degree if no angular unit specified)


Center longitude to use for wrapping (see below)


Allow longitude output outside -180 to 180 range, disables wrapping (see below)


Alternate prime meridian (typically a city name, see below)


Projection name (see proj -l)


Horizontal coordinate system units (meters, US survey feet, etc.)


Vertical coordinate system units.


False easting (always in meters)


False northing (always in meters)

In the sections below most of the parameters are explained in details.


Horizontal coordinate system units can be specified using the +units keyword with a symbolic me for a unit (i.e. us-ft). Alternatively the translation to meters can be specified with the +to_meter keyword (i.e. 0.304800609601219 for US feet). The -lu argument to cs2cs or proj can be used to list symbolic unit names. The default unit for projected coordinates is the meter. A few special projections deviate from this behavior, most notably the latlong pseudo-projection that returns degrees. Note that this does not affect the units of linear parameters such as +x_0, +y_0, +a or +b which should always be specified in meters.

Vertical (Z) units can be specified using the +vunits keyword with a symbolic name for a unit (i.e. us-ft). Alternatively the translation to meters can be specified with the +vto_meter keyword (i.e. 0.304800609601219 for US feet). The -lu argument to cs2cs or proj can be used to list symbolic unit names. If no vertical units are specified, the vertical units will default to be the same as the horizontal coordinates.


proj does not handle vertical units at all and hence the +vto_meter argument will be ignored.

Scaling of output units can be done by applying the +k_0 argument (unitless). The returned coordinates are scaled by the value assigned with the +k_0 parameter. This parameter is only used by projections that mention using it, and its exact effect is projection dependent.

Input units for angular parameters (+lon_0, +lat_0, +pm, etc.) are interpreted to be decimal degrees by convention. Explicit specification of input angular units can be accomplished by adding the appropriate suffix to input values.




Decimal degrees






The sign of an angle is taken from either a - or + prefix, or the last character specifying a cardinal direction, where e/E (East) or n/N (North) are positive and w/W (West) or s/S (South) are negative.

Example of use. The longitude of the central meridian +lon_0=90, can also be expressed more explicitly with units of decimal degrees as +lon_0=90d or in radian units as +lon_0=1.570796r (approximately).

Angles can be expressed in DMS notation, using ' after arcminutes and " after arcseconds, ending with optional cardinal direction. For example, +pm=3d41'14.55"W, but character escapes +pm=3d41\'14.55\"W may be required.

Degree-minute notation does not require any quotation symbols. All of these are equivalent values: +pm=-17d40, +pm=17D40W, +pm=17°40w or +pm=17d40'W (escaped as +pm=17d40\'W).

False Easting/Northing

Virtually all coordinate systems allow for the presence of a false easting (+x_0) and northing (+y_0). Note that these values are always expressed in meters even if the coordinate system is some other units. Some coordinate systems (such as UTM) have implicit false easting and northing values.

Longitude Wrapping

By default PROJ wraps output longitudes in the range -180 to 180. The +over switch can be used to disable the default wrapping which is done at a low level in pj_inv(). This is particularly useful with projections like the Equidistant Cylindrical (Plate Carrée) or Mercator where it could be desirable for X values past -20000000 (roughly) to continue past -180 instead of wrapping to +180.

Note however that for most projections where the 180 meridian does not project to a straight line, +over will have no effect or will not lead to expected results.

The +lon_wrap option can be used to provide an alternative means of doing longitude wrapping. It has only effect with operations that output angular coordinates, such as +proj=longlat The argument to this option is a center longitude. So +lon_wrap=180 means wrap longitudes in the range 0 to 360.

$ echo -1 0 cs2cs +proj=longlat +to +proj=longlat +lon_wrap=180
359dE       0dN 0.000

Note that +over does not disable +lon_wrap.

Prime Meridian

A prime meridian may be declared indicating the longitude offset between the prime meridian of the declared coordinate system and that of greenwich. A prime meridian is declared using the +pm parameter, and may be assigned an angle in DMS or decimal degrees format, or as a hard-coded name.

Currently prime meridian declarations are not used by the pj_inv() and pj_fwd() calls. Consequently the user utility cs2cs does honour prime meridians but the proj user utility ignores them.

Hard-coded prime meridians can be listed with cs2cs -lm. Note that the following list is no longer updated, and some values may conflict with other sources.































Example of use. The location long=0, lat=0 in the greenwich based lat/long coordinates is translated to lat/long coordinates with Lisbon as the prime meridian.

cs2cs +proj=latlong +datum=WGS84 +to +proj=latlong +datum=WGS84 +pm=lisbon
0 0
9d7'54.862"E        0dN 0.000

Decimal degrees can also be simply specified for the prime meridian.

echo 13d30E 45N | proj +proj=merc +pm=13.5
0.00    5591295.92

See Units for other examples of angular inputs.

Axis orientation

Starting in PROJ 4.8.0, the +axis argument can be used to control the axis orientation of the coordinate system. The default orientation is "easting, northing, up" but directions can be flipped, or axes flipped using combinations of the axes in the +axis switch. The values are:

  • "e" - Easting

  • "w" - Westing

  • "n" - Northing

  • "s" - Southing

  • "u" - Up

  • "d" - Down

They can be combined in +axis in forms like:

  • +axis=enu - the default easting, northing, elevation.

  • +axis=neu - northing, easting, up - useful for "lat/long" geographic coordinates, or south orientated transverse mercator.

  • +axis=wnu - westing, northing, up - some planetary coordinate systems have "west positive" coordinate systems


The +axis argument does not work with the proj command line utility.

Order of applications of parameters

In the forward direction (from geodetic to projected coordinates), steps are performed in the following order:

  • subtracting prime meridian (+pm) to input coordinate longitude

  • subtracting central meridian (+lon_0) to input coordinate longitude

  • normalizing input coordinate longitude to [-180, 180], unless +over is specified

  • application of map projection formula on a spheroid of radius 1 and with the eccentricity of the target spheroid specified. Includes taking into account projection parameters such as +k_0, +lat_0, and other projection specific parameters

  • scaling of output x, y values by the semimajor axis

  • addition of false easting +x_0 to x and false northing +y_0 to y

  • scaling of output x, y by the output horizontal unit (+units / +to_meter)

  • scaling of output z by the output vertical unit (+vunits / +vto_meter)

  • application of axis orientation and order (+axis)

This is implemented mostly in fwd.cpp

For the reverse direction (from projected coordinates to geodetic coordinates), reverse steps are performed in the reverse order.