# 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.

Parameter

Description

+a

Semimajor radius of the ellipsoid axis (always in meters)

+axis

Axis orientation

+b

Semiminor radius of the ellipsoid axis (always in meters)

+ellps

Ellipsoid name (see

`proj -le`

)+k

Scaling factor (deprecated)

+k_0

Scaling factor

+lat_0

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

+lon_0

Central meridian (in degree if no angular unit specified)

+lon_wrap

Center longitude to use for wrapping (see below)

+over

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

+pm

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

+proj

Projection name (see

`proj -l`

)+units

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

+vunits

Vertical coordinate system units.

+x_0

False easting (always in meters)

+y_0

False northing (always in meters)

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

## Units¶

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.

Note

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.

Suffix

Unit

d

Decimal degrees

D

°

r

Radians

R

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.

Meridian

Longitude

greenwich

0dE

lisbon

9d07'54.862"W

paris

2d20'14.025"E

bogota

74d04'51.3"W

madrid

3d41'16.58"W

rome

12d27'8.4"E

bern

7d26'22.5"E

jakarta

106d48'27.79"E

ferro

17d40'W

brussels

4d22'4.71"E

stockholm

18d3'29.8"E

athens

23d42'58.815"E

oslo

10d43'22.5"E

copenhagen

12d34'40.35"E

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

Note

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 longitudesubtracting central meridian (

`+lon_0`

) to input coordinate longitudenormalizing input coordinate longitude to [-180, 180], unless

`+over`

is specifiedapplication 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 parametersscaling of output x, y values by the semimajor axis

addition of false easting

`+x_0`

to x and false northing`+y_0`

to yscaling 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.