Lambert Conformal Conic

A Lambert Conformal Conic projection (LCC) is a conic map projection used for aeronautical charts, portions of the State Plane Coordinate System, and many national and regional mapping systems. It is one of seven projections introduced by Johann Heinrich Lambert in 1772.

It has several different forms: with one and two standard parallels (referred to as 1SP and 2SP in EPSG guidance notes). Additionally we provide “2SP Michigan” form which is very similar to normal 2SP, but with a scaling factor on the ellipsoid (given as k_0 parameter). It is implemented as per EPSG Guidance Note 7-2 (version 54, August 2018, page 25). It is used in a few systems in the EPSG database which justifies adding this otherwise non-standard projection.

Classification

Conformal conic

Available forms

Forward and inverse, spherical and ellipsoidal . One or two standard parallels (1SP and 2SP). “LCC 2SP Michigan” form can be used by setting +k_0 parameter to specify ellipsoid scale.

Defined area

Best for regions predominantly east–west in extent and located in the middle north or south latitudes.

Alias

lcc

Domain

2D

Input type

Geodetic coordinates

Output type

Projected coordinates

Lambert Conformal Conic

proj-string: +proj=lcc +lon_0=-90 +lat_1=33 +lat_2=45

Parameters

Required

+lat_1=<value>

First standard parallel.

Defaults to 0.0.

Note

The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the “r” character.

Example: +lat_1=1.5708r

See Projection Units for more information.

Optional

+lon_0=<value>

Longitude of projection center.

Defaults to 0.0.

Note

The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the “r” character.

Example: +lon_0=1.5708r

See Projection Units for more information.

+lat_0=<value>

Latitude of projection center.

Defaults to 0.0.

Note

The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the “r” character.

Example: +lat_0=1.5708r

See Projection Units for more information.

+lat_2=<value>

Second standard parallel.

Defaults to 0.0.

Note

The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the “r” character.

Example: +lat_2=1.5708r

See Projection Units for more information.

+ellps=<value>

The name of a built-in ellipsoid definition.

See Ellipsoids for more information, or execute proj -le for a list of built-in ellipsoid names.

Defaults to “GRS80”.

+R=<value>

Radius of the sphere, given in meters. If used in conjunction with +ellps, +R takes precedence.

See Ellipsoid size parameters for more information.

+x_0=<value>

False easting.

Defaults to 0.0.

+y_0=<value>

False northing.

Defaults to 0.0.

+k_0=<value>

This parameter can represent two different values depending on the form of the projection. In LCC 1SP it determines the scale factor at natural origin. In LCC 2SP Michigan it determines the ellipsoid scale factor.

Defaults to 1.0.

Further reading

  1. Wikipedia

  2. Wolfram Mathworld

  3. John P. Snyder “Map projections: A working manual” (pp. 104-110)

  4. ArcGIS documentation on “Lambert Conformal Conic”

  5. EPSG Guidance Note 7-2 (version 54, August 2018, page 25)