# Equidistant cylindrical

## Description

The equidistant cylindrical is also known as equirectangular, simple cylindrical, rectangular, or when the standard parallel is the equator, plate carrée map projection. A grid of parallels and meridians forms equal rectangles from east to west and from pole to pole. It is one of the simplest cylindrical projections and therefore its usage was more common in the past. The equidistant cylindrical projection was invented by Marinus of Tyre about A.D. 100. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.

## Projection properties

The subsections below describe the equidistant cylindrical projection properties.

### Graticule

Equidistant cylindrical is a cylindric projection. The meridians and parallels are equally spaced straight lines forming a Cartesian grid. Each rectangular grid cell has the same size, shape, and area only in the projected space. The standard parallels can be at any latitude, except the poles. When the standard parallel is the equator, resulting in the plate carrée projection, the grid cells are perfect squares, but if any other parallel is used, the grids are rectangular. In this projection, the poles are represented as straight lines across the top and bottom of the grid, the same length as the equator. The graticule is symmetric across the equator and the central meridian.

### Distortion

The projection is equidistant along any meridian and both standard parallels. Shape, scale, and area distortion increase with the distance from the standard parallels. North, south, east, and west directions are always accurate, but general directions are distorted, except locally along the standard parallels. Distortion values are symmetric across the equator and the central meridian.

## Usage

This projection can be used for simple portrayals of the world or regions with minimal geographic data and not requiring accurate areas. This makes the projection useful for index maps and to map phenomena that change with longitude such as time zones. Most often, data in a geographic coordinate system is displayed in a pseudo-plate carrée projection, which looks exactly like equidistant cylindrical with the standard parallel at the equator, and the decimal degree values are treated as if they are linear.

## Variants

There are three variants available in ArcGIS. All three variants correctly support spheres.

• The equidistant cylindrical variant is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later. It uses the semimajor axis and spherical equations for ellipsoids.
• The equidistant cylindrical auxiliary sphere variant is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 9.3 and later. This variant uses a sphere specified by the Auxiliary Sphere Type parameter and spherical equations.
• The equidistant cylindrical ellipsoidal variant is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 10.0 and later. For ellipsoids, this is the only variant that correctly maintains the projection's properties.

## Limitations

Equidistant cylindrical is supported on spheres only. Only the equidistant cylindrical ellipsoidal variant supports ellipsoids.

## Parameters

Equidistant cylindrical parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Standard Parallel 1

Equidistant cylindrical auxiliary sphere parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Standard Parallel 1
• Auxiliary Sphere Type, with values as follows:
• 0 = use semimajor axis or radius of the geographic coordinate system
• 1 = use semiminor axis or radius
• 2 = calculate and use authalic radius
• 3 = use authalic radius and convert geodetic latitudes to authalic latitudes

Equidistant cylindrical ellipsoidal parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Standard Parallel 1

### Particular parameter cases

When standard parallel is set at the equator, the projection results in the plate carrée map projection.

## Sources

Snyder, J. P. (1987). Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, DC: United States Government Printing Office.

Snyder, J. P. and Voxland, P. M. (1989). An Album of Map Projections. U.S. Geological Survey Professional Paper 1453. Washington, DC: United States Government Printing Office.

Yang, Q., Snyder, J. P. and Tobler, W. R. (2000). Map Projection Transformation: Principles and Applications. London: Taylor & Francis Group.