# Cylindrical equal area

## Description

The cylindrical equal area projection presents the world as a rectangle while maintaining relative areas on a map.

The projection was first described by the Swiss mathematician Johann H. Lambert in 1772. Since then, many variations appeared over the years. The projection is appropriate for large-scale mapping of the areas near the equator and generally not recommended for small-scale (world) maps. 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 cylindrical equal-area projection properties.

### Graticule

Cylindrical equal area is a cylindric projection. The meridians are vertical lines, parallel to each other, and equally spaced. The lines of latitude are horizontal straight lines, perpendicular to meridians, and the same length as the equator, but their spacing decreases toward the poles. Both lines form a rectangular grid where each cell covers the same area size on a spheroid. 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

Cylindrical equal area is an equal-area (equivalent) projection. The scale is correct along the standard parallels. Shape, scale, direction, angle, and distance distortion increase with the distance from the standard parallels. Shapes are distorted north-south between the standard parallels (if the equator is not used as the standard parallel) and east-west above the standard parallels. The distortion values are severe near the poles and symmetric across the equator and the central meridian.

## Usage

The projection is appropriate for large-scale mapping of the areas near the equator such as Indonesia and parts of the Pacific Ocean. Its recommended use is for narrow areas extending along the standard lines. The projection is often misused for small-scale mapping.

## Limitations

The standard parallels can be at any latitude except the poles.

## Parameters

Cylindrical equal area parameters are as follows:

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

### Particular parameter cases

When the standard parallel is set to the equator, the resulting projection is the Lambert cylindrical equal-area. The Behrmann projection is obtained when the standard parallel is set at 30°, Smyth equal-surface or Craster rectangular at 37°04′17″, Trystan Edwards at 37°24′, Gall orthographic at 45°, Balthasart at 50°, and Tobler's world in a square when the standard parallel is set at 55°39′14″.

## Sources

Maling, D. H. (1992). Coordinate Systems and Map Projections, 2nd ed. Oxford: Pergamon Press.

Smyth, C. P. (1870). On an Equal-Surface Projection and its Anthropological Applications. Edinburgh: Edmonton & Douglas.

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. (1993). Flattening the Earth. Two Thousand Years of Map Projections. Chicago and London: University of Chicago Press.

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.

Tobler, W. and Chen, Z. (1986). "A Quadtree for Global Information Storage." Geographical Analysis, 18(4), p. 360-371.