# Eckert III

## Description

The Eckert III is a compromise pseudocylindrical map projection for world maps. The lateral meridians are semicircles, which give the projection a rounded shape and smooth corners where the lateral meridians meet the pole lines.

This projection was introduced by Max Eckert in 1906. 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 Eckert III projection properties.

### Graticule

Eckert III is a pseudocylindric projection. The meridians are regularly distributed semiellipses concave toward the central meridian. The lateral meridians are semicircles, which give the graticule a rounded shape. The central meridian is a straight line, half the length of the projected equator. The parallels are equally distributed straight lines perpendicular to the central meridian. The poles are straight lines half the length of the equator. The corners where lateral meridians meet the pole lines are smooth. The graticule is symmetric across the equator and the central meridian.

### Distortion

The Eckert III projection is neither conformal nor equal-area. It generally distorts shapes, areas, distances, directions, and angles. The scale is constant along any given parallel. The distortion patterns are similar to other compromise pseudocylindrical projections. Area distortion grows with latitude and does not change with longitude. High latitude areas are exaggerated. Angular distortion is zero at the equator and increases toward the poles. Distortion values are symmetric across the equator and the central meridian.

## Usage

The Eckert III projection is appropriate for general world maps not requiring accurate areas.

## Limitations

This projection is supported on spheres only. For an ellipsoid, the semimajor axis is used for the radius.

## Parameters

Eckert III parameters are as follows:

• False Easting
• False Northing
• Central Meridian

## Sources

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.