# Robinson

## Description

The Robinson projection is perhaps the most commonly used compromise pseudocylindrical map projection for world maps. National Geographic used the Robinson projection for their world maps for about a decade until 1998.

The projection was designed by Arthur H. Robinson in 1963 at the request of the Rand McNally Company using graphic design rather than mathematical equation development. It was briefly called the orthophanic ("right appearing") projection after its introduction. 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 Robinson projection properties.

### Graticule

Robinson is a pseudocylindric projection. The meridians are regularly distributed curves mimicking elliptical arcs. They are concave toward the central meridian and do not intersect the parallels at right angles. The parallels are unequally distributed straight lines. The equator, both poles, and the central meridian are projected as straight lines. The central meridian is 0.5072 times the length of the projected equator and pole lines are 0.5322 as long as equator. The graticule is symmetric across the equator and the central meridian.

### Distortion

The Robinson projection is neither conformal nor equal-area. It generally distorts shapes, areas, distances, directions, and angles. The distortion patterns are similar to common compromise pseudocylindrical projections. Area distortion grows with latitude and does not change with longitude. High latitude areas are exaggerated. Angular distortion is moderate near the center of the map and increases toward the edges. Distortion values are symmetric across the equator and the central meridian.

## Usage

The Robinson projection is primarily appropriate for general world maps. National Geographic used it for their world maps for about a decade until 1998.

## Variants

There are two variants available in ArcGIS:

• Robinson uses computation algorithm described by J.P. Snyder. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.
• Robinson ArcInfo was added later to support the implementation of the projection in ArcInfo workstation. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 9.0 and later.

## Limitations

Both variants support spheres only. For an ellipsoid, the Robinson variant uses an authalic radius and the Robinson ArcInfo variant uses the semimajor axis for the radius.

## Parameters

Robinson parameters are as follows:

• False Easting
• False Northing
• Central Meridian

Robinson ArcInfo parameters are as follows:

• False Easting
• False Northing
• Central Meridian

## Sources

Robinson, A. (1974). "A new map projection: its development and characteristics." In: Kirschbaum, G. M. (eds.), Meine, K.-H. (eds.). International Yearbook of Cartography, Bonn-Bad Godesberg, Germany: Kirschbaum, 145-55.

Snyder, J. P. (1990). "The Robinson projection: A computation algorithm." Cartography and Geographic Information Systems, 17 (4), p. 301-305.

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.