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.  The subsections below describe the Robinson projection properties. 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. 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. The Robinson projection is primarily appropriate for general world maps. National Geographic used it for their world maps for about a decade until 1998. There are two variants available in ArcGIS:
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. Robinson parameters are as follows:
Robinson ArcInfo parameters are as follows:
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. Feedback on this topic? The Robinson projection is a map projection of a world map which shows the entire world at once. It was specifically created in an attempt to find a good compromise to the problem of readily showing the whole globe as a flat image.[1] The Robinson projection was devised by Arthur H. Robinson in 1963 in response to an appeal from the Rand McNally company, which has used the projection in general-purpose world maps since that time. Robinson published details of the projection's construction in 1974. The National Geographic Society (NGS) began using the Robinson projection for general-purpose world maps in 1988, replacing the Van der Grinten projection.[2] In 1998 NGS abandoned the Robinson projection for that use in favor of the Winkel tripel projection, as the latter "reduces the distortion of land masses as they near the poles".[3][4] The Robinson projection is neither equal-area nor conformal, abandoning both for a compromise. The creator felt that this produced a better overall view than could be achieved by adhering to either. The meridians curve gently, avoiding extremes, but thereby stretch the poles into long lines instead of leaving them as points.[1] Hence, distortion close to the poles is severe, but quickly declines to moderate levels moving away from them. The straight parallels imply severe angular distortion at the high latitudes toward the outer edges of the map – a fault inherent in any pseudocylindrical projection. However, at the time it was developed, the projection effectively met Rand McNally's goal to produce appealing depictions of the entire world.[5][6]
The projection is defined by the table:[7][8][9]
The table is indexed by latitude at 5-degree intervals; intermediate values are calculated using interpolation. Robinson did not specify any particular interpolation method, but it is reported that others used either Aitken interpolation (with polynomials of unknown degrees) or cubic splines while analyzing area deformation on the Robinson projection.[10] The X column is the ratio of the length of the parallel to the length of the equator; the Y column can be multiplied by 0.2536[11] to obtain the ratio of the distance of that parallel from the equator to the length of the equator.[7][9] Coordinates of points on a map are computed as follows:[7][9] x = 0.8487 R X ( λ − λ 0 ) , y = 1.3523 R Y , {\displaystyle {\begin{aligned}x&=0.8487\,RX(\lambda -\lambda _{0}),\\y&=1.3523\,RY,\end{aligned}}} where R is the radius of the globe at the scale of the map, λ is the longitude of the point to plot, and λ0 is the central meridian chosen for the map (both λ and λ0 are expressed in radians).Simple consequences of these formulas are:
The Central Intelligence Agency World Factbook uses the Robinson projection in its political and physical world maps. The European Centre for Disease Prevention and Control recommends using the Robinson projection for mapping the whole world.[12]
Wikimedia Commons has media related to Maps with Robinson projection.
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