The Robinson Projection

The Robinson projection is the prototypical compromise projection. Where the /learn/mercator-projection preserves angles exactly at the cost of area, and the /learn/peters-projection preserves area exactly at the cost of shape, Robinson preserves nothing exactly. Instead it distributes the distortion that Gauss's Theorema Egregium (covered in /learn/what-is-a-map-projection) guarantees must exist across all four properties, making each as small as possible. The result is a world map that “looks right” in a way that area-preserving and angle-preserving projections often do not.

How the projection looks

Robinson is pseudocylindrical: the parallels are straight horizontal lines (like a cylindrical projection), but the meridians are smooth curves (unlike a true cylindrical projection where they would be straight). The shape is a rounded rectangle — wider than it is tall, with the corners flattened.

Key visual properties:

• Parallels are straight horizontal lines, evenly spaced from the equator out to about 38° N and S, then progressively closer together toward the poles.
• Meridians are smooth curves, evenly spaced along each parallel and meeting at short pole lines rather than at single points. The pole lines are about 53% of the length of the equator.
• Aspect ratio is approximately 1.97 : 1 (width : height).
• Distortion is minimised in mid-latitudes (where most populated land sits) and grows toward the poles, but never reaches the extreme stretching of either Mercator or Peters.

The pole lines instead of pole points are a distinctive feature. A pseudocylindrical projection has freedom in how it terminates the meridians; Robinson chose pole lines to prevent the high-latitude landmasses (Greenland, Antarctica, northern Russia) from being pinched into unrecognisable shapes.

Arthur Robinson's design process

Robinson's 1974 paper “A New Map Projection: Its Development and Characteristics” describes the design process. It was not mathematical in the usual sense. Rand McNally had asked Robinson, then a professor at the University of Wisconsin-Madison, to design a world-map projection that would look better than the cylindrical projections then in use at the publisher (notably the Van der Grinten projection, which has its own distortion issues).

Robinson started with a set of design goals that were partly mathematical (low area distortion, reasonable shape, smooth meridians) and partly aesthetic (“looks like the world”). He then drew dozens of trial graticules with different meridian-curve and parallel-spacing schemes, and showed each to colleagues, students, and a sample of the general public. The projection he eventually published was the one that consistently received the most favourable visual responses.

This is an unusual approach for a major map projection. Most projection families come from a closed-form mathematical recipe chosen for a specific property: conformality, equal-area, equidistance. Robinson's projection came from human visual preference. The closest analogue is in industrial design rather than in mathematics.

The lookup table

Because Robinson designed by trial rather than by formula, his projection cannot be expressed in a single closed-form equation. Instead it is defined by a table of two scaling factors — call them A(φ) for the meridian spacing and B(φ) for the parallel spacing — at 5° intervals of latitude. Robinson published the table in his 1974 paper; it has since been republished in Snyder's Map Projections and many other cartographic references.

The map coordinates for a point at (φ, λ) are then:

x = R · 0.8487 · A(φ) · (λ − λ₀)
y = R · 1.3523 · B(φ)

where A(φ) and B(φ) are interpolated from the table. Different implementations use different interpolation schemes: linear interpolation between adjacent table entries is the simplest, cubic-spline interpolation is smoother, and various proprietary schemes exist in commercial GIS software. The choice of interpolation introduces small differences in the rendered projection — the “Robinson projection” in different software products is not bit-identical, although the differences are small.

The dependence on a table is mildly inconvenient for software that prefers closed-form math, but it has not slowed adoption. Most modern cartographic libraries (PROJ, GDAL, D3.js, MapLibre) include Robinson as a standard projection.

Distortion in numbers

The Robinson projection's compromise is quantifiable. Standard distortion measures used in cartographic literature — angular deformation, area scale factor, maximum distortion ω — show:

| Property | Robinson | Mercator | Peters | Equal Earth | |---|---|---|---|---| | Area preservation at 0° | 1.00 | 1.00 | 1.00 | 1.00 | | Area preservation at 60° | 1.18 | 4.00 | 1.00 | 1.00 | | Area preservation at 80° | 1.59 | 33.16 | 1.00 | 1.00 | | Maximum angular distortion ω | ~37° at the poles | 0° (conformal) | ~67° at the equator | ~27° | | Equator-to-pole ratio | 1.00 to 0.53 | 1.00 to infinity | 1.00 to 1.00 | 1.00 to 0.42 |

(Approximate values; precise numbers depend on the interpolation scheme used to fill in between Robinson's table entries.)

Robinson's areas at high latitudes are larger than truth but modestly so — about 18% inflation at 60°, less than the 33× inflation of Mercator at the same latitude. Its shape distortion at the poles is real but visually mild because the pole line, not a pole point, prevents the worst pinching. The compromise produces a map where no single distortion is bad enough to be objectionable.

Arthur Robinson's career

The projection bears Robinson's name because his broader cartographic career was substantial. Robinson was born in Montclair, NJ in 1915, took his PhD at Ohio State in 1947, and joined the University of Wisconsin-Madison cartography faculty that same year, remaining there until his retirement in 1980.

During the Second World War, Robinson worked in the Office of Strategic Services (OSS) Map Division in Washington, DC, producing operational maps for Allied military planning. The wartime experience shaped his thinking about what makes a useful map — a perspective he carried into his peacetime academic work.

His 1953 textbook Elements of Cartography, written with several co-authors across multiple editions, was the standard introductory cartography textbook in English for over four decades; it ran through six editions, the last published in 1995. Generations of geographers, surveyors, and GIS professionals learned cartography from it.

Robinson also served as president of the International Cartographic Association from 1972 to 1976, was awarded the Carl Mannerfelt Gold Medal in 1988 (the highest honour in international cartography), and authored more than 80 academic papers across a 50-year career. He died in 2004. The projection that bears his name is his most publicly visible contribution but is far from the only one.

National Geographic 1988

Robinson's projection was used in Rand McNally atlases from 1963 onward but achieved its iconic status only when the National Geographic Society adopted it for its world map series in 1988. The Society had previously used the Van der Grinten projection (since 1922) and before that the Mercator. The 1988 switch was an editorial decision motivated partly by the Peters controversy of the previous decade — National Geographic wanted a projection that preserved its neutral editorial stance, neither preserving angle the way Mercator does (and provoking the Peters argument) nor preserving area the way Peters does (and inviting endless arguments about shape distortion).

The Robinson projection, with its compromise philosophy, fit the Society's position. Robinson's map became the world map that most Americans recognised through the late 1980s and 1990s. It appeared on classroom walls, in school textbooks, on television news graphics, and on countless products that used a Society-licensed world map.

National Geographic 1998 — the Winkel Tripel switch

In 1998 National Geographic switched to the Winkel Tripel projection. The Winkel Tripel was designed by Oswald Winkel in 1921; it is a modified azimuthal projection that arrives at compromise distortion through a different construction than Robinson but with broadly similar visual results. National Geographic cited slightly better area-distortion properties and improved high-latitude shape preservation as the reasons for the switch.

Robinson himself, in his last years, reportedly approved the change. He had always characterised his projection as the best he could achieve with the design constraints he faced; he did not consider it the final word on compromise projections, and the Winkel Tripel was an evolution along the same philosophical path.

The compromise-projection landscape

Robinson is one of several major compromise projections in current use. The landscape includes:

• Robinson (1963) — the projection of this article; tabular definition, used widely in atlases since 1988.
• Winkel Tripel (1921, popularised 1998) — modified azimuthal; current National Geographic standard.
• Natural Earth (2007) — designed by Tom Patterson, a former US National Park Service cartographer; tabular like Robinson but with slightly different priorities.
• Equal Earth (2018) — designed by Bojan Šavrič, Tom Patterson, and Bernhard Jenny; preserves area exactly while still looking visually balanced. A response to the Peters/Mercator argument that preserves area without the shape distortion of cylindrical equal-area projections.

All four projections are widely available in modern cartographic software. Each makes a slightly different trade-off; none is universally “best”, in the sense that no projection can be best when the impossibility theorem precludes preserving every property.

In practical software terms, Robinson is exposed in PROJ via the projection code +proj=robin, in D3.js via d3.geoRobinson(), in GDAL and QGIS as a standard built-in, and in MapLibre and Mapbox via runtime projection configuration. The implementations all interpolate between Robinson's tabular values; the small differences between implementations are visible only on careful side-by-side comparison. Web atlases that need a single static world map for thematic display still reach for Robinson by default, because its visual familiarity makes the map immediately legible to a general audience without requiring any explanation of projection trade-offs.

The trend over the past two decades has been toward Natural Earth and Equal Earth for new design work, with Robinson retained for legacy compatibility and for its specific historical association with National Geographic. For web mapping (zoom-and-pan tile maps), Web Mercator remains dominant regardless of static-map projection preferences; see the /learn/web-mercator-projection support for why.

Sources

• Robinson, “A New Map Projection: Its Development and Characteristics” (International Yearbook of Cartography 14, 1974) — Robinson's own description.
• Snyder, Map Projections — A Working Manual (USGS Prof. Paper 1395) — the projection table and discussion.
• Snyder, Flattening the Earth (University of Chicago Press, 1993) — historical context including the National Geographic adoption.
• National Geographic Society — projection history and editorial statements.

For closely related topics, see /learn/winkel-tripel-projection for the projection that replaced Robinson at National Geographic, /learn/peters-projection for the controversy Robinson sidestepped, and /learn/what-is-a-map-projection for the impossibility theorem that makes compromise projections necessary.