Equal Earth projection

The Equal Earth map projection is an equal-area pseudocylindrical global map projection invented by Bojan Šavrič, Bernhard Jenny, and Tom Patterson in 2018. It is inspired by the widely used Robinson projection, but unlike the Robinson projection, it retains the relative size of areas, and the projection equations are designed to be simple to implement and fast to evaluate. As with other equal-area projections, the Equal Earth projection distorts shapes.

Following a public campaign called "Correct the Map" to promote the Equal Earth projection, and a resolution by the African Union to officially adopt the projection, the United Nations General Assembly approved a resolution addressing the projection in September 2026. The resolution discouraged use of the Mercator projection for most uses other than navigation, while encouraging the use of equal-area projections instead, and favorably mentioning Equal Earth as an option.

Design motivation

Some map projections distort the relative size of different regions on the map, with non-equatorial regions depicted larger than equatorial regions of the same area. For example, on the Mercator projection, Greenland appears to be larger than the whole of Africa, when in reality it is only 7% as big. An equal-area projection solves this problem by depicting regions in proportion to their original area, at the expense of shape distortion.

In March 2017, Boston Public Schools adopted the equal-area Gall–Peters projection for world maps, to accurately show the relative sizes of equatorial and non-equatorial regions. The decision generated controversy in the world of cartography due to that projection's extreme shape distortion in the polar regions. Šavrič, Jenny, and Patterson examined alternative equal-area projections of the world, but could not find any that met their aesthetic criteria, so decided to create a new projection which they considered more visually appealing.

According to Šavrič, Jenny, and Patterson, equal-area projections are not an ideal solution to every mapping problem, as continental shapes are distorted. Equal Earth is only intended for situations calling for an equal-area map.

Formulation

As with the earlier Natural Earth projection (2012) introduced by Patterson, a visual method was used to choose the parameters of the projection. A combination of Putniņš P4ʹ and Eckert IV projections was used as the basis. Mathematical formulas for the projection were derived from a polynomial used to define the spacing of parallels. The projection is formulated as the equations:

$${\displaystyle {\begin{aligned}x&={\frac {2{\sqrt {3}}}{3}}\lambda \cdot {\frac {\cos {\theta }}{9A_{4}\theta ^{8}+7A_{3}\theta ^{6}+3A_{2}\theta ^{2}+A_{1}}},\\[3pt]y&=A_{4}\theta ^{9}+A_{3}\theta ^{7}+A_{2}\theta ^{3}+A_{1}\theta ,\end{aligned}}}$$ where ${\displaystyle \varphi }$ is the latitude and ${\displaystyle \lambda }$ is the longitude, ⁠${\displaystyle \theta }$⁠ is a function of latitude defined by $${\displaystyle \sin \theta ={\tfrac {\sqrt {3}}{2}}\sin {\varphi },}$$ and the polynomial coefficients are $${\displaystyle {\begin{aligned}A_{1}&=1.340264,\quad A_{2}=-0.081106,\\A_{3}&=0.000893,\quad A_{4}={\phantom {-}}0.003796,\end{aligned}}}$$ with all angles expressed in radians.

The resulting map has an aspect ratio of 2.05458:1, a value chosen for aesthetic reasons and very close to the "natural ratio" of a sphere (180°/90°).

Distortion

Since the surface of a sphere cannot be mapped onto a plane without distortion, all (planar) maps distort shapes in one way or another. The distortion can be visualized using an index called "Tissot's Indicatrix", which shows how the size and shape of an infinitesimal circular area is projected onto the map.

In the Equal Earth projection, a small area on the surface of the Earth shows its accurate shape on the central meridian (0°) at a latitude of 40.4° North or South. At locations closer to the equator than this, shapes are elongated in the north-south direction and compressed in the east-west direction, reaching a maximum shape distortion of 1.35. At locations poleward of 40.4°, shapes are elongated E-W and compressed N-S, with an elongation ratio approaching infinity at the pole (mapping the pole itself to a horizontal line rather than a point.) East and west of the central meridian of 0°, at locations away from the equator the ellipses become tilted, with the north-south axis of the ellipse pointed toward the central meridian.

Use

An Equal Earth Political Wall Map by Tom Patterson, designed for schools and organisations, is labelled using United States Central Intelligence Agency map data. Countries are mostly the same as US government maps; however, Patterson made changes in the depiction of Myanmar (and Naypyidaw), Taiwan (and Taipei), Western Sahara (Western Sahara conflict), depiction of Crimea, a border between Kenya and South Sudan, and boundaries between China, India, and Pakistan.

One of the first known thematic maps published using the Equal Earth projection is a map of the global mean temperature anomaly for July 2018, produced by NASA's Goddard Institute for Space Studies.

United Nations resolution

On September 4, 2026, the Correct the Map resolution, put forward by African Union member states and The Bahamas, was adopted at the 80th session of the United Nations General Assembly. The resolution encourages the world to phase out the Mercator projection in favour of the Equal Earth projection and other equal-area projections, which depict equatorial regions larger, and polar regions smaller, compared to the Mercator projection. The resolution links more accurate maps to "cognitive justice, historical recognition and equitable representation". UN resolutions are non-enforceable and use of the projection is not mandated, and other projections are not banned.

The Guardian wrote the outcome was expected to result in the update of education curriculums and general technology. Agence France-Presse published a handout map. Šavrič, Jenny, and Patterson were surprised by the projection's near-universal acceptance by the United Nations.

Positions of member states

Of the 193 member states of the United Nations, 164 voted in favour of the resolution, six abstained (Estonia, Georgia, Lithuania, Moldova, Serbia, and Ukraine), and one voted against (United States).

The United States opposed the resolution on the grounds that it did not address "genuine problems", saying that it "mocks the work and purpose" of the United Nations, and calling it part of a "larger and more radical ideological project". Ukraine abstained from the vote, taking issue with the fact that maps published by Tom Patterson on equal-earth.com depicted Crimea in a different color from Ukraine, which the Ukrainian representative called "wholly unacceptable". Similarly, after the vote, Japanese diplomats contacted Patterson asking for a change to the Kuril Islands, which were depicted in the same color as Russia.

France's foreign minister Jean-Noël Barrot announced that France will discontinue teaching the Mercator projection in schools in response to the resolution.

Alternatives

The Winkel tripel projection has more accurate shapes than Equal Earth with less accurate sizes, and is regarded as one of the least distorted compromise projections. The National Geographic Society and many educational institutions use Winkel tripel projection for global mapping.

The Equal Earth projection is one of many equal-area pseudocylindrical map projections.

The Natural Earth projection looks much like Equal Earth, while better preserving the shapes of the continents, but is not equal-area. The Robinson projection is another alternative of this type.

Earlier attempts to give "a truer sense of area while retaining a visually intuitive layout" and replace the Mercator projection include the Goode homolosine and Gall–Peters projection.

See also

• List of map projections

Footnotes

References

External links

• "Equal Earth Wall Map". equal-earth.com. – a wall map for schools and organizations
• Marit Jentoft-Nilsen (March 31, 2019). "Long-term Global Warming trend, 2018 update – Global temperature anomaly for 2018". NASA's Goddard Space Flight Center, NASA Goddard Institute for Space Studies.
• "OpenEqualEarthMap". openequalearthmap.com. – a basic map showing OpenStreetMap data