Equal Earth: properties, uses, and limitations
A 2018 equal-area pseudocylindrical projection built as an answer to Gall-Peters. Area is exact at every latitude; the whole bill lands on shape, 24.6 times stretched at 84 degrees.
Description
Equal Earth was published in 2018 by Bojan Savric, Tom Patterson and Bernhard Jenny. The trigger was specific: Boston Public Schools switched to Gall-Peters in March 2017, the three authors went looking for an equal-area world map they found acceptable to look at, could not find one, and built this.
Its silhouette follows Robinson - curved meridians, rounded outline - but Robinson is a compromise projection and Equal Earth is strictly equal-area. It is the youngest of the five projections on this site.
Projection properties
- Family
- Equal-area pseudocylindrical
- Frame ratio
- 2.055:1
- Latitudes drawn
- The whole world
- Pole line
- 59% of the equator
- True-shape parallel
- 40.4°
- Area distortion doubles
- Never
- Shape distortion doubles
- 63.8°
- Held at 1.00 by definition
- Area distortion
Parallels are straight horizontal lines but their spacing narrows towards the poles, which is what pays for the area; meridians curve; each pole is a line 59 percent the length of the equator. The frame is 2.055:1.
Equal-area: area distortion is exactly 1.00 at every latitude. This site verifies it with 0.02-degree patches at six latitudes, agreeing to within one part in a million.
Shape is where it pays. 1.35 at the equator, 1.15 at 30 degrees, down to 1.00 at 40.4 - its one true-shape parallel, and, as with Natural Earth 1, not part of its definition - then up again: 1.69 at 60, doubling at 63.8, and 24.6 at 84.
Measured distortion
| Latitude | 0° | 30° | 45° | 60° | 72° | 84° |
|---|---|---|---|---|---|---|
| Area distortion | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Shape distortion | 1.35 | 1.15 | 1.09 | 1.69 | 3.43 | 24.6 |
Both rows are measured against this projection's own equator, taken as 1. They compare with each other and with nothing on another projection's page - every projection is normalised to itself.
Uses
World thematic maps whose subject is quantity spread over ground: population, land cover, emissions, election results, economic data. Equal area is a precondition there - draw the areas wrong and the conclusion is wrong.
It has become a default world base for a number of organisations, because it satisfies equal-area and inoffensive-looking at once, which had been hard to get together. If you need one equal-area world map, this is usually it.
Limitations
Not conformal. High-latitude shapes are visibly stretched - the axis ratio at 84 degrees is 24.6 - so it is the wrong map for discussing polar shape.
The poles are lines rather than points, so polar geography arrives as a band stretched across the top of the map instead of converging to a point.
And the constraint every equal-area projection lives under: area and angle cannot both be preserved. That is a result in the geometry of curved surfaces, not an engineering regret.
Parameters
How this site builds it (w and h are the canvas; sphere is the whole globe):
geoEqualEarth().fitExtent([[0, 0], [w, h]], sphere)Its formulas are polynomials with fixed coefficients. There is no standard parallel to set; only the central meridian moves.
It is cheap to evaluate - a few polynomial terms forwards, Newton iteration backwards. The authors pursued that deliberately, because a world base map has to redraw live in a browser.