Gall-Peters: properties, uses, and limitations
A cylindrical equal-area projection with standard parallels at 45 degrees. Area is exact; the shape bill is the heaviest of the five - exactly 2 at the equator, 45.8 at 84 degrees.
Description
James Gall presented it in 1855 as his orthographic cylindrical projection. In 1973 Arno Peters built a political argument around it: Mercator systematically draws the wealthy high-latitude countries too large, so schools and agencies should use a map that does not inflate area. The two names were later joined.
Mathematically it is the Lambert cylindrical equal-area projection with standard parallels at plus and minus 45 degrees, and nothing more. Peters' contribution was to make it a public argument; some of his claims about other projections were later shown by cartographers to be factually wrong. The half of the argument that is about area is correct, and the numbers on this page are the evidence.
Projection properties
- Family
- Equal-area cylindrical
- Frame ratio
- 1.571:1
- Latitudes drawn
- The whole world
- Pole line
- As long as the equator
- True-shape parallel
- 45.0°
- Area distortion doubles
- Never
- Shape distortion doubles
- 60.0°
- Held at 1.00 by definition
- Area distortion
Meridians are evenly spaced vertical lines; parallels are horizontal with spacing narrowing towards the poles. Each pole is a straight line as long as the equator.
The frame is exactly pi/2, about 1.571. A cylindrical equal-area projection's frame ratio is pi times cos squared of its standard parallel, and only 45 degrees gives this number - so that single figure is enough to prove the standard parallel was applied. This site's registry test checks it that way.
Equal-area: area distortion is exactly 1.00 everywhere.
Shape: exactly 2.00 at the equator, squashed east-west and stretched north-south; 1.50 at 30 degrees; exactly 1.00 at 45, its standard parallel and the only undistorted circle on the map; back to 2.00 at 60, which is also where it doubles; 5.24 at 72; 45.8 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 | 2.00 | 1.50 | 1.00 | 2.00 | 5.24 | 45.8 |
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
Teaching. It is the most direct illustration that a map need not inflate area, and it is the physical object the whole argument was about.
If equal area is all you need, Equal Earth pays far less for the same exactness: 1.35 against 2.00 at the equator, 24.6 against 45.8 at 84 degrees. On cartographic quality there is no longer a reason to reach for this one first.
Limitations
Countries near the equator are drawn as tall thin strips. That is the standing complaint: it fixed the area row and left the shape row worse than Mercator's or any compromise projection's.
Priority is disputed. Gall published more than a century before Peters, which is why the cartographic literature usually writes Gall-Peters rather than the Peters projection.
As a cylindrical equal-area projection its shape cost has no ceiling at high latitude: 45.8 at 84 degrees is the largest single distortion figure anywhere on this site.
Parameters
How this site builds it (w and h are the canvas; sphere is the whole globe):
geoConicEqualArea().parallels([45, -45]).center([0, 0]).fitExtent([[0, 0], [w, h]], sphere)d3-geo core has no dedicated Gall-Peters, and needs none: geoConicEqualArea degenerates from conic to cylindrical when its two standard parallels are symmetric about the equator, so parallels([45, -45]) is the Lambert cylindrical equal-area at 45 degrees. Its default centre of [0, 33.6442] has to be cleared, or the result is a different map.
The family is parameterised by that standard parallel: zero gives Lambert's original, conformal at the equator; 30 degrees gives Behrmann; 45 gives the map drawn here. Moving it only moves which circle comes out undistorted - the area property belongs to the whole family.
Sources
- Snyder, J. P. (1987). Map Projections: A Working Manual. USGS Professional Paper 1395.
- Monmonier, M. (2004). Rhumb Lines and Map Wars: A Social History of the Mercator Projection.
- ArcGIS Pro help: gall-peters