Mercator vs Gall-Peters
Mercator and Gall-Peters, measured item by item. Every figure below is labelled with the projection whose equator it is normalised to.
What each one is
| Property | Mercator | Gall-Peters |
|---|---|---|
| Family | Conformal cylindrical | Equal-area cylindrical |
| Axis held at 1.00 | Shape | Area |
| Leads with | Area distortion | Shape distortion |
| True-shape parallel | Everywhere | 45.0° |
| Aspect ratio | 1.288 : 1 | 1.571 : 1 |
| Pole drawn as a line | None | As long as the equator |
The same parallel, under each
Six parallels, two axes. The area columns are normalised to that projection's own equator; the shape columns are the ratio of the Tissot indicatrix's axes at the same point, where 1.00 means the shape there is unchanged. Each projection reads against its own baseline, so the two area figures on a row are not two readings on one axis.
| Latitude | Mercator area | Gall-Peters area | Mercator shape | Gall-Peters shape |
|---|---|---|---|---|
| 0° | 1.00 | 1.00 | 1.00 | 2.00 |
| 30° | 1.33 | 1.00 | 1.00 | 1.50 |
| 45° | 2.00 | 1.00 | 1.00 | 1.00 |
| 60° | 4.00 | 1.00 | 1.00 | 2.00 |
| 72° | 10.5 | 1.00 | 1.00 | 5.24 |
| 84° | 91.5 | 1.00 | 1.00 | 45.8 |
What they disagree about most
The objects Mercator and Gall-Peters treat most differently. The first two columns stand alone: each is the area that object is painted at under that projection, against that projection's own equator. The third is the ratio between them.
Once more, because it matters: the Mercator multiples are normalised to Mercator's equator and the Gall-Peters multiples to Gall-Peters's. The two do not share an axis. What the third column exactly means is this - print both maps with equators the same length, and this shape comes out that many times larger on the first than on the second. It is a checkable statement about two pictures, not a physical quantity.
| Object | Mercator area | Gall-Peters area | Mercator ÷ Gall-Peters |
|---|---|---|---|
| Greenland | 16.5 | 1.00 | 16.5 |
| Norway | 9.38 | 1.00 | 9.38 |
| Iceland | 5.64 | 1.00 | 5.64 |
| Finland | 5.46 | 1.00 | 5.46 |
| Canada | 5.21 | 1.00 | 5.21 |
| Russia | 4.90 | 1.00 | 4.90 |
| Sweden | 4.88 | 1.00 | 4.88 |
| North America | 4.64 | 1.00 | 4.64 |
Area multiples are integrated over the whole polygon as drawn, not estimated from a centroid latitude. Shape ratios are taken at the object's anchor.
Which to use
This is the cleanest pairing there is: one holds area, the other holds angle, and there is no middle ground between them. If the map is for comparing sizes - which place is bigger, how many fit, anything per square kilometre shaded across a map - use the equal-area one. It is exact about that, not approximately right about it.
If the map is for measuring direction, for a compass bearing that comes out as a straight line, or for large-scale local work, use the conformal one. This is not a preference: an equal-area projection cannot do that job and does not claim to.
You cannot have both. That is Gauss, not a cartographic tradition anybody is free to break with.
See it in the tool
Switching projections in the tool morphs the map between the two - it interpolates projected pixel coordinates, so which places shrink and which swell is visible at a glance. It is the fastest way on this site to understand what separates a pair.