Map Projections
Greenland is not the size of Africa. It is about a fourteenth of it. The reason your world map disagrees is the single most interesting problem in cartography.
You cannot flatten a sphere
This is not a limitation of technology or of effort. It is a mathematical fact, proved by Gauss in 1827 and known as his Theorema Egregium: a sphere and a plane have different intrinsic curvature, so no amount of cleverness can flatten one into the other without stretching, tearing or squashing it somewhere.
Peel an orange and try to press the skin flat. It splits. Push the splits closed and the peel buckles. Every world map you have ever seen is a solution to that problem, and every solution ruins something.
Four things a map can get right
A projection can preserve shape, area, distance or direction. It cannot preserve all of them at once, and most preserve at most one properly. Which one it keeps is the whole personality of the map.
A conformal projection preserves shape locally, so small features look right and angles are correct, but areas inflate badly away from where the map touches the globe. An equal-area projection preserves relative size everywhere, so countries can be compared honestly, at the cost of visibly squashed or stretched shapes. A compromise projection preserves nothing exactly but distributes the error so that nothing looks alarming.
Mercator, and why it will not die
Gerardus Mercator published his projection in 1569 to solve a specific problem for sailors: he wanted a map on which a constant compass bearing is a straight line. He succeeded, and that property, called a rhumb line, made ocean navigation dramatically simpler. It is a genuinely brilliant piece of work.
The price is area. Mercator stretches east to west more and more as you move away from the equator, and to keep shapes correct it must stretch north to south by the same amount. That squaring effect is why the distortion becomes enormous near the poles: Greenland, at around 70 degrees north, is inflated roughly fourteen times.
It survives because it is still right for navigation, and because it is what nearly every online slippy map uses. Web Mercator is the reason a projection designed for sixteenth-century sailors is on the phone in your pocket.
Projections you will actually meet
| Projection | Preserves | Where you see it |
|---|---|---|
| Web Mercator | Shape and direction | Google Maps, OpenStreetMap, almost every web map |
| Mercator | Shape and direction | Nautical charts, old classroom maps |
| Gall-Peters | Area | Development and equity campaigning |
| Robinson | Nothing exactly | Atlases, National Geographic until 1998 |
| Winkel tripel | Nothing exactly | National Geographic since 1998 |
| Equal Earth | Area | Modern data visualisation and science |
| Azimuthal equidistant | Distance from one point | The UN emblem, radio range maps |
If a world map has straight vertical lines of longitude and a rectangular outline, it is almost certainly a Mercator variant, and its areas cannot be trusted.
Check what you learned
Five questions on projections and distortion. Pass at 70% or better to complete the lesson.
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Map projections, in one paragraph
A map projection is a method of representing the curved surface of the Earth on a flat plane. It is mathematically impossible to do this without distortion, a result proved by Gauss in 1827, so every flat map misrepresents shape, area, distance or direction, and usually several at once. Conformal projections such as Mercator preserve shape and direction but inflate areas away from the equator, which is why Greenland appears roughly the size of Africa despite being about a fourteenth of it. Equal-area projections such as Gall-Peters, Mollweide and Equal Earth keep relative sizes honest but visibly distort shapes. Compromise projections such as Robinson and Winkel tripel preserve nothing exactly and instead spread the error so no region looks badly wrong. Mercator persists because a constant compass bearing is a straight line on it, which is ideal for navigation, and because Web Mercator underpins nearly every online map.
Common questions about map projections
Why does Greenland look so big on world maps?
Because most world maps use the Mercator projection or a variant of it. Mercator stretches the map east to west increasingly towards the poles, and stretches north to south by the same factor to keep shapes correct. At Greenland's latitude that inflates its apparent area about fourteen times. Africa is genuinely about fourteen times larger than Greenland.
What is the most accurate map projection?
There is no single most accurate one, because accuracy depends on which property you need. Equal-area projections are accurate for size, conformal ones for shape and angle, and azimuthal equidistant ones for distance from a chosen centre. A globe is the only representation that gets all of them right at once.
What is the difference between Mercator and Gall-Peters?
Mercator preserves shape and direction while badly exaggerating the area of high-latitude regions. Gall-Peters preserves area, so countries can be compared fairly by size, but it noticeably stretches shapes, particularly near the equator. They represent the two opposite trade-offs.
Why do online maps still use Mercator?
Web Mercator is conformal, so at street level shapes and angles look correct and a square building stays square at any zoom. It also maps neatly onto square tiles at every zoom level, which makes it efficient to serve. Its area distortion barely matters when you are looking at one city.
What is a compromise projection?
One that deliberately preserves no property exactly, spreading the error so that nothing looks badly wrong. Robinson and Winkel tripel are the best-known examples, and they are common in atlases precisely because they look plausible everywhere rather than being perfect anywhere.