Map projections and area

Web Mercator draws ground at 60° latitude at 4.0 times the area of the same ground at the equator, and at 10.5 times at 72°, the latitude of central Greenland. The panels below shade one sphere by how much each of three projections enlarges or shrinks it, and the map below them is an ordinary Web Mercator choropleth.

Equal Earthequal-area

Web Mercatorconformal

Lambert cylindricalequal-area

Area, against true

1/81/2.8true2.8×8×

One diverging ramp for all three panels, centred on true area and spaced logarithmically, because a factor of four and a factor of a quarter are the same amount of error in opposite directions. Brown cells are drawn smaller than true and teal cells larger. The colour stops changing at 8× and at 1/8, so the darkest cells mean at least that much: Mercator reaches 134 times true area at its 85° cut-off.

How much larger one square kilometre is drawn

Area scale factor by latitude under each projection, relative to the equator.
Latitude	Equal Earth	Web Mercator	Lambert cylindrical	Roughly
the equator	1.00×	1.00×	1.00×	Singapore, Quito, Nairobi
30°	1.00×	1.33×	1.00×	Cairo, New Orleans, Shanghai
45°	1.00×	2.00×	1.00×	Milan, Minneapolis, Vladivostok
60°	1.00×	4.00×	1.00×	Oslo, Anchorage, St Petersburg
72°	1.00×	10.5×	1.00×	central Greenland, Arctic Siberia
82°	1.00×	51.6×	1.00×	northern Ellesmere Island

Relative to the equator, so 1.00× means drawn at the same scale as equatorial ground. The two equal-area columns are 1.00× at every latitude, which is what equal-area means. Both distort shape instead, and Lambert cylindrical is included because its shapes are the most distorted of the three while its areas are as true as Equal Earth’s.

GDP per capita, 2023, on Web Mercator

Move the pointer over the map to mark that latitude on the panels above.

The measure changes the map’s colours and nothing about the panels, because distortion belongs to the projection and not to the data.

The panels draw a graticule and no countries. The country outlines on this site are vector tiles drawn by the map renderer, with no coordinate table a second renderer could project, so the panels draw the one thing that can be projected exactly. A choropleth on an equal-area projection would need the country outlines as coordinates, which the site does not serve.

Map: World Bank NY.GDP.PCAP.CD, 2023 · boundaries: Natural Earth 1:110m, public domain · panels: computed from the projection formulas for Web Mercator, Equal Earth (Šavrič, Patterson and Jenny, 2018) and Lambert cylindrical equal-area, with equal area checked numerically cell by cell against the area on the sphere

What each projection keeps

A choropleth paints a value into an area, so the projection sets how much of the map each country’s colour covers before any colour is chosen. Web Mercator, the projection of standard web map tiles, gives high latitudes far more of the map than their land: a square kilometre at 60° is drawn 4.0 times the size of one at the equator, and at the 85° cut-off 134 times.

On a world choropleth that decides how much colour each country gets. Greenland, Canada, Russia and the Nordic countries take up more of a Mercator map than their land would on an equal-area one, so their values get more of the reader’s attention. The countries page also offers a globe, which has no area enlargement at the centre of view and shows half the world at a time, so comparing two countries on opposite sides means turning it and remembering the first.

Lambert cylindrical, the third panel, keeps area exactly as Equal Earth does, and its polar regions stretch into horizontal bands. Equal-area names one preserved property and says nothing about shape, angle or distance, and no flat map keeps area and shape true everywhere at once.

Shows: How much area each projection adds or removes, at every latitude, as a number.
Hides: Every property except area. An equal-area map still shears shapes, distorts distances and has to cut the sphere somewhere, and these panels show no data, only the frame the data would be painted into.