Plate Carrée world map: how country sizes change

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Plate Carrée (equirectangular) projection: key facts and what it does to country sizes

Distortion class
Equidistant
Graticule type
Cylindrical
Creator
Marinus of Tyre
Year
c. AD 100
Area
Highly distorted: grows with distance from the equator (horizontal stretching toward the poles)
Shape
Highly distorted (horizontal stretching near the poles)
Distances
Partially preserved: true along every meridian and along the equator
Angles and directions
Distorted; only north, south, east, and west are always correct (plus local directions along the equator)

Plate Carrée is the simplest grid there is: equal spacing between parallels and between meridians. The result shows at once in the Tissot indicatrices. They all have the same height, because the scale along the meridians is true across the whole map. Only the width changes. On the equator the ellipses are circles, at 30° they are 15% wider, and at 60° twice as wide as they should be. Area grows at exactly the same rate, so at 60° it has doubled.

The distance from the equator to a pole along any meridian, about 10,000 km, always has the same length on this map. The pole, however, which is really a point, is stretched into a line as long as the equator. The isocoles show how fast the error builds: angles change by 5° as early as about 24°, by 15° at 40°, by 30° at 54° and by 60° at 71°. Area is one and a half times larger at 48.5°, double at 60° and four times larger at 76°. On the layer with the equator, tropics and polar circles the spacing is directly proportional to degrees: the polar circle lies 74% of the way from the equator to the edge of the map, because 66.6° is 74% of 90°.

Drag Poland from its 52°N up to 72° and it keeps its height but becomes twice as wide, because the horizontal enlargement rises from 1.6 to 3.2. On the equator it loses almost 40% of its width and regains its true proportions. Compare that with Mercator, which at 72° stretches the map sideways by the same amount but also vertically, so it enlarges area 10.5 times rather than 3.2 times as here.

Plate Carrée map: frequently asked questions

How much does Plate Carrée stretch countries near the poles?

The height of shapes is true everywhere and only the width grows: on the equator ellipses are circles, at 30° they are 15% wider, and at 60° twice as wide as they should be. Area grows at the same rate, so at 60° it is doubled.

At which latitudes does Plate Carrée enlarge area one and a half, two and four times?

Area is one and a half times larger at 48.5°, double at 60° and fourfold at 76°. Angles change by 5° already at about 24°, by 15° at 40°, by 30° at 54° and by 60° at 71°.

How does Plate Carrée differ from Mercator?

Mercator stretches the map both horizontally and vertically at high latitudes, so at 72°N it enlarges area 10.5 times. Plate Carrée stretches it horizontally only, so at the same latitude area grows 3.2 times.

Why do GIS systems use the Plate Carrée grid?

Every degree of longitude and latitude gets the same space, so raster data and globe textures are easiest to store in it. As a world map the grid stretches high latitudes horizontally, because the meridians stay parallel.