Five projections

No map tells the truth about everything; you only choose where it lies. Each of these five stands for a family, and the table below is their distortion curves - computed from the projections this site actually runs, not transcribed.

Local distortion at each latitude, normalised to each projection's own equator. Bold marks the axis a projection holds fixed by definition.
ProjectionLatitude0°30°45°60°72°84°
EquirectangularArea distortion1.001.151.412.003.249.57
Shape distortion1.001.151.412.003.249.57
MercatorArea distortion1.001.332.004.0010.591.5
Shape distortion1.001.001.001.001.001.00
Natural EarthArea distortion1.001.111.261.491.973.47
Shape distortion1.161.051.121.552.519.24
Equal EarthArea distortion1.001.001.001.001.001.00
Shape distortion1.351.151.091.693.4324.6
Gall-PetersArea distortion1.001.001.001.001.001.00
Shape distortion2.001.501.002.005.2445.8

Equirectangular

The naive one: plot longitude as x and latitude as y. Area and shape both distort as sec(latitude), exactly half the exponent of Mercator's.

Properties, uses and limitations

Mercator

Conformal: shape survives at every point, and area pays for it, growing as sec squared of latitude - already 91 times over at 84 north.

Properties, uses and limitations

Natural Earth

A compromise: a little area distortion and a little shape distortion, neither severe. It promises to conserve nothing, which is what a compromise is.

Properties, uses and limitations

Equal Earth

A modern equal-area projection. Area is conserved exactly everywhere, so the multiplier reads 1.00x wherever you drag. The whole cost lands on shape, about 25 times at high latitude.

Properties, uses and limitations

Gall-Peters

Cylindrical equal-area at the 45-degree standard parallel. Area is conserved exactly here too, but the shape cost is harsher than Equal Earth's: about 46 times at 84 north.

Properties, uses and limitations