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.

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.

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.

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.

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.