Projections

Mercator - EPSG::3395

$$x = a \lambda$$

$a$ – semi-major axis of the ellipsoid (radius at the Equator)

$\lambda$ – longitude (in radians)

$$y = a \tanh^{-1}{\sin{(\phi)}} - a e \tanh^{-1}{(e \sin{\phi})}$$

$a$ – semi-major axis of the ellipsoid (radius at the Equator)

$e$ – eccentricity of the ellipsoid (shape of the ellipsoid)

$\phi$ – latitude (in radians)

Web Mercator - EPSG::3857

Earth is a perfect square, cutoff at 85.0511°

$$x = a \lambda$$

$a$ – semi-major axis of the ellipsoid (radius at the Equator)

$\lambda$ – longitude (in radians)

$$y = a \tanh^{-1}{\sin{(\phi)}}$$

$a$ – semi-major axis of the ellipsoid (radius at the Equator)

$\phi$ – latitude (in radians)

https://www.sedris.org/wg8home/Documents/WG80605.pdf

Links

https://ihatecoordinatesystems.com/