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Mercator Scale Factor Calculator

How far a Web Mercator map stretches at a given latitude, and what that stretching does to the printed scale, to lengths and to areas.

Decimal degrees, negative for the southern hemisphere. Accepted up to the Web Mercator limit of ±85.0511°, where the projection stops being usable.

The published denominator only: the scale the map reaches at the equator. Elsewhere the same map is larger than 1:N by the scale factor.

A scale factor whose latitude you want, for example 2 for the parallel where features are drawn twice their true size.

Mercator is a cylindrical projection that touches the globe at the equator, so its scale is exact there and grows away from it. Every parallel has radius R cos φ on the globe but is drawn the full R on the map, so the parallel and the meridian are both stretched by the point scale factor k = 1 / cos φ = sec φ: 1.0000 at the equator, 1.1547 at 30°, 1.4142 at 45°, 2.0000 at 60° and about 11.59 at the Web Mercator limit. Because both directions stretch equally, angles and small shapes stay correct, while area inflates by k²: a parcel at 60° covers four times the map area of the same parcel on the equator, which is why Greenland looks larger than Africa on web maps. The local scale of a 1:N map at latitude φ is 1:(N / k), and the Mercator northing is R ln tan(45° + φ/2) with R = 6 378 137 m, the sphere radius Web Mercator uses, which puts the limit at 20 037.5 km from the equator. The latitude for a target factor is arccos(1 / target), and a factor above 11.5905 lands beyond the Web Mercator limit. Web Mercator projects coordinates surveyed on the WGS 84 ellipsoid with spherical formulas, so it is not exactly conformal and this page does not correct for that or for a secant Mercator with standard parallels away from the equator. Values are refused outside the Web Mercator latitude limit of ±85.0511287798066°, a 1:100 to 1:1 000 000 000 nominal scale and a 1.01 to 100 target factor, and decimal commas are accepted. Everything runs in your browser with no storage, uploads or network access.