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I can not understand why Web Mercator projection is strictly square.

In my mention:

We have a planet as a sphere. We have 360 degrees of longitude and only 180 degrees of latitude. That means if we measure equator it gives us 360n, and if we measure meridian from pole to pole, it gives us 180n.

Additionally WM projection does not project 80-90 latitude. This means we have linear size about 360n x 160n.

The planet as an ellipsoid is nearly spherical. The diameter in equator section is not 2 times larger than diameter between poles, the ratio De/Dp is about 1.1, not 2x...

This means if we project 360nx160n to a square, the scale of one side will be >2 times bigger.

But WM is equiangular (conformal) projection, this means that scales should be equal, or nearly equal due to some features of projection, but not 2x times.

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    Your major misconception here: Googles Web Mercator is hand tailored to be square, it's no true projection; it's based on a Spherical (Pseudo) Mercator projection, with the poles cut off and approximated into a square, heavily distorted map of the globe. It's initial purpose was to be able to serve square map tiles to Google Maps, as it was way easier and more performant to implement back in the days.
    – geozelot
    Sep 3, 2019 at 9:07
  • Since the Mercator on which Web Mercator is based has poles which are infinitely far from the Equator, any proportion rectangle could have been chosen.
    – Vince
    Sep 3, 2019 at 10:42
  • Am I right, that due to projection to cylinder, scale of the map grows towards the pole? And the cutting poles is made at latitude to make it square?
    – filimonic
    Sep 3, 2019 at 16:21
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    Yes, you're correct. The latitude cutoff is around 85.0511 because that gives the same Y/northing value as 180 longitude gives for the X/easting value. Also, meridians should converge to poles, but don't in Mercator, so north-south must be stretched to match the east-west stretching.
    – mkennedy
    Sep 3, 2019 at 18:47
  • Thank you very much. It is much more clear now.
    – filimonic
    Sep 3, 2019 at 20:12

1 Answer 1

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Web Mercator is square because it is designed to be.

The purpose behind Web Mercator is to have a map projection suitable for quickly and easily displaying a map at a wide range of scales, ranging from individual city streets to the entire world. As a part of this, you can break the map up into square tiles such that, if you zoom out by a factor of two, you can replace any cluster of four tiles with a single tile of half the detail without (visible) distortion.

Taken to the limit, once you zoom out to see the entire world, you're looking at a single, square map tile. The math behind the Web Mercator projection means this tile encompasses the entire equator, but cuts off approximately five degrees before the poles.

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