Web Mercator is different than Mercator projection

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The use of mobile apps and online maps is increasing. Everybody has access to and uses online map services such as google maps, street view or ESRI online maps. However, very often when GIS professionals use such maps as base for geo-referencing, they forget that they use a different coordinate system. 

This new reference system is the so-called Web Mercator or Pseudo Mercator or EPSG3857. Many people wonder what's the difference? and why a Feature class using a Mercator projection changes when transformed into Web Mercator?

What is the difference?

A first and simple difference is that they have different false Easting and false Northing data. However, that is not the main difference.

A standard Mercator projection is cylindrical conformal projection. I stress the word conformal because it is a key feature that made this projection so popular and the big difference with the Web Mercator.

A conformal projection, as defined by J Snyder, means that the shape of every small feature of the map is shown correctly, the relative angles at each point are correct, and the local scale in every direction around any one point is constant. Thus, it preserves shapes and angles. On the other hand, Web Mercator is not a conformal projection.

ellipsoid vs sphere projections
Fig 1. Conceptual difference between spherical and ellipsoid projections

Why Web Mercator is not a conformal projection?

Standard Mercator assumes an ellipsoid, while Web Mercator assumes a sphere. Web Mercator assumes a sphere because the equation are simpler and faster to calculate. NOTE: We must consider that online maps are projected online; that means that all the calculations are performed online, which is slower than off-line calculation. This is why sometimes zooming online takes so long.

The ellipsoid-sphere differences generate differences that should be corrected by a scale factor Fig 1.). However, including such correction would be computationally expensive. Web Mercator is used online and requires simple equations. Otherwise, the visualization would be slow. Thus, Web Mercator neglects such corrections.

The differences are function of the latitude (Fig. 2). Latitudes closer to the equator have small errors, and the error increases as the latitude distances from the equator. The shape error in most populated areas (less than 50 degrees latitude) are small and negligible for a general visualization purposes; the computational cost of correcting such differences would be too high for such little differences. However, if detailed measurements are required, the errors would become important.

geodetic errors with latitude
Fig 2. Error of Web Mercator projection