Web Mercator, Pseudo-Mercator, or Google Web Mercator is a variant of the Mercator map projection used for coordinates in WGS 84 Web Mercator or WGS 84 / Pseudo-Mercator and visualisation. It became the de facto standard for Web mapping applications after Google Maps adopted it in 2005. It is used by virtually all major online map providers, including Google Maps, CARTO, Mapbox, Bing Maps, OpenStreetMap, Mapquest, Esri, and many others. The EPSG identifier for the CRS is EPSG:3857, although others have been used historically.
Properties Web Mercator is a slight variant of the Mercator projection, one used primarily in Web-based mapping programs. It uses the same formulas as the standard Mercator as used for small-scale maps. However, the Web Mercator uses the spherical formulas at all scales whereas large-scale Mercator maps normally use the ellipsoidal form of the projection. The discrepancy is imperceptible at the global scale but causes maps of local areas to deviate slightly from true ellipsoidal Mercator maps at the same scale. While the Web Mercator's formulas are for the spherical form of the Mercator, geographical coordinates are required to be in the WGS 84 ellipsoidal datum. This discrepancy causes the projection to be slightly non-conformal. General lack of understanding that the Web Mercator differs from standard Mercator usage has caused considerable confusion and misuse. Mistaking Web Mercator for the standard Mercator during coordinate conversion can lead to deviations as much as 40 km on the ground. For all these reasons, the United States Department of Defense through the National Geospatial-Intelligence Agency has declared this map projection to be unacceptable for any official use. Unlike most map projections for the sphere, the Web Mercator uses the equatorial radius of the WGS 84 spheroid, rather than some compromise between the equatorial and polar radii. This results in a slightly larger map compared to the map's stated (nominal) scale than for most maps.
Formulas Formulas for the Web Mercator are fundamentally the same as for the standard spherical Mercator, but before applying zoom, the "world coordinates" are adjusted such that the upper left corner is (0, 0) and the lower right corner is ( 2 zoom level − 1 {\displaystyle 2^{\text{zoom level}}-1} , 2 zoom level − 1 {\displaystyle 2^{\text{zoom level}}-1} ):
x = ⌊ 1 2 π ⋅ 2 zoom level ( π + λ ) ⌋ pixels y = ⌊ 1 2 π ⋅ 2 zoom level ( π − ln [ tan ( π 4 + φ 2 ) ] ) ⌋ pixels {\displaystyle {\begin{aligned}x&=\left\lfloor {\frac {1}{2\pi }}\cdot 2^{\text{zoom level}}\left(\pi +\lambda \right)\right\rfloor {\text{ pixels}}\\[5pt]y&=\left\lfloor {\frac {1}{2\pi }}\cdot 2^{\text{zoom level}}\left(\pi -\ln \left[\tan \left({\frac {\pi }{4}}+{\frac {\varphi }{2}}\right)\right]\right)\right\rfloor {\text{ pixels}}\end{aligned}}}
where λ {\displaystyle \lambda } is the longitude in radians and φ {\displaystyle \varphi } is geodetic latitude in radians. Because the Mercator projects the poles at infinity, a map using the Web Mercator projection cannot show the poles. Services such as Google Maps cut off coverage at 85.051129° north and south. This is not a limitation for street maps, which is the primary purpose for such services. The value 85.051129° is the latitude at which the full projected map becomes a square, and is computed as φ {\displaystyle \varphi } given y = 0:
… excerpt ends here. Continue reading the full article.
