Spherical Mercator - World bounds

Question

What are the correct world bounds in the Spherical Mercator projection (EPSG:3857 and EPSG:900913)

minx: -20037508.3427892
miny: -20037508.3427892
maxx: 20037508.3427892
maxy: 20037508.3427892

However in FME, I got those bounds:

minx: -40075016.6855785
miny: -20037508.3427892
maxx: 40075016.6855785
maxy: 20037508.3427892

Mathematically, there are no bounds to the x coordinate. What, then, would "correct" mean to you? — whuber, Apr 29, 2015 at 15:55
Ok, I need to set this for an OpenLayers app but I would be curious to understand why they double the x coordinate in FME — Below the Radar, Apr 29, 2015 at 17:16
I couldn't tell you about FME specifically--probably only their developers could answer that. — whuber, Apr 29, 2015 at 18:11
Why would you quote world coordinates to sub-micron level of precision? — Martin F, May 1, 2015 at 15:44
Thats how those sources are defining the world extent in spherical mercator — Below the Radar, May 1, 2015 at 15:45

Ralph Tee · Accepted Answer · 2018-04-30 09:08:59Z

The bounds for EPSG 3857 are:

xmin: -PI * 6378137,
ymin: -PI * 6378137,
xmax:  PI * 6378137,
ymax:  PI * 6378137

which result in the following bounds:

xmin: -20037508.3427892,
ymin: -20037508.3427892,
xmax: 20037508.3427892,
ymax: 20037508.3427892

The extent is a square. And, the unit is in SI meter.
OpenLayer sets this bound for you by default when you work with a data source that is in EPSG 3857.
If you regularly perform (sizeable) map caching or map tile generation - knowing where the bounds are lets you have fine control over the tools you use, and thus planning, monitoring, concurrent/parallel generations, and etc.
If you write codes that convert coordinates to map tile indexes and vice-versa - you need to know where the bounds are.
However, do note that the valid geodetic bounds (i.e., latitude and longitude) that can be projected into EPSG 3857 are [xmin, ymin, xmax, ymax] = [-180, -85.06, 180, 85.06].

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