# Spherical Mercator - World bounds

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

In some source I got those bounds see this link in the maxExtent parameter:

``````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? Commented 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 Commented Apr 29, 2015 at 17:16
• I couldn't tell you about FME specifically--probably only their developers could answer that. Commented Apr 29, 2015 at 18:11
• Why would you quote world coordinates to sub-micron level of precision? Commented May 1, 2015 at 15:44
• Thats how those sources are defining the world extent in spherical mercator Commented May 1, 2015 at 15:45

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
``````

Source: https://epsg.io/3857

• 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].
• Why it is 85.06? Could you give calc meoth? I calced it 71.57. tanX = PI*R/R = PI = 3.1415925， so X = 71.57. the result is not same. Commented Jun 6 at 19:14