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I am querying out spatial information from a SQL database that stores locations that users input on a map as GML snippets. See below for an example:

<gml:Point xmlns:gml="http://www.opengis.net/gml">
  <gml:coordinates>-7823471.2337636035,5113510.302636641</gml:coordinates>
</gml:Point>

This coordinate format is not familiar to me and I would like to be able to convert the coordinates to WGS84 but I will need the original spatial reference system EPSG which is not a part of the snippet.

I have access to ESRI shapefiles that our system generates for us so that we can view this data in ArcMap. I am able to see what these coordinates are in WGS84 Lat/Long by looking at those shapefiles, but I have no information indicating how the shapefiles are created from the original coordinates and our contract with the vendor who built the system has long expired.

Given that I am able to see their WGS84 Lat/Long equivalent, how might I go about determining the original spatial reference system so that I can convert the coordinates from the mystery system in the GML snippets to WGS84?

The shapefiles I have are only a small recent subset of the entire data set. I am seeking the spatial reference system of the GML snippet coordinates so that I can convert them into WGS84 for every record in the database (12,000 + records).

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If its a global coordinate set and has come from a web-based mapping system there's always a good chance its in EPSG:3857 - google's web mercator. Try that, and if everything is in the right place then that's probably job done.

If you want to consider more possible obscure options, then this handy web page lets you input some coordinates:

http://projfinder.com/

then you zoom to the map where you think the point might be, and it will list projections that take that point onto your zoomed map. If I try your example points and zoom to north america, I see that epsg:3857 is on the way to Cape Cod, and epsg:3408 puts it in the middle of the Pacific. Other CRSs seem to be between those in plausibility.

The more precisely you know where that point is supposed to be, and the more points you have, the better you can use projfinder to hunt down the right projection code.

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