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I am using the projection EPSG:3857 to plot out points on the map. Since the Earth is closer to the shape of an ellipsoid instead of a sphere, I am interested to find out what is the range of error if I were to plot some points using this spherical mercator projection. Using examples of prominent points of interest such as the tip of Mount Everest, Statue of Liberty, etc, would be helpful.

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As long as you project from the source SRS to EPSG:3857, then the point position will be accurate (to within the projection accuracy - some are a bit "off"). Projection from EPSG:4326 to EPSG:3857 should be very accurate - a few metres at the most. Size of objects will obviously be in error depending on latitude.

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Can you elaborate this point "As long as you project from the source SRS to EPSG:3857, then the point position will be accurate" further? Example, if I were to read the coordinates of the tip of the flaming torch on the Statue of Liberty with the map projection, would it correspond to the exact same spot on Planet Earth, assuming my GPS reader is perfect? –  Question Overflow Oct 12 '12 at 6:39
    
I'm not sure I understand your question (or you don't understand what you are asking). Lets say you set your GPS to output latitude and longitude in degrees on a WGS-84 ellipsoid, and you record that output. You can't plot that (directly) on EPSG:3857 - the coordinates are in metres for a start. So you need to do a projection (e.g. using proj.4 or similar) to convert into the right spatial reference system. There are inherent errors in the projection process, but they are mostly pretty small. –  BradHards Oct 12 '12 at 6:46
    
If you do a search on Google Maps for a known lat/lon, you will find that the point plots slightly SE of the mapped location. The distance is usually not more than ~20 meters. Google Maps doesn't use EPSG:3857, but it's a similar projection. –  L_Holcombe Oct 12 '12 at 7:11
    
Let me rephrase my question: given that the Earth is neither a perfect sphere or a perfect ellipsoid, would the use of an idealised projection algorithm such as EPSG:3857 or EPSG:4326 cause some points to be off from the actual LatLon geographical coordinates. I understand that EPSG:3857 is in metres but how about EPSG:4326. Hope I am clearer now. Or maybe it is my understanding that is not correct. Please enlighten me if that is the case. Thanks :) –  Question Overflow Oct 12 '12 at 7:51

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