Web Mercator to Lat Long Converter

How to convert Web Mercator to latitude and longitude

1. Enter x and y. Use the EPSG:3857 values in metres, for example -8242596.04 and 4966621.82.
2. Click Convert. The latitude and longitude appear in decimal degrees on the WGS84 datum, with a link to open the point in Google Maps.
3. Check the order. x comes first and is the east-west value; y is the north-south value.
4. Or convert a list. Paste many, one per line, and download the results as a CSV.

The formula

Web Mercator is the Mercator projection on a sphere of radius R = 6,378,137 m. The inverse gives longitude λ and latitude φ from x and y:

λ = x / R
φ = 2 × atan( exp( y / R ) ) - π/2

Both results are in radians and are converted to degrees for display. The latitude and longitude are then read as WGS84.

Worked example

Convert x = -8,242,596.04 m and y = 4,966,621.82 m:

longitude = -8242596.04 / 6378137 = -1.29231 rad = -74.044500°
latitude  = 2×atan(exp(4966621.82 / 6378137)) - π/2 = 40.689306°

That is the Statue of Liberty in New York harbour.

Valid range

• x: -20,037,508.34 to 20,037,508.34 m, which is longitude -180° to 180°.
• y: -20,048,966 to 20,048,966 m, which is latitude -85.06° to 85.06°, the area of use of EPSG:3857.
• Web map tiles use x and y inside the square ±20,037,508.34 m (latitude 85.0511°). A y beyond ±20,048,966 m has no real location, and the tool says so.

Common mistakes

• Treating the numbers as degrees. A value such as -8242596 is metres. If your numbers are already between -180 and 180, they are probably latitude and longitude already.
• Swapping x and y. x is the east-west value (about ±20 million at the date line). Swapping them usually gives an error or a point in the wrong ocean.
• Thousands separators. Commas inside numbers such as -8,242,596.04 are read as thousands separators when they sit between groups of three digits. Prefer plain numbers.
• Confusing 3857 with a local grid. Many national grids are also in metres. If your coordinates are from a UTM zone or a state plane system, use UTM to lat long or the CRS Converter.

What this converter does and does not do

• EPSG:3857 only. It does not guess the CRS. If your numbers are in another projection, the result will be wrong.
• Accuracy. We compared random points from around the world with PROJ and the inverse agrees to far better than a millimetre.
• Runs in your browser. No coordinates are sent to a server.

Related converters

To go the other way, use WGS84 to Web Mercator. For other grids see UTM to lat long and the CRS Converter.