WGS84 to Web Mercator Converter

How to convert WGS84 to Web Mercator

1. Enter the latitude and longitude. In decimal degrees or DMS. West and south are negative, or use W and S.
2. Click Convert. The x (easting) and y (northing) appear in metres, each with a copy button.
3. Use the values in your map or script. They are in EPSG:3857, the CRS used by web map tile services and by libraries such as Leaflet, OpenLayers and Mapbox GL.
4. Or convert a list. Paste many, one per line, and download the results as a CSV.

The formula

Web Mercator (EPSG:3857, also written 900913 or ESRI:102100) is the Mercator projection applied with a sphere of radius R = 6,378,137 m, which is the WGS84 semi-major axis. With the longitude λ and latitude φ in radians:

x = R × λ
y = R × ln( tan( π/4 + φ/2 ) )

The input latitude and longitude are taken from the WGS84 ellipsoid but projected as if the Earth were a sphere. That choice makes the maths simple, and it is also why the projection is not conformal on the ellipsoid and is not suitable for precise survey work.

Worked example

Convert 40.689306° N, 74.044500° W:

x = 6378137 × (-74.0445 × π/180)  = -8242596.04 m
y = 6378137 × ln(tan(45° + 40.689306°/2)) =  4966621.82 m

For comparison, Sydney (-33.8688, 151.2093) gives x = 16832542.28 m, y = -4011198.65 m.

Valid range

• Latitude: -85.06° to 85.06°, the area of use of EPSG:3857. Web map tiles stop slightly earlier, at 85.0511°, where y equals the x value at 180° and the world is a square about 40,075,016.7 m on a side.
• Longitude: -180° to 180°, which is x = ±20,037,508.34 m.
• The poles themselves cannot be shown because y goes to infinity.

Common mistakes

• Measuring in Web Mercator. Distances and areas in EPSG:3857 are exaggerated by 1/cos(latitude) and 1/cos²(latitude). At 60° N distances are about twice as long and areas four times as large. Use a UTM zone or an equal-area projection to measure.
• Swapping x and y. x is longitude-based (east-west) and y is latitude-based. Some libraries use latitude-first order for geographic coordinates and x-first for projected, so check the axis order.
• Using EPSG:3857 values as degrees. The numbers are metres. Values like -8242596 are not degrees.
• Calling it "WGS84". The input is WGS84 latitude and longitude, but EPSG:3857 is its own projected CRS.

What this converter does and does not do

• Input is WGS84. Latitude and longitude are taken as WGS84 and mapped with the spherical formula above. No other datum is applied.
• Accuracy. We compared random points from around the world with PROJ, in both directions, and the results agree to far better than a millimetre.
• Latitude limit. Points beyond ±85.06° are rejected rather than clipped silently.
• Runs in your browser. No coordinates are sent to a server.

Related converters

To go the other way, use Web Mercator to lat long. For an accurate projected CRS see lat long to UTM and the CRS Converter, which reprojects whole files.