# Converting lat/long to EPSG:3857 coordinates

The map widget I'm using gives me click locations in lat/long. I need to convert those coordinates to EPSG:3857 to query a database.

Most of the solutions I've found use the formula described in this gist: convert from long/lat to google mercator (or EPSG:4326 to EPSG:900913) . But I'm in doubt about the constant `90` used in the `y` calculation:

``````var y = Math.log(Math.tan((90 + lat) * Math.PI / 360)) / (Math.PI / 180);
``````

The formula described on Wikipedia seems to suggest that instead of `90`, I should use `85.051129`. I've found other references to that value in questions such as Transforming EPSG:3857 to EPSG:4326.

Which is correct, and why?

• The gist is using feet, plus yeah, I haven't seen those values. John Snyder gives y = R*ln(tan(PI/4.0 + phi/2)) with phi in radians. Aug 31, 2016 at 19:11
• @mkennedy Where do you get that the gist is using feet? The function is called `degrees2meters`, and the magic number `20037508.34` is half the Earth's circumference at the equator in meters. Sep 1, 2016 at 22:27
• Oops, my mistake. Radius of wgs84/grs80 is 20.9 million feet. I saw the 20 million and jumped to the wrong conclusion. Sep 1, 2016 at 22:32