javascript coordinate conversions between 900913(3857) - 4326(lat lon)

degrees2meters.js

var degrees2meters = function(lon,lat) {
  var x = lon * 20037508.34 / 180;
  var y = Math.log(Math.tan((90 + lat) * Math.PI / 360)) / (Math.PI / 180);
  y = y * 20037508.34 / 180;
  return [x, y]
}
//test
lon= -77.035974
lat = 38.898717

console.log(degrees2meters(lon,lat))

// should result in: -8575605.398444, 4707174.018280

meters2degrees.js

var meters2degress = function(x,y) {
  var lon = x *  180 / 20037508.34 ;
  //thanks magichim @ github for the correction
  var lat = Math.atan(Math.exp(y * Math.PI / 20037508.34)) * 360 / Math.PI - 90; 
  return [lon, lat]
}
//test
x= -8575605.398444
y = 4707174.018280

console.log(meters2degress(x,y))

//should result in: -77.035974, 38.898717

May I know where did you get a formula for conversion?

Based on geometric knowledge and you can see the fixes happened in the past by contribution of commenters.

you saved my life, thank you

you saved my life, thank you

I'm glad that I could help. But don't forget that it is just to translate 4326 to 900913(3857) and visa versa. This calculation cannot be used for length measurements because of high error margin.