I've been trying to plot a set of lat and long coordinates to a Mercator map using the following set of equations:

x = long - long0
y = ln(tan(pi/4 + lat/2))

These equations are from a page on Wolfram.

I'm using a Mercator map from Wikipedia, it's from 82 N to 82 S. Based on this I've got the current set of equations to fully map the lat/long to the image:

height = image height in pixels
width = image width in pixels

x = long * PI/180
x = x * width/(2 * PI) + width/2

latRange = 2 * 82 * PI/180
y = ln(tan(PI/4 + lat/2))
y = -(y*height/latRange - height/2)

However when I make the image I get points on my map that are higher than expected (I try to plot the tropic of cancer and I hit the north coast of Algeria).

So, can someone please tell me where I'm going wrong?

  • Why not simply use the adequate Python modules: pyproj or GDAL/OGR
    – gene
    Jan 17, 2016 at 8:50
  • 1
    @gene At the moment I'm less interested in getting an output and more interested in the inner workings of making these types on map. I could use a python module, but I'd like to make my own. Jan 17, 2016 at 8:52
  • I see you converted your ´long´ to radians but not your ´lat´, maybe that's the issue. Also, have you tried with another Mercator map (just to be sure)?
    – ArMoraer
    Jan 17, 2016 at 10:57
  • @ArMoraer Sorry, I should have shown that line in the question, I do convert the lat to radians. I've tried with 4 or 5 maps :/ Jan 17, 2016 at 11:03
  • heigh/2 seems like a typo
    – user1462
    Jan 17, 2016 at 15:56

1 Answer 1


The link you are using is a map transform and not a coordinate pair transform. The correct transform is on the main Stack Overflow site at:


latitude = φ and longitude = λ are:

E = FE + R (λ – λₒ)
N = FN + R ln[tan(π/4 + φ/2)]   

where λO is the longitude of natural origin and FE and FN are false easting and false northing.

The formulae are best simplified to (as FE and FH are ignored in most use cases):

Use this formuale

The stack overflow link provides pseudocode for use in all languages as well.

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