I have a map, the centre of that map (centrepoint) is = -37,175 ( gps)
I know the zoom of the map = 13
I know the size = 320x320px
I know there is 111111m in a degree of latitude and a varying degree in longitude

I want to be able to calculate the value to add and subtract from the centre coordinate that will give me an upperleft/lowerright gps coordinate.

For a zoom of 13 I used to achieve this by Note :centrelat= -37
eg :-37 - (-37/1650) = -36.9776 deg. In other words to find the southeast corner we subtracted .0228 degrees from the centre coordinate. I did the same for longitude but used the value 6250
eg :175 - (175/6250) (.02804 degrees). = 174.792, ie the northwest corner
the ratio between .0228 degrees (lat)and .0280 degrees(long) is correct

So, I want this calculation to be dynamic and work for all zooms
so I'm using (cos Latitude x 111111) / 2^Zoom(13) = 10.72095
for longitude I'm using 111111/2^13 = 13.56
This is the same ratio as well so I'm on the right track!
but how do I use these values in a calculation to add or subtract degrees from the centre coordinates for lat and long to get the coordinates for the corners of the bounding box.

any help is appreciated, and I do mean that.

  • For what purpose are using this Bounding box? In what projection will the bounding box be? It is often easier to project the GPS point to your intended projection (usually Web Mercator) and then create he bounding Box in Meters. Mar 9, 2013 at 14:09
  • Thanks for the reply, I am trying to plot multiple points on a canvas, the background of which is a map. I cant do this server side or with Javascript, it must be done on the device. So the bounding box will give me the corner coordinates and from there I hope to draw the points in relation to the known corners and centrepoint Mar 10, 2013 at 5:11

1 Answer 1


Assuming you are using the Web Mercator projection (Google Maps, MapBox etc), the key lies in these two equations:

Formulas from Web Mercator on Wikipedia: https://en.wikipedia.org/wiki/Web_Mercator#Formulas

where λ is the longitude in radians and φ is geodetic latitude in radians. The x and y values are the so-called 'pixel coordinates' as originally defined by Google.

What you actually need are the inverse of these two equations, so that you can convert the latitude and longitude into x and y values. The inverse equations are:

Inverse lambda equation

Inverse phi equation


F equation

Given the centre co-ordinates of your image as defined by λ and φ, convert these into the x and y pixel coordinates for your chosen zoom level using the first two equations above.

If h is the height of your image, and w is its width, you can then calculate the (l)eft, (r)ight, (t)op and (b)ottom pixel coordinates of your image:

l = x - (w/2)
r = x + (w/2)
t = y - (h/2) (minus since zero is at the top for Web Mercator pixels)
b = y + (h/2)

Then, convert back into latitude and longitude using the original equations, substituting l or r for x, and t or b for y.

EDIT: Trying this with the non-Retina MapBox Static API, I found that I had to use a factor of 4 instead of 2 in the last four equations. Not sure why this is, but probably something to do with internal scaling in the MapBox servers.

  • I am able to convert longitude back and forth, but converting latitude to pixel and then convert pixel to latitude is not giving same latitude. Also can you provide the reference of this document. May 21, 2021 at 5:05
  • Which document? The equations come from the Web Mercator Wikipedia page.
    – Matti Wens
    May 25, 2021 at 12:35

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