Converting Latitude and Longitude to Tile Numbers

Level: Beginner

To work out which tile you need for a given latitude and longitude, you first need to pick a zoom level that you're interested in. Then calculate:

n = 2 ^ zoom
xtile = ((lon_deg + 180) / 360) * n
ytile = (1 - (ln(tan(lat_rad) + sec(lat_rad)) / Pi)) / 2 * n

Note: ln stands for natural logarithm

round down xtile and ytile to get the integer tile numbers.

If you need to go the other way:

n = 2 ^ zoom
lon_deg = xtile / n * 360.0 - 180.0
lat_rad = arctan(sinh( Pi * (1 - 2 * ytile / n)))
lat_deg = lat_rad * 180.0 / Pi

That should be enough to get you up and running. To get help with any of CloudMade's APIs and to keep up-to-date with our latest releases, take a look at the developers mailing list.

Function GetTiles(lon:Float,lat:Float,z:Int)
    Local rad:Double=lat*(Pi/180.0)
    Local n:Float = 2 ^ z
    xtile = ((lon + 180) / 360) * n
    ytile = (1-(    Log(Tan(rad)+sec(rad))    /  Pi)   )/2*n
End Function

Function Sec:Float(val:Float)
    Return 1/Cos(val)
End Function

Function GetCoords(xtile:Float,ytile:Float,zoom:Int)
    Local n:Float = 2 ^ zoom
    lon_deg= xtile / n * 360.0 - 180.0
    lat_rad= ATan(Sinh( Pi * (1 - 2 * ytile / n)))
    lat_deg= lat_rad * 180.0 / Pi
End Function