# [Proj] Geocentric vs. Geodetic latitude

Frank Warmerdam warmerdam at pobox.com
Wed Apr 28 12:36:58 EDT 2004

```Glynn Clements wrote:
> So:
>         L = atan((a²/b²).tan(L'))
> and:
>         L' = atan((b²/a²).tan(L))
>
> where a is the equatorial axis and b the polar axis.

Glynn,

Well done!  I have tried (in python):

import math

a = 6378137.0
b = 6356752.3142

gc_lat = 32.98333333333333
gc_lat_rad = gc_lat * math.pi / 180.0

gd_lat = gd_lat_rad * 180.0 / math.pi

print gc_lat
print gd_lat

The results is 33.1593159397 as opposed to the  33.1593160 (rounded)
I was getting.  There would appear to be some difference in the 8th
decimal place (the 10th digit) but I don't know why that is.

In any event, your solutions is much briefer than mine, and I will replace
my solution with yours.

Thank you,
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```