[Proj] Beginner Question: Latitude/Longitude to x, y conversion - understanding output

Antti Castrén antti.castren at iki.fi
Mon Feb 24 06:54:20 EST 2014

 Hi Adam,

Units are meters. But they are true meters only at the latitude of
true scale of Mercator projection, which in your case is the Equator
(+lat_ts=0, +k=1.0). The string actually tells you that units are
meters (+units=m). At other latitudes meters are 'scaled' as the
projection formulae show. I personally call them pseudo-meters or
Mercator-meters, since they don't represent the correct distance. They
are just units of rectangular coordinates.

The longitude you are projecting (0.1275) is 14 193.25 m away from the
Central Meridian at the Equator. At latitude of London the true
distance from the Central Meridian is less since the meridians are
closer each other.

The latitude you are projecting (51.5072) is 5 733 755.28
pseudo-meters north of the Equator. The first meter is quite close to
real meter, but the scaling affects more and more the further you go
from the Equator. The true distance is only about 4 973 600 m.

To output the map onto 900x1100 rectangle you have to scale the length
and width of your projected map coordinates to 900 and 1100. And then
you have to apply shift of origin of course.

Hope this helps,


2014-02-24 11:37 GMT+02:00 AdamDynamic <helloadamdynamic+proj4 at gmail.com>:
> Hi,
> I've been scouring the internet for a couple of days now and getting
> absolutely nowhere - I appreciate this is probably a simple question once
> you know the answer but any help on this would be appreciated!
> I have a series of latitude/longitude coordinates that i want to plot as xy
> coordinates (i.e. a flat, rectangular map).
> I'm using the PyProj Python library to perform the conversion, the problem
> is I can't determine what the output of the function means or represents?
> e.g. Converting [51.5072,0.1275] (what Google tells me is the lat/long for
> London in the UK) returns [5733755.276187301, 14193.246790158479] for a
> Mercator projection - my question is '5733755.276187301 of what'? I
> understand that the library converts to Proj.4 notation (?) but I can't seem
> to find what the units are, or how I'd map the output onto a 900x1100
> rectangle?
> I'm using the following conversion formula which I found  here
> <http://osgeo-org.1560.x6.nabble.com/Google-Mercator-Projection-td3841191.html>
> +proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0
> +k=1.0 +units=m  +no_defs
> Any assistance would be great as I haven't been able to get any information
> from anywhere else. Please let me know if more information would be useful.
> Thanks,
> Adam
> --
> View this message in context: http://osgeo-org.1560.x6.nabble.com/Beginner-Question-Latitude-Longitude-to-x-y-conversion-understanding-output-tp5105455.html
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