# [Proj] GRS80 vs GRS80 +towgs84=0,0,0

Frank Warmerdam warmerdam at pobox.com
Sat Dec 3 15:43:20 EST 2005

```On 12/3/05, Maciek Sieczka <werchowyna at epf.pl> wrote:
> Hi,
>
> I've encountered one small thing using cs2cs I don't understand. There
> is a difference in results when converting between WGS84 and GRS80 based
> systems - when the towgs84=0,0,0 is given for GRS80 and when it is not:
>
> cs2cs -f "%.6f" +proj=latlong +ellps=WGS84 +to +proj=tmerc +lat_0=0
> lon_0=19 +k=0.9993 +x_0=500000 +y_0=-5300000 +ellps=GRS80 +towgs84=0,0,0
>
> 17d01'0.0E 51d07'0.0N
> 361227.112181   362969.278159 0.000063
>
> But, if I don't specify the +towgs84=0,0,0 in the target coordinate
> system, I obtain a slightly different result:
>
> cs2cs -f "%.6f" +proj=latlong +ellps=WGS84 +to +proj=tmerc +lat_0=0
> +lon_0=19 +k=0.9993 +x_0=500000 +y_0=-5300000 +ellps=GRS80
>
> 17d01'0.0E 51d07'0.0N
> 361227.112178   362969.278057 0.000000
>
> The difference is less than 1 mm, but anyway - why? I thought that no
> matter if I specify the towgs84=0,0,0 for GRS80 or not I would obtain
> the same results.

Maciek,

In the case you specify the +towgs84, no ellipsoid conversion
is done.  In the case without +towgs84, an ellipsoid conversion
is done.  The WGS84 and GRS80 are essentially the same
but there is a small difference.

WGS84 a=6378137.0      rf=298.257223563 WGS 84
GRS80 a=6378137.0      rf=298.257222101 GRS 1980(IUGG, 1980)

Best regards,
--
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I set the clouds in motion - turn up   | Frank Warmerdam, warmerdam at pobox.com
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and watch the world go round - Rush    | Geospatial Programmer for Rent

```