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To get to know the size of the study area and how far objects are separated, I need to know x- and y-coordinate values.

Although the $x and $y of Field Calculator returned latitudes and longitudes, x- and y-coordinate values were not obtained when it was in Universal Transverse Mercator (UTM). I think it should be possible to get x- and y-coordinate values since more complicated calculations, i.e. latitudes and longitudes, are possible.

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Reproject the dataset (using "Save as ...") to UTM and use Field Calculator on the reprojected data.

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If you enabled OTF projection does it still work in the Field Calculator. – Nathan W Nov 8 '11 at 10:32
Thank you for the tips. It worked!. A few days ago, when I saved my file as UTM, it did not worked. But this time, I successfully got UTM coordinates. – user4805 Nov 15 '11 at 6:56
Good to hear that. Please accept the answer too. – underdark Nov 15 '11 at 7:52

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