I'm simply looking for an online tool or a utility to calculate the surface area of the same polygon (i.e shapefile) in different projection (projected and geographic projection system) systems. It would be great if you could share your suggestions.

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You can do that from command line with ogrinfo http://www.gdal.org/ogrinfo.html and SQLite SQL dialect http://www.gdal.org/ogr_sql_sqlite.html.

Example: Select state called "Colorado" from spapefile, convert geometry into EPSG:3857 and compute the area. Unit corresponds with the base unit of the projection and in this case will be square meter.

ogrinfo -dialect sqlite -sql "select st_area(st_transform(geometry,3857)) from states where STATE_NAME='Colorado'" states.shp INFO: Open of states.shp' using driverESRI Shapefile' successful.

Layer name: SELECT Geometry: None Feature Count: 1 Layer SRS WKT: (unknown) st_area(st_transform(geometry,3857)): Real (0.0) OGRFeature(SELECT):0 st_area(st_transform(geometry,3857)) (Real) = 447323265912.94

Change the projection code parameter in st_transform into 26913 for UTM zone 13 http://www.spatialreference.org/ref/epsg/26913/ and you will get quite different number:

OGRFeature(SELECT):0 st_area(st_transform(geometry,26913)) (Real) = 269618280090.583

ST_Area does not give reasonable results for geographic projections. For example area of Colorado is 28.041027282727 square degrees in EPSG:4326 which is rather useless information.

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