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I am trying to calculate the areas of some polygons and i want to use the field calculator to measure the area. The result i got using this method is different from using the QGIS measurement tool. I am confused on which is correct. How can i do this correctly? Also is it possible to change the measurement unit of the field calculator to give result in meter square?

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If you calculate area with field calculator by $area expression, your result will depend on the projection of your shapefile. Ex. if your projection is EPSG:4326 you will get an area in degrees. If you want meters, you need to reproject your shapefile to another projection (metric).

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