I am using QGIS version 2.12.3.
I have 3 polygon shapefiles: A, B and the intersect of A and B, which we can call C.
All I want is to add a field to the attributes table of each shapefile giving the area (in square m or square km) of each feature in that layer. A, B and C each contain upwards of 10,000 individual features (polygons of protected areas), distributed over every continent.
I have used a global projection (WGS 84/NSIDC EASE Grid-Global EPSG:3975, have also tried 3410), which is listed under 'Projected Coordinate Systems' so I assume it is projected and not geographical, and set this as the coordinate system for the project and each one of the layers.
When I use the field calculation tool and the $area function, the resulting field values are definitely not in square m or square km and bear no resemblance to area as I understand it.
I have run it several times having fiddled with settings that I'm fairly sure I don't understand, and I've ended up with either really tiny values (e.g. 0.0000002345) or random sets of values including negative numbers.
Can anyone identify where I've gone wrong and suggest how I can go about completing this fairly simple task?