$area calculation incorrect for equal area projections in QGIS

Question

I have shapefiles for multiple countries in Europe, with places as individual polygons in each file.

I want to use the field calculator to add a column for each polygon's area, but every time I run the "$area" calculation the number returned is much less than it should be. They are typically off by two orders of magnitude.

I have put these files in every equal area projection I can think of (focusing on ones that use meters as units instead of lat/long), and the numbers are still incorrect. This happens both with OTF enabled and disabled, and when the map units are in km and meters. I've also had this issue both when I define the project CRS or just the CRS for one layer.

I've tried:

-UTM (different zones for each country) EPSG:32231 and EPSG:32631
-EPSG:3408, NSIDC EASE-Grid North
-EPSG:2163 - US National Atlas Equal Area
-EPSG:53012 - Sphere_Eckert_IV
-ETRS89 LAEA (EPSG:3035)

Answer 1

If your layers don't line up with any base map, you have misused Define CRS of the layer.

You MUST set them back to the original CRS (or better take a fresh copy to start off), then reproject them using Save As ... to a different filename and the CRS you want.