Unit of $area in the field calculator in Albers Equal Area projection (ESRI: 102033)

Question

I need to find the area of a set of polygons that are spread across South America. I researched a bit, and found that the Albers Equal Area projections reduces distortion and can be used for calculating areas within large landmasses.

My question is: What unit is the output of the $area function in the field calculator when using the ESRI: 102033 projection?

Answer 1

In QGIS, when you set the CRS, there is a window t the bottom that shows the WKT version of the CRS, and the Proj version. It contains the length unit. The area is the square of that.

For South America Albers Equal Area Conic (ESRI 102033), for example, it is:

WKT
PROJCRS["South_America_Albers_Equal_Area_Conic",
    BASEGEOGCRS["SAD69",
        DATUM["South American Datum 1969",
            ELLIPSOID["GRS 1967 Modified",6378160,298.25,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["South_America_Albers_Equal_Area_Conic",
        METHOD["Albers Equal Area",
            ID["EPSG",9822]],
        PARAMETER["Latitude of false origin",-32,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8821]],
        PARAMETER["Longitude of false origin",-60,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8822]],
        PARAMETER["Latitude of 1st standard parallel",-5,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8823]],
        PARAMETER["Latitude of 2nd standard parallel",-42,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8824]],
        PARAMETER["Easting at false origin",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8826]],
        PARAMETER["Northing at false origin",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8827]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["unknown"],
        AREA["South America"],
        BBOX[-60,-90,15,-30]],
    ID["ESRI",102033]]

The Proj version has the units of length (so does the WKT, but the proj is quicker to read.)

Proj4
+proj=aea +lat_0=-32 +lon_0=-60 +lat_1=-5 +lat_2=-42 +x_0=0 +y_0=0 +ellps=aust_SA +units=m +no_defs
Extent
-90.00, -60.00, -30.00, 15.00

So the length units are metres. Therefore area units will be square metres.