I have a raster that is projected to a state plane CRS and I am adding polygon/polyline shapefiles that are projected to WGS84. On the fly transformation is set to reproject to my raster CRS. When I use the identify features tool to select a feature, under derived I can see the correct area/length measurements. Is there a way to transfer that exact information into a new column(s) in the attributes by using the field calculator?
If you are not sure about the right units of measurements, save a copy of the shapefile into the CRS of the raster.
That way you will get the correct values using the $area function in field calculator.
Note that identify tool and field calculators use different methods to calculate areas: https://hub.qgis.org/issues/4252
Vector -> Geometry Tools -> Export/Add geometry columns
lets you choose if measurement of the new columns shall be in layer CRS, project CRS or ellipsodial (which the identify tool uses).