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I am trying to calculate the polygon area using 2 different methods I saw on previous posts here.

The first method: Layer > Open attribute table > Field Calculator/Ctrl+I or right-click shapefile > Open attribute table > Field Calculator/Ctrl+I). There is a function $area that will calculate the area of each row in the table.

Second method: Vector | Geometry Tools | Add/export geometry columns, which creates a new shapefile with area and perimeter (or length) columns added.

But I still get different results. I would like to know why it gives different results, even though, it's for the same area?

The problem I am trying to solve is to find the percentage of the population who live within 10 minutes walk from parks, and I need to be as precise as possible but I am super confused with these 2 different results.

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The reason is that $area is calculating the geographic area which takes into account the curvature of the earth, while the other method is calculating the planimetric area which does not account for the curvatature of the earth. You see the same difference between $area and area($geometry).

To accurately solve your problem you can use either method as long as you are consistent.

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    You should also consider the layer's CRS. The kind of projection used does influence the result
    – Babel
    Sep 28, 2020 at 16:16

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