# Intersection and area calculations in geographic vs. projected coordinates

I think one should do intersection calculations when layers are in the same coordinate system, and one should do area calculations in the appropriate projected coordinate system.

The order matters, but is one preferred? In my system, I get slightly different areas if I

1) Perform intersection of two layers that are in the same geographic coordinate systems, project the resulting intersection to a projected coordinate system, and then calculate areas, or

2) Project two layers to the same projected coordinate system, intersect them, and then calculate areas of the resulting intersection.

Without getting into details of my specific situation, I wonder if one of these approaches is theoretically preferable? I assume the 2nd would be, but I can't articulate why that would be.

(I assume terms are standard, but this is the intersection I'm looking for: http://wiki.gis.com/wiki/index.php/Intersect)

• There are sufficient imponderables to make this an opinion-based question. Among the variables: The projections involved, the coordinate envelopes of the data the vertex accuracy and precision, whether densification is used in the reprojection process,... Jan 4, 2019 at 21:01
• If performance is a consideration, and the intersection results in a smaller dataset, I would think option 1 would be preferable. Jan 4, 2019 at 21:37
• It comes down to what your vector representation of polygonal features really means. Typically, successive vertices are connected by line segments in the coordinates, treating them as elements of a Euclidean space. That might be fine for representing a feature when it is originally digitized, but when you reproject it, those line segments ought to be curved arcs--yet the calculations in the reprojected system will treat them as being straight in the new coordinate system. That's where the differences arise. One rule, then, is do the intersection calculations in the original coordinates. Jan 4, 2019 at 23:21
• Maybe you do need to go into more details. Why would you not choose option (0) Perform both the intersection and area calculation in the same geographic coord system? Jan 8, 2019 at 19:47
• Even these short responses suggest that my first assumption, about the necessity of doing area calculations in a projected coordinate system, was incorrect. I wished to keep this theoretical and avoid details to make it more broadly applicable. @whuber (echoed by Martin F) seem to be the most generalizable: stay in original coordinate systems when possible.
– JPC
Jan 10, 2019 at 20:22