Shoelace area calculation
The page applies the coordinate or shoelace formula to a closed polygon. Coordinates can be clockwise or counter-clockwise, but each row must move to the next adjacent boundary point.
Worked coordinate area example
Enter the four corners E 0, N 0; E 20, N 0; E 20, N 10; and E 0, N 10 in boundary order. The closed rectangle has area 200 m², perimeter 60 m and centroid E 10, N 5. The first point does not need to be repeated.
Large project Eastings and Northings give the same area after a constant coordinate shift. Use the entered coordinate units consistently and keep the vertices in adjacent boundary order.
Units
When Easting and Northing are in metres, the result is in square metres. Hectares use 10,000 m² and acres use the international conversion of 4,046.8564224 m².
Crossing boundaries
A self-crossing coordinate order can produce a misleading signed area. The tool checks non-adjacent boundary segments and warns when they intersect.
Frequently asked questions
Do I repeat the first coordinate at the end?
No. The calculator automatically closes the polygon from the final point back to the first. Repeating the first point is unnecessary.
Does this calculate surface area on a slope?
No. This is two-dimensional plan area. Surface area requires a terrain model or sufficient three-dimensional geometry.
Why is the centroid outside my polygon?
For some concave shapes the area centroid can lie outside part of the visible boundary. Also check that the coordinate order is correct and non-crossing.