🔷 Shoelace Polygon Area Calculator

Click vertices onto a grid (or type coordinates) and get the exact area of any polygon — even weird L-shapes, arrowheads and plots of land — using the surveyor's shoelace formula, with the full cross-multiplication table shown, plus perimeter, centroid, convexity and self-intersection checks.

Click the grid to add a vertex, drag dots to move them, double-click a dot to delete it. Area works in any units — m² for a plot of land, px² for a game sprite.

Results

The shoelace sum

Pair each x with the next y (↘) and each y with the next x (↗); the area is half the difference of the two totals.
Add at least three vertices to see the table.