About the polygon area (coordinates) calculator
Type or paste the corners of any simple polygon, such as a plot of land or a floor plan, and get the exact area with the shoelace (surveyor’s) formula, plus perimeter, centroid and side lengths. Drag vertices on the grid, add or remove them, and watch everything update.
Vertices must be listed in order around the shape (either direction). If the edges cross each other, the polygon isn’t simple and you’ll get a warning.
Formulas
| Shoelace formula | A = ½|Σ (xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)| |
| Centroid | Cₓ = (1/6A)Σ(xᵢ + xᵢ₊₁)(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ) |
Frequently asked questions
How does the shoelace formula work?
Multiply each x by the next vertex’s y, subtract each y times the next x, add these up and halve the absolute value. It works for any simple polygon, convex or not.
Can I paste coordinates?
Yes, paste pairs like “0,0 4,0 4,3” or one pair per line into the text box.