What this calculator does
Polygon area from vertices (shoelace formula) works out area, perimeter and centroid of a simple polygon from its ordered vertices. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaSigned area = ½Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ); centroid Cx,Cy = (1/6A)Σ(xᵢ+xᵢ₊₁)(xᵢyᵢ₊₁−xᵢ₊₁yᵢ), similarly for Cy
The inputs explained
| Field | What to enter |
|---|---|
| Vertices in order, x,y pairs separated by ; (e.g. 0,0; 6,0; 6,4; 0,4) | A list of numbers, separated by commas or spaces. |