Any Shape, One Formula

Rectangles and triangles have neat formulas; real polygons don't. This polygon area calculator applies the shoelace formula, which handles any simple polygon — regular or wildly irregular — using nothing but its corner coordinates.

How the Shoelace Works

Walk the perimeter, multiplying each x by the next vertex's y and subtracting the reverse, then sum and halve. The cross products measure signed trapezoid areas that cancel for everything outside the polygon — leaving exactly the enclosed area.

Beyond Area

The same vertex list yields the perimeter and centroid almost for free. That makes the tool useful for surveying plots, mapping irregular regions, or any layout work where the shape defies a textbook formula.