Polygon Area Calculator
Calculate the area and perimeter of any polygon from its vertex coordinates using the shoelace formula.
How it works
- 1Enter each vertex as an x, y pair on its own line — coordinates may be separated by a comma or whitespace.
- 2The shoelace formula sums the signed cross-products of consecutive vertices: Area = ½ |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)|, wrapping the last vertex back to the first.
- 3Perimeter is the sum of the Euclidean distances between adjacent vertices, including the closing edge.
Use cases
- Surveying and land measurement — compute the area of an irregular plot from corner coordinates.
- Game and graphics development — find the area or bounds of a polygon collision shape.
- Architecture and interior design — estimate floor or surface area from measured corners.
Frequently asked questions
Does the order of vertices matter?
Yes. List the vertices in consistent order (clockwise or counter-clockwise) around the polygon. The formula works for either winding because the absolute value is taken at the end.
Does it work for concave polygons?
Yes — the shoelace formula works for any simple (non-self-intersecting) polygon, convex or concave. Self-intersecting outlines give incorrect results.
What units does it use?
Whatever units you supply. Coordinates in metres give an area in square metres and a perimeter in metres; feet give square feet and feet.
Related tools
See all →Calculate the area and perimeter of a rectangle from its width and height, with a labeled diagram.
Calculate the area and circumference of a circle from its radius, with a labeled diagram.
Calculate the area (Heron’s formula) and perimeter of a triangle from its three sides.
Calculate the area and perimeter of a trapezoid from its two parallel sides, height, and legs.