📐Polygon Area Calculator

Calculate polygon area and perimeter from vertex coordinates using the shoelace formula

Shoelace Formula

How to Use the Polygon Area Calculator

The Polygon Area Calculator computes the area and perimeter of any polygon from its vertex coordinates using the shoelace formula. This method works for triangles, quadrilaterals, and even concave polygons, making it useful for land area estimation, architectural design, and collision-area calculations in game development.

Simply enter each vertex as "x,y" on its own line, following the order around the polygon's perimeter, and the area, perimeter, and vertex count update instantly with no extra button needed. At least 3 valid coordinates are required to form a polygon, and if all entered points fall on a single line, the tool shows a message explaining that the area cannot be calculated.

Frequently Asked Questions

Does this work for concave polygons?

Yes, the shoelace formula works for concave polygons too, as long as vertices are entered in order around the perimeter (clockwise or counter-clockwise).

Does the order of coordinates matter?

Yes. If the vertex order is mixed up, the polygon’s edges can cross each other and produce an incorrect area.

Can I enter negative coordinates?

Yes, since this is a free-text "x,y" input, negative coordinates work fine. Example: -3,2