Math Calculators

Shoelace Formula Calculator (Irregular Polygon Area)

Calculate the area of any simple polygon from its vertex coordinates using the shoelace formula — choose the coordinate unit and the area unit independently.

Area —

Vertices used —

About the Shoelace Formula Calculator (Irregular Polygon Area)

The shoelace formula (also called the surveyor's formula) finds the area of any simple polygon directly from the coordinates of its vertices, without needing to split it into triangles by hand. Pick the unit your coordinates are in, and the unit you'd like the area reported in, independently.

Formula: Area = 0.5 × |Σ(xⁱ × yⁱ₁₊ − xⁱ₁₊ × yⁱ)|, summing over all vertices in order and wrapping back to the first

This method works for any non-self-intersecting polygon, whether regular or irregular, and is widely used in land surveying and computer graphics.