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🔺 Polygon Area Calculator (Shoelace Formula)

Calculate the area of any simple polygon by entering its vertex coordinates in order, using the shoelace formula.

Number of Vertices

Vertex 1: x

Vertex 1: y

Vertex 2: x

Vertex 2: y

Vertex 3: x

Vertex 3: y

Vertex 4: x

Vertex 4: y

Vertex 5: x

Vertex 5: y

Vertex 6: x

Vertex 6: y

Vertex 7: x

Vertex 7: y

Vertex 8: x

Vertex 8: y

What the shoelace formula does

The shoelace formula (also called the surveyor’s formula) computes the area of any simple polygon directly from the coordinates of its vertices, as long as they are entered in order (either clockwise or counter-clockwise) around the shape.

The formula

For vertices (x₁,y₁), (x₂,y₂), …, (xₙ,yₙ), the area is: Area = ½ |Σ(xⁱ · yⁱ₊₁ − xⁱ₊₁ · yⁱ)|, summed around the polygon and wrapping back to the first vertex. This calculator supports 3 to 8 vertices.

Enter each vertex’s x and y coordinate in the order they appear walking around the polygon’s edge.
Leave unused vertex fields at their defaults if your shape has fewer sides than the maximum.

Note: the polygon must be “simple” (its edges must not cross each other) for the result to be accurate. This tool is for general math and educational purposes.

Last reviewed August 2026