Irregular Polygon Area Calculator

Interactive Polygon Analysis Tool

A comprehensive calculator to calculate the area and the side lengths of polygons whose vertices may be entered and changed by either:

The Shoelace formula (also known as Gauss's area formula) is used to calculate the area of any simple polygon – whether convex or concave. Each side length is calculated using the distance formula between consecutive vertices.

\[ \text{Area} = \frac{1}{2} \left| \sum_{i=1}^{n} (x_i y_{i+1} - x_{i+1} y_i) \right| \]

where \((x_{n+1}, y_{n+1}) = (x_1, y_1)\) and side lengths are \(\sqrt{(x_{i+1}-x_i)^2 + (y_{i+1}-y_i)^2}\)

Interactive Polygon Area

Click and drag any numbered point • New points appear near existing ones • Adjustable scale

Edit coordinates directly or drag points on canvas

Smaller for large coordinates
Vertices: 5
Type: Concave
IMPORTANT:

The vertices must be arranged in order (either clockwise or counterclockwise) around the polygon. No edge should intersect another - the polygon must be simple (non-self-intersecting) for the shoelace formula to give a meaningful area.

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