Area of a Polygon Calculator

Calculate the area of any polygon by entering the coordinates of its vertices

Input Parameters

Calculation Results

Calculation Formula

Using the Shoelace formula:

Area = 0.5 × |Σ(xiyi+1 - xi+1yi)|
Where:
(x1,y1) is the first vertex
(xn,yn) is the last vertex
(xn+1,yn+1) is the first vertex

Area of a Polygon Calculator Calculator Usage Guide

Learn how to use the Area of a Polygon Calculator calculator and its working principles

How to Use This Calculator

  1. Enter the coordinates of your polygon's vertices in the text area. Each vertex should be in the format "x,y", and vertices should be separated by commas.
  2. For example, a square with corners at (0,0), (4,0), (4,4), and (0,4) would be entered as: "0,0, 4,0, 4,4, 0,4"
  3. Click the "Calculate" button to compute the area.
  4. The calculator uses the Shoelace formula (or Gauss's area formula) to calculate the area of the polygon.

Understanding the Shoelace Formula

The Shoelace formula is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane.

For a polygon with vertices (x₁,y₁), (x₂,y₂), ..., (xn,yn), the formula is:

Area = 0.5 × |Σ(xiyi+1 - xi+1yi)|

Where Σ denotes the sum over all edges of the polygon.

Examples of Polygons You Can Calculate

  • Triangles
  • Quadrilaterals
  • Regular polygons (like pentagons, hexagons)
  • Irregular polygons

Important Notes

Make sure your vertices are listed in order (either clockwise or counterclockwise) for accurate results.

The calculator assumes that the vertices form a simple polygon (they don't cross each other).