Polygon Area Calculator

Enter the coordinates of each vertex of your polygon. Points will be connected in order, and the last point will connect back to the first.

Visual Representation

Grid: Each square = 1 unit

Area: Click "Calculate Area" to compute

How the Shoelace Formula Works

The Shoelace formula (also known as the surveyor's formula) calculates the area of a polygon by:

  1. Multiplying each x-coordinate by the next point's y-coordinate
  2. Subtracting the product of each y-coordinate with the next point's x-coordinate
  3. Taking half of the absolute value of the sum

Formula: Area = ½|Σ(xiyi+1 - xi+1yi)|

Related Geometry Calculators

  • Triangle Area Calculator
  • Circle Area Calculator
  • Rectangle Area Calculator
  • Perimeter Calculator
  • Distance Between Points Calculator
  • Midpoint Calculator
  • Coordinate Geometry Tools

This tool calculates polygon areas fast and simply. It starts with a default rectangle. The area for this shape is 12 square units.

Overview

The calculator works by letting you enter vertex coordinates. When you type in the numbers, the tool redraws the shape on a grid. A diagram shows each plotted point and side. The calculator uses the shoelace formula to compute the area.

How to Use This Tool

  1. Enter Coordinates: Fill in the x and y values for each point. Default points form a rectangle.
  2. Add or Remove Points: Click "Add Point" for extra vertices or "Remove Point" to delete one. A polygon needs at least three points.
  3. Watch the Diagram: Check the canvas. The grid shows each unit square and the plotted points form the shape.
  4. Calculate Area: Click the "Calculate Area" button. The tool uses the shoelace formula and shows the steps along with the area.
  5. Clear Data: Use "Clear All" to reset the inputs and the diagram.

Input Field Details

Each input field asks for two numbers. The first is the x-coordinate. The second is the y-coordinate. The numbers are joined in order to create a shape. The last point connects back to the first.

Output Explanation

The output shows the computed area in square units. It is displayed with four decimals. The tool also shows the steps of the shoelace formula. This helps you see how each term adds up.

Limitations and Special Notes

This calculator works only with simple polygons. It needs at least three points. Enter correct numbers to avoid errors. The diagram may not display if you use non-numeric values.

Common Use Cases

Related Geometry Calculators

This tool makes area calculations clear and simple. Follow the steps and see the shape drawn instantly. The detailed steps help you understand the computation process. Give it a try and see how easy it is to work with coordinates.