How to Use the Polygon Area Calculator
Choose Regular polygon for equal sides and angles, or Coordinates for a simple irregular polygon defined by ordered vertices.
- Choose Regular polygon or Coordinates.
- Enter the required values and select a length unit.
- Click Calculate.
- Review the Result section and Formula & steps.
- Use Copy result or Download result (.txt) to save the output.
- Use Reset to clear both input modes, restore meters, select Regular polygon, and hide the result.
If clipboard copying fails, the tool tells you to copy the result manually.
Choose the Calculation Method
Regular polygon requires a whole-number side count from 3 to 200 and a positive side length. The sides and interior angles must be equal.
Coordinates accepts 3 to 200 vertices. Enter one x,y pair per line in boundary order, consistently clockwise or counter-clockwise. The points must describe a simple, non-self-intersecting polygon.
What the Calculator Returns
- Regular mode returns area, perimeter, apothem, circumradius, and interior angle.
- Coordinate mode returns area, perimeter, and vertex count.
- Formula & steps shows the governing formula and the main aggregate calculation steps.
- Area uses the squared selected length unit. Perimeter uses the selected length unit.
- The downloaded file is named
polygon-area-calculator-result.txt.
Formulas Used
Regular polygon with n sides of length s:
- Apothem:
a = s / (2 * tan(pi / n)) - Perimeter:
P = n * s - Area:
A = 1/2 * P * a - Circumradius:
R = s / (2 * sin(pi / n)) - Interior angle:
((n - 2) * 180) / ndegrees
Coordinate mode uses vertices listed around the boundary:
- Shoelace formula:
A = 1/2 * |sum of (xi * yi+1 - xi+1 * yi)|, with the last vertex wrapping back to the first. - Perimeter: sum of the straight-line distance between each pair of consecutive vertices.
Inputs, Units, and Validation
- Regular polygon: number of sides (a whole number from 3 to 200) and a positive side length.
- Coordinates: valid
x,ypairs, one per line, with 3 to 200 vertices. Both coordinates use the selected unit. - Supported units: mm, cm, m, km, in, ft, yd, and mi.
- Area unit: automatically the squared version of the length unit you choose.
- Side length and coordinate values cannot exceed
1e12in absolute value; coordinates outside that range are rejected. - Collinear coordinate sets are rejected because they do not enclose an area.
Assumptions and Limitations
The calculation assumes a two-dimensional polygon based on the values you enter. Coordinate vertices must be in boundary order and describe a simple, non-self-intersecting shape. The tool does not detect or correct self-intersections, infer measurement error or real-world tolerances, or replace professional or certified calculations.
Calculation and Data Handling
The polygon calculation logic in script.js runs in your browser, and the calculator code does not include a request that submits calculator values to a server. This statement describes the calculator logic only; the page also loads third-party analytics and includes other server-backed page features.
Frequently Asked Questions
What is the formula for the area of a regular polygon?
Area = 1/2 x perimeter x apothem, where perimeter = n x s (n sides of length s) and apothem = s / (2 x tan(pi/n)).
What is the shoelace formula?
For vertices (x1,y1)...(xn,yn) listed in order around the polygon, Area = 1/2 x |sum of (xi * yi+1 - xi+1 * yi)|, wrapping the last vertex back to the first.
Does vertex order matter for the coordinate method?
Yes. Vertices should be entered in order around the polygon (clockwise or counter-clockwise, consistently). The shoelace formula assumes a simple, non-self-intersecting polygon; entering points out of order will produce an incorrect area.
What units does this calculator support?
Millimeters, centimeters, meters, kilometers, inches, feet, yards, and miles. Area is shown in the squared version of the unit you choose.
Can this calculator handle any polygon shape?
It handles regular polygons with 3 to 200 sides and simple irregular polygons defined by ordered vertex coordinates. It does not detect or correct self-intersecting shapes.