How Perimeter Calculator
Polygon Calculator works out Number of sides and Polygon name from Polygon type, Number of sides and Known measurement. The default figures on this page give area of 2.598076; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
6 steps
- Regular hexagon: n = 6, half the central angle is pi/n = 0.5235987755982988 rad.
- Side length s = 1 (derived from the given sideLength).
- Apothem a = s / (2 tan(pi/n)) = 0.8660254037844387; circumradius R = s / (2 sin(pi/n)) = 1.0000000000000002.
- Perimeter P = n*s = 6; area = (1/2) P a = 2.598076211353316.
- Interior angle = (n-2)*180/n = 119.99999999999999 degrees; exterior angle = 360/n = 60 degrees.
- Diagonals = n(n-3)/2 = 9.
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the Polygon Calculator calculates
Computes area, perimeter, apothem, circumradius, interior and exterior angles and diagonal count for a regular n-sided polygon, or the shoelace area, perimeter and centroid of an irregular polygon given by its vertex coordinates.
How to use this Polygon Calculator
Enter Polygon type, Number of sides, Known measurement and Its value. Number of sides updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Number of sides, Polygon name and Area.
The method follows Weisstein, Eric W. "Regular Polygon" and "Polygon Area", MathWorld, B. Braden, "The Surveyor's Area Formula", The College Mathematics Journal 17(4), 326-337 and CRC Standard Mathematical Tables and Formulae, Geometry: regular polygons.
Regular hexagon with side 6 example
With Polygon type: regular, Number of sides: 6, Known measurement: sideLength, Its value: 6, the calculator returns Area: 93.5307436, Perimeter: 36, Apothem (inradius): 5.19615242. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Number of sides, Polygon name and Area. The inputs you can vary are Polygon type, Number of sides, Known measurement, Its value, Vertex x coordinates and Vertex y coordinates.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
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Frequently asked questions
How do I calculate the perimeter?
Computes area, perimeter, apothem, circumradius, interior and exterior angles and diagonal count for a regular n-sided polygon, or the shoelace area. Open “How this is worked out” beside the result to see each step for your own figures.
What is a formula for perimeter?
Computes area, perimeter, apothem, circumradius, interior and exterior angles and diagonal count for a regular n-sided polygon, or the shoelace area. On this page it is computed from Polygon type, Number of sides and Known measurement and shown as Number of sides, Polygon name and Area.
What is perimeter in an easy way?
It needs Polygon type, Number of sides, Known measurement, Its value, Vertex x coordinates and Vertex y coordinates. Nothing else is required, and the figures stay in your browser.
How to calculate area to perimeter?
The result gives Number of sides, Polygon name, Area, Perimeter, Side length and Apothem (inradius), each labelled with its unit so the figure can be read on its own.
What information do I need for the Polygon Calculator?
You need Polygon type, Number of sides, Known measurement, Its value, Vertex x coordinates, Vertex y coordinates and Angle unit. The page opens with default figures that give area of 2.598076, so you can see the scale before entering your own.
What does this Polygon Calculator show?
It shows Number of sides, Polygon name, Area, Perimeter, Side length, Apothem (inradius), Circumradius and Interior angle, with the working and any warnings for your entries.