Regular Polygon Calculator
Enter the number of sides and any one measurement (side, area, perimeter, circumradius or inradius) of a regular polygon to find the rest.
Change the values and press Calculate to work out your own figures.
Enter the number of sides and any one measurement.
Show the working
- From the side (a): side a = 3
- Area = n a² ÷ (4 tan(180° ÷ n)) = 4 × 3² ÷ (4 tan(45°))
- Area (A) = 9
How to use it
Enter the number of sides and any one measurement.
Enter the measurements (decimals, fractions such as 3/4, or mixed numbers such as 1 1/2) and, if you like, their unit; the answer is then also given in other units. Show the working gives the formula.
Key facts
A = n a² ÷ (4 tan(π/n)); R = a ÷ (2 sin(π/n)); r = a ÷ (2 tan(π/n))
Towards a circle
As n grows the polygon approaches its circumcircle: with 1,000 sides the area is within 0.001% of π R².
Questions
What is the area of a square with side 3?
9.
Interior angle of a regular n-gon?
(n − 2) × 180° ÷ n.
Formulas
A = n a² ÷ (4 tan(π/n)); R = a ÷ (2 sin(π/n)); r = a ÷ (2 tan(π/n))
Sources
Limitations
- All measurements in one calculation use the same unit; the answer is also given in other units.
- Measurements up to 10¹⁵.