A regular polygon has equal sides and equal angles: equilateral triangle, square, pentagon, hexagon and so on.
How to use the Regular Polygon Calculator
- Number of sides
- Side length
Results update as you type, and every field accepts the units shown in its menu.
How it works
The polygon splits into n identical isosceles triangles from the centre, which gives the area and radii.
Inputs explained
| Field | What to enter |
|---|---|
| Number of sides | A number |
| Side length | Units: m, cm, mm, km, in, ft … |
What each result means
- Area = [Number of sides] × [Side length]^2 ÷ (4×tan(pi÷[Number of sides]))
- Perimeter = [Number of sides]×[Side length]
- Interior angle = ([Number of sides] – 2)×180÷[Number of sides]
- Apothem (inradius) = [Side length] ÷ (2×tan(pi÷[Number of sides]))
- Circumradius = [Side length] ÷ (2×sin(pi÷[Number of sides]))
Example values
How the main result changes when Number of sides changes and everything else stays at the example values above:
| Number of sides | Area (m²) |
|---|---|
| 3 | 6.93 |
| 4.5 | 21.45 |
| 6 | 41.57 |
| 7.5 | 67.38 |
| 9 | 98.91 |
| 12 | 179.14 |
Formula
Area = n s² ÷ (4 tan(π ÷ n))Interior angle = (n − 2) × 180° ÷ nWorked example
Inputs — Number of sides: 6; Side length: 4 m.
Results — Area = 41.57 m²; Perimeter = 24 m; Interior angle = 120 °; Apothem (inradius) = 3.46 m; Circumradius = 4 m.
Key terms
- Apothem
- Perpendicular distance from the centre to a side.
Frequently asked questions
What is an apothem?
The distance from the centre to the middle of a side.
What happens as n grows?
The polygon approaches a circle.
What formula does the Regular Polygon Calculator use?
Area = n s² ÷ (4 tan(π ÷ n)).