Works for any regular n-gon — triangle, square, pentagon, hexagon, octagon, and beyond. Set the number of sides, tell the tool whether you know a side length, a radius, or the area, and it derives every other property: area, perimeter, circumradius, inradius (apothem), and the interior and exterior angles.
How it works
A regular polygon with n sides of length s has these exact relationships, which the tool uses:
- Perimeter = n × s
- Area = ¼ × n × s² × cot(π/n) — equivalently ½ × perimeter × apothem
- Circumradius (R) = s ÷ (2 × sin(π/n))
- Inradius / apothem (r) = s ÷ (2 × tan(π/n))
- Interior angle = (n − 2) × 180 ÷ n degrees
- Exterior angle = 360 ÷ n degrees
If you supply a radius or the area instead of the side, the tool inverts the matching formula to recover the side length, then computes everything else from it.
Example
A regular hexagon (n = 6) with side 10:
- Perimeter = 6 × 10 = 60
- Area = ¼ × 6 × 100 × cot(30°) = 150 × √3 ≈ 259.81
- Circumradius = 10 ÷ (2 × sin 30°) = 10
- Apothem = 10 ÷ (2 × tan 30°) ≈ 8.66
- Interior angle = (6 − 2) × 180 ÷ 6 = 120°
- Exterior angle = 360 ÷ 6 = 60°
| Sides (n) | Interior angle | Exterior angle |
|---|---|---|
| 3 (triangle) | 60° | 120° |
| 4 (square) | 90° | 90° |
| 5 (pentagon) | 108° | 72° |
| 6 (hexagon) | 120° | 60° |
| 8 (octagon) | 135° | 45° |
All calculations stay in your browser.