Regular Polygon Calculator
Find the area, perimeter and angles of any regular polygon.
What the Regular Polygon Calculator does
A regular polygon has equal sides and equal angles. Its area is half the perimeter times the apothem — the perpendicular distance from the centre to a side. As the side count rises the shape converges on a circle.
Formula
Area = (n × s²) ÷ (4 × tan(π ÷ n))Interior angle = ((n − 2) × 180) ÷ nApothem = s ÷ (2 × tan(π ÷ n))
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Number of sides | number | Yes | Accepts 3 or more. |
| Side length | number | Yes | Accepts more than 0. |
How to use it
- Enter Number of sides and Side length.
- Select Calculate.
Worked example
A regular hexagonal tile with 10 cm sides.
- Sides
- 6
- Side length
- 10
Area ≈ 259.81 cm², perimeter 60 cm, interior angle 120°.
Frequently asked questions
Why do hexagons tile so well?
Their 120° interior angle divides evenly into 360°, so three meet perfectly at every vertex with no gaps — which is why honeycombs use them.