Regular Polygon Calculator
Find the area, perimeter, angles, apothem and diagonals of any regular polygon from its number of sides and side length.
About the Regular Polygon Calculator
A regular polygon has equal sides and equal angles. It splits into n identical triangles meeting at the centre, each with base s and height equal to the apothem, which is how the area formula works.
The formula
Area = ½ × perimeter × apothem = n·s² ÷ (4·tan(π/n))
- Interior angle
- (n − 2) × 180° ÷ n
- Apothem
- s ÷ (2·tan(π/n))
- Diagonals
- n(n − 3) ÷ 2
Worked example
Hexagon, side 5
- Apothem ≈ 4.330
- Area ≈ 64.952
Questions people ask
Why do bees build hexagons?
Hexagons tile without gaps and enclose the most area for their perimeter of any tiling shape.
What happens as n gets large?
The polygon approaches a circle: its perimeter approaches 2πR.