Hexagon and Regular Polygon Calculator
Choose the number of sides and enter the side length. The calculator returns the area and the other dimensions of the regular polygon.
Result
- Apothem (inradius)
- 3.4641 cm
- Circumradius
- 4 cm
- Width across flats
- 6.9282 cm
- Width across corners
- 8 cm
- Interior angle
- 120°
- Exterior angle
- 60°
- Sum of interior angles
- 720°
Formula
- Area = n × s² ÷ (4 × tan(π ÷ n))
- Hexagon: Area = (3√3 ÷ 2) × s²
- Perimeter = n × s
- Interior angle = (n − 2) × 180° ÷ n
How the Hexagon and Regular Polygon Calculator works
A regular polygon has equal sides and equal angles. It can be cut into n identical triangles meeting at the center. Each has a base of one side and a height equal to the apothem, which gives the area formula.
A regular hexagon is made of six equilateral triangles, so its circumradius equals its side length. That is why hexagons tile a plane and appear in honeycombs and bolt heads.
Worked example
A regular hexagon with 4 cm sides has an area of (3√3 ÷ 2) × 4² = 41.5692 cm², a perimeter of 24 cm and an apothem of 3.4641 cm.
Frequently asked questions
How do I find the area of a hexagon from the distance across flats?
The distance across flats is twice the apothem. Area = (√3 ÷ 2) × (across flats)². For 10 units across flats the area is 86.60.
What is the interior angle of a regular octagon?
135 degrees. Each interior angle is (8 − 2) × 180 ÷ 8.
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