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Regular Polygon Calculator

Enter the number of sides and the side length of a regular polygon, such as a hexagon or octagon, to get its area, perimeter, angles, apothem and circumradius.

Rules last checked 25 October 2026Every step shown

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Area

259.8076

Perimeter
60
Each interior angle
120 °
Apothem (centre to side)
8.6603
Circumradius (centre to corner)
10

A regular hexagon with sides of 10 has an area of 259.8076 and interior angles of 120°.

How it's worked out

  1. Arean × s² ÷ (4 tan(180° ÷ n)) = 6 × 10² ÷ (4 tan 30°)259.8076
  2. Interior angle(n − 2) × 180° ÷ n120°

The formulas

Interior angle = (n − 2) × 180° ÷ n · Apothem a = s ÷ (2 tan(180°/n))

Area = n × s × a ÷ 2 · Circumradius R = s ÷ (2 sin(180°/n))

Example

A regular hexagon with 10 cm sides has a perimeter of 60 cm, interior angles of 120°, an apothem of 8.66 cm and an area of 259.81 cm². Its circumradius equals its side, 10 cm.

Questions people ask

What is the interior angle of a regular polygon?

(n − 2) × 180° ÷ n. A pentagon's is 108°, a hexagon's 120° and an octagon's 135°.

How do I find the area of a hexagon?

For side s, the area is (3√3 ÷ 2) × s². A hexagon with 10 cm sides covers about 259.81 cm².

What is the apothem?

The distance from the centre to the middle of a side. The area of any regular polygon is half the perimeter times the apothem.

Do the exterior angles always add up to 360°?

Yes, for any convex polygon. In a regular one each exterior angle is 360° ÷ n.

Formula and rules last checked 25 October 2026Written and tested by the CalculatorDex teamReport a problem