Regular Polygon Calculator

Area, perimeter, apothem, circumradius and interior angle of a regular polygon (pentagon, hexagon, octagon…) from side length.

3 = triangle, 4 = square, 5 = pentagon, 6 = hexagon, 8 = octagon.
Area
10.392
Perimeter
12
Apothem (inradius)
1.7321
Circumradius
2
Interior angle
120.00
Exterior angle
60.00

Estimate generated with SortedSums: https://sortedsums.com/polygon-calculator/. For informational purposes only; verify before relying on it.

How it’s calculated

A regular polygon has n equal sides and equal angles. The apothem a is the distance from the centre to the middle of a side; the area is half the apothem times the perimeter.

Perimeter P = n × s Apothem a = s ÷ (2 tan(180° ÷ n)) Area = ½ × a × P Circumradius R = s ÷ (2 sin(180° ÷ n)) Interior angle = (n − 2) × 180° ÷ n

Example: a hexagon with 2 ft sides has P = 12 ft, a = 2 ÷ (2 tan 30°) = √3 ≈ 1.732 ft and Area = ½ × 1.732 × 12 ≈ 10.39 ft² (exactly 6√3). Each interior angle is 120°.

Frequently asked questions

What is an apothem?

The perpendicular distance from the centre of a regular polygon to the midpoint of any side. It is the radius of the inscribed circle.

What is the interior angle of a hexagon or octagon?

Hexagon: (6 − 2) × 180° ÷ 6 = 120°. Octagon: (8 − 2) × 180° ÷ 8 = 135°.

Does this work for irregular polygons?

No. For irregular shapes, split them into triangles and rectangles and add the areas.

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Sources

Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.

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