Regular Polygon Formulas
Regular Polygon
- Area
- A = n s2 ⁄ (4 tan(180° ⁄ n))
- Perimeter
- P = n × s
- Interior angle
- α = (n − 2) × 180° ⁄ n
- n number of sides
- s side length
Regular Polygon formulas explained
A regular polygon has n equal sides and n equal angles: pentagons, hexagons, octagons and more. Below are all the regular polygon formulas with what each letter means, a worked example and a free calculator.
- Area:
A = n s² ⁄ (4 tan(180° ⁄ n)) - Perimeter:
P = n × s - Interior angle:
α = (n − 2) × 180° ⁄ n
Regular Polygon calculator
Regular Polygon calculator
Worked example: area of a regular polygon
Given Sides n = 6 cm, Side s = 4 cm, substitute the values into each regular polygon formula:
- A = 6 × 4² ⁄ (4 tan(180° ⁄ 6)) = 41.57 cm²
- P = 6 × 4 = 24 cm
- α = (6 − 2) × 180° ⁄ 6 = 120°
Regular Polygon formulas FAQ
What is the formula for the area of a regular polygon?
The area of a regular polygon is A = n s² ⁄ (4 tan(180° ⁄ n)), where n is the number of sides, s is the side length.
What is the formula for the perimeter of a regular polygon?
The perimeter of a regular polygon is P = n × s, where n is the number of sides, s is the side length.
What is the formula for the interior angle of a regular polygon?
The interior angle of a regular polygon is α = (n − 2) × 180° ⁄ n, where n is the number of sides.
Can I download the regular polygon formulas as a PDF?
Yes. Use the Download PDF button on this page for a free printable regular polygon formula sheet with a worked example and practice questions.