Regular Polygon Area Calculator
Compute the area of a regular polygon from the number of sides and the side length, plus perimeter, apothem, circumradius and interior angle.
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Input
Enter the number of sides and the side length to compute the area of a regular polygon along with its perimeter, apothem, circumradius and interior angle.
Result
Area
259.807621
Perimeter
60
Apothem (inradius)
8.660254
Circumradius
10
Interior angle
120°
Lengths use the same unit as the input and the area is in that unit squared.
How it works
- For a regular polygon with n sides and side length a, the area is area = (n × a²) / (4 × tan(π/n)).
- The perimeter is n × a and each interior angle is (n − 2) × 180 ÷ n degrees.
- The apothem (inradius) is a ÷ (2 × tan(π/n)) and the circumradius is a ÷ (2 × sin(π/n)).
- The number of sides must be an integer of 3 or more, and the side length must be positive.
- Lengths use the same unit as the input and the area is in that unit squared.
Frequently asked questions
- How is the area of a regular polygon calculated?
- With side length a and n sides, the area is (n × a²) / (4 × tan(π/n)). For a regular hexagon with a = 2, the area is about 10.39.
- What is the difference between the apothem and the circumradius?
- The apothem (inradius) is the distance from the center to the midpoint of a side, a ÷ (2 × tan(π/n)), while the circumradius reaches the vertices, a ÷ (2 × sin(π/n)). The circumradius is always the larger of the two.
- What values can I enter for the number of sides and side length?
- The number of sides must be an integer of 3 or more, and the side length must be positive. The area is expressed in the square of your length unit.
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