Regular Polygon Calculator
Compute area, perimeter and interior angles of any regular polygon from its number of sides and side length. The calculator also reports the apothem, circumradius and the total interior-angle sum.
Enter polygon details
Enter the number of sides and the side length.
Regular polygon formulas
Perimeter: P = n · s
Interior angle: θ = (n − 2) · 180° / n
Apothem: a = s / (2 · tan(π / n))
Circumradius: R = s / (2 · sin(π / n))
Area: A = ½ · n · s · a = ¼ · n · s² / tan(π / n)
Common regular polygons
| Name | Sides | Interior angle |
|---|---|---|
| Triangle | 3 | 60° |
| Square | 4 | 90° |
| Pentagon | 5 | 108° |
| Hexagon | 6 | 120° |
| Heptagon | 7 | ≈128.57° |
| Octagon | 8 | 135° |
| Nonagon | 9 | 140° |
| Decagon | 10 | 144° |
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Frequently asked questions
A regular polygon has all sides equal in length and all interior angles equal in measure. Equilateral triangles and squares are the simplest examples.
The apothem is the perpendicular distance from the center of the polygon to the midpoint of any side. It equals the radius of the polygon's inscribed circle.