Regular Polygon Area Calculator
A regular polygon is a polygon with all sides of equal length and all interior angles equal. The calculator works with any regular polygon from a triangle (3 sides) to a polygon with many sides. Given the number of sides and the length of one side, the calculator computes the area, perimeter, circumradius (radius of the circumscribed circle through all vertices), and apothem (radius of the inscribed circle touching all sides). The area formula uses trigonometry and works universally for any regular polygon. This calculator also includes reference values for common polygons like pentagons, hexagons, and octagons.
Regular polygon formulas
Area = (n * s^2) / (4 * tan(pi / n))
Perimeter = n * s
Circumradius (R) = s / (2 * sin(pi / n))
Apothem (a) = s / (2 * tan(pi / n))
Reference table
| Polygon | Sides | Interior Angle |
|---|---|---|
| Triangle | 3 | 60 degrees |
| Square | 4 | 90 degrees |
| Pentagon | 5 | 108 degrees |
| Hexagon | 6 | 120 degrees |
| Heptagon | 7 | 128.57 degrees |
| Octagon | 8 | 135 degrees |
| Nonagon | 9 | 140 degrees |
| Decagon | 10 | 144 degrees |
Regular polygon calculator: frequently asked questions
What is a regular polygon?
A regular polygon is a polygon with all sides of equal length and all interior angles equal. Examples include equilateral triangles, squares, regular pentagons, and regular hexagons. The number of sides can be any integer greater than or equal to 3.
What is the formula for the area of a regular polygon?
The area of a regular polygon with n sides and side length s is: Area = (n * s^2) / (4 * tan(pi / n)). This formula works for any regular polygon regardless of the number of sides.
What is the apothem of a regular polygon?
The apothem is the distance from the center of the polygon to the midpoint of any side. It is the radius of the inscribed circle (incircle) that touches all sides. The apothem is calculated as: a = s / (2 * tan(pi / n)).
What is the circumradius of a regular polygon?
The circumradius is the distance from the center of the polygon to any vertex (corner). It is the radius of the circumscribed circle that passes through all vertices. The circumradius is: R = s / (2 * sin(pi / n)).
What are some common regular polygons?
Triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides), heptagon (7 sides), octagon (8 sides), nonagon (9 sides), decagon (10 sides), and dodecagon (12 sides) are common regular polygons.
Official sources
- Wolfram MathWorld: Regular Polygon.
- ISO 80000-2: Mathematical signs and symbols.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.