Enter the number of sides and the side length of the polygon below, then click Calculate Area. Use a period or comma as the decimal separator.
Regular Polygon Area Calculator
Result:
How to use the calculator
- Enter the Number of Sides (minimum 3).
- Enter the Side length.
- Select the unit of measure.
- Click Calculate Area to see the result.
Regular polygon area formula
The area of a regular polygon with n sides of length L is:
A = (n × L²) ÷ (4 × tan(π/n))
This formula works for any regular polygon, from 3 (equilateral triangle) to any number of sides. The apothem is a = L / (2 × tan(π/n)) and the area equals A = (n × L × a) / 2.
Practical examples (side = 5 m)
| Polygon (n) | Side (L) | Area |
|---|---|---|
| Triangle (3) | 5 m | 10.825 m² |
| Square (4) | 5 m | 25.000 m² |
| Pentagon (5) | 5 m | 43.012 m² |
| Hexagon (6) | 5 m | 64.952 m² |
| Octagon (8) | 5 m | 120.711 m² |
Frequently asked questions
What is the formula for the area of a regular polygon?
The general formula is A = (n × L²) / (4 × tan(π/n)). For n=6 and L=5: A = (6 × 25) / (4 × tan(30°)) = 150 / (4 × 0.577) ≈ 64.95 m².
Can I calculate the equilateral triangle with this formula?
Yes. With n=3: A = (3 × L²) / (4 × tan(60°)) = (3 × L²) / (4√3) = (√3/4) × L², which is exactly the equilateral triangle area formula.
What is the apothem of a regular polygon?
The apothem is the perpendicular distance from the centre to the midpoint of each side: a = L / (2 × tan(π/n)). The area can also be calculated as A = (Perimeter × a) / 2.
Can I use a comma instead of a decimal point?
Yes. This calculator accepts both a comma and a period as the decimal separator in the Side field.
See also…
