Regular Polygon Calculator (Hexagon, Octagon…)
Regular polygon calculator: area, perimeter, apothem, circumradius and interior angle of a hexagon, octagon or any n-sided regular polygon.
A = n · s²4 · tan(π/n)
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
Area = n s² ÷ (4 tan(π/n)). Each interior angle is (n − 2) × 180° ÷ n: 120° for a hexagon, 135° for an octagon.
Formula
A = n · s²4 · tan(π/n)
| Symbol | Quantity | Units |
|---|---|---|
| n | Number of sides | — |
| s | Side length | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| A | Area | m², km², cm², mm², ha, ft², in², yd², ac, mi² |
Worked example
Given: n = 6 · s = 10 cm
A = n s²4 tan(π/n)
Result: A = 259.808 cm²
Area for different values of Number of sides
| n · Number of sides | A · Area |
|---|---|
| 3 | 43.301 cm² |
| 4.5 | 134.07 cm² |
| 5.4 | 205.26 cm² |
| 6 | 259.81 cm² |
| 6.6 | 320.06 cm² |
| 7.5 | 421.13 cm² |
| 9 | 618.18 cm² |
| 12 | 1 119.6 cm² |
Other values as in the worked example.
Frequently asked questions
Area of a regular hexagon with 10 cm sides?
About 259.8 cm².
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