Reviewed by CalcMulti Editorial Team·Last updated: ·← Geometry Hub
A regular polygon has all sides equal and all interior angles equal. The area formula for a regular polygon with n sides of length s is: A = (n × s²) / (4 × tan(π/n)). Equivalently, if you know the circumradius R: A = ½nR²sin(2π/n).
The apothem a (perpendicular distance from center to the midpoint of a side) is related to side length by: a = s / (2 × tan(π/n)). The area can also be written as A = ½ × perimeter × apothem.
This calculator handles all regular polygons from triangles (3 sides) to dodecagons (12 sides). Enter the side length, circumradius (corner-to-center), or apothem (center-to-side).
A = (n × s²) / (4 × tan(π/n))
| Shape | Sides | Interior Angle | Area (s=1) |
|---|---|---|---|
| Triangle | 3 | 60.00° | 0.4330 |
| Square | 4 | 90.00° | 1.0000 |
| Pentagon | 5 | 108.00° | 1.7205 |
| Hexagon | 6 | 120.00° | 2.5981 |
| Heptagon | 7 | 128.57° | 3.6339 |
| Octagon | 8 | 135.00° | 4.8284 |
| Nonagon | 9 | 140.00° | 6.1818 |
| Decagon | 10 | 144.00° | 7.6942 |
| Dodecagon | 12 | 150.00° | 11.1962 |
½bh — equilateral, scalene, all types
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Surface Area Calculator3D prisms and pyramids built on polygons
Right Triangle CalculatorPythagorean theorem + all angles
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.