What is a regular polygon?
A polygon with all sides equal and all interior angles equal.
Polygon Calculator
Work with regular polygons: equal sides and equal interior angles.
Enter n and side length
Provide the number of sides (n ≥ 3) and the side length s > 0.
About this calculator
How to use Polygon Calculator, plus the formulas and logic behind the results.
Tool description
A regular n-gon can be split into n congruent isosceles triangles from the center. Area and perimeter have closed forms in n and s.
How to use
- Enter an integer n ≥ 3.
- Enter a positive side length.
- Select Calculate.
- Review perimeter, area, and apothem.
Formulas & reference
P = n sA = (n s²) / (4 tan(π/n))Apothem = s / (2 tan(π/n))
Polygon examples
- n=3 equilateral triangle
- n=4 square
- n=6 regular hexagon
- As n grows, shape approaches a circle
Calculation logic
Uses M_PI in the tangent expressions for a regular polygon.
n is interpreted as an integer ≥ 3.
Polygon Calculator FAQ
Common questions about this calculator and how to use the results.
How do you find perimeter?
Multiply n by the side length s.
How do you find area?
A = (n s²)/(4 tan(π/n)).
What is the apothem?
The distance from center to the midpoint of a side.
Can n be 2?
No. A polygon needs at least 3 sides.
Are irregular polygons supported?
Not in this tool—sides must be equal.