Calculator
Example data table
| Polygon | n | Known | Value | Perimeter (P) | Area (A) |
|---|---|---|---|---|---|
| Equilateral triangle | 3 | Side (s) | 5 | 15 | 10.825 |
| Square | 4 | Side (s) | 8 | 32 | 64 |
| Regular hexagon | 6 | Circumradius (R) | 10 | 60 | 259.808 |
| Regular decagon | 10 | Perimeter (P) | 100 | 100 | 769.421 |
Formula used
- θ = π/n (half central angle, radians)
- s = 2R·sin(π/n)
- s = 2a·tan(π/n)
- P = n·s
- A = (P·a)/2 = n·s² / (4·tan(π/n))
- Interior angle = (n−2)·180/n
- Exterior angle = 360/n
- Central angle = 360/n
- Diagonal: dk = 2R·sin(kπ/n), k ≥ 2
How to use this calculator
- Enter the number of sides n.
- Select what you already know: side, perimeter, radius, apothem, or area.
- Type the value using your preferred units.
- Press Submit to view full results above the form.
- Use Download CSV or Download PDF for saving.
FAQs
1) What is a regular polygon?
A regular polygon has all sides equal and all interior angles equal. Common examples include equilateral triangles, squares, and regular hexagons.
2) Which input should I choose?
Choose the value you trust most: side length, perimeter, circumradius, apothem, or area. The calculator derives the side length first, then computes everything else.
3) What is the apothem?
The apothem is the distance from the center to the midpoint of any side. It is also the inradius, which is the radius of the inscribed circle.
4) What is the circumradius?
The circumradius is the distance from the center to any vertex. It is the radius of the circle passing through all polygon vertices.
5) Why do I see multiple diagonal lengths?
In many regular polygons, diagonals come in distinct lengths depending on how many vertices you skip. The table lists unique lengths using step k.
6) Can I use decimals and units?
Yes. Use decimals like 12.5, and keep units consistent. If the input is in centimeters, perimeter is centimeters and area is square centimeters.
7) Are the results exact?
Calculations use trigonometric formulas and are shown with trimmed decimals. For very large n, rounding and floating-point limits can slightly affect precision.
Tip: Save downloads after calculating at least one result.