Calculator Input
Example Data Table
| Polygon | Sides | Known Input | Input Value | Perimeter |
|---|---|---|---|---|
| Pentagon | 5 | Side Length | 8 cm | 40 cm |
| Hexagon | 6 | Circumradius | 10 cm | 60 cm |
| Octagon | 8 | Apothem | 12 cm | 79.53 cm |
| Decagon | 10 | Area | 500 cm² | 80.61 cm |
Formula Used
For a regular polygon with n sides, every side and angle is equal. The calculator supports several direct perimeter routes.
- From side length: P = n × s
- From circumradius: P = 2nR sin(π/n)
- From apothem: P = 2na tan(π/n)
- From area: P = √(4An tan(π/n))
- Supporting area relation: A = ½aP
- Interior angle: ((n - 2) × 180) / n
- Exterior angle: 360 / n
- Diagonal count: n(n - 3) / 2
How to Use This Calculator
- Enter the number of sides for the regular polygon.
- Select the measurement you already know.
- Provide side length, circumradius, apothem, or area.
- Set your preferred unit label and decimal precision.
- Choose the graph limit to compare side-count changes.
- Press Calculate Perimeter to view results above the form.
- Download the result summary as CSV or PDF.
FAQs
1. What makes a polygon regular?
A regular polygon has equal side lengths and equal interior angles. Because of that symmetry, one known measurement can determine many other geometric properties accurately.
2. Can I calculate perimeter without side length?
Yes. This tool can derive perimeter from circumradius, apothem, or area, provided the polygon remains regular and the number of sides is known.
3. What is the circumradius?
The circumradius is the distance from the polygon center to any vertex. It is useful when the shape is inscribed inside a circle.
4. What is the apothem?
The apothem is the perpendicular distance from the polygon center to any side. It is often used in area and perimeter formulas for regular polygons.
5. Why does the graph change with side count?
The graph keeps your chosen input fixed and recalculates perimeter for different numbers of sides. This helps compare how shape complexity affects the boundary length.
6. Does this work for irregular polygons?
No. Irregular polygons do not have equal sides and equal angles, so these formulas no longer apply. Use direct side-by-side addition for irregular shapes.
7. What units should I use?
Use any consistent unit such as mm, cm, m, ft, or in. Area inputs should match squared versions of the same chosen unit.
8. Why is area shown in the results?
Area is a useful supporting property. Once the calculator finds side length and apothem, it can compute area and provide a fuller geometric summary.