Calculator
This calculator supports direct side length, circumradius, apothem, and area methods for advanced regular polygon work.
Plotly Graph
The graph shows how perimeter changes with side count while keeping the computed side length constant.
Formula Used
Using side length: P = n × s
Using circumradius: P = 2nR sin(π/n)
Using apothem: P = 2na tan(π/n)
Using area: s = √(4A tan(π/n) / n), then P = n × s
Here, n is the number of sides, s is side length, R is circumradius, a is apothem, and A is area. These formulas work only for regular polygons because all sides and angles must be equal.
How to Use This Calculator
- Select the input method that matches your known value.
- Enter the number of sides for the regular polygon.
- Fill in the required measurement such as side length, radius, apothem, or area.
- Choose the number of decimal places for the output.
- Click Calculate Perimeter to view the result above the form.
- Use the CSV or PDF buttons to export your result summary.
Example Data Table
| Polygon | Sides (n) | Side Length | Perimeter | Formula |
|---|---|---|---|---|
| Equilateral Triangle | 3 | 8 cm | 24 cm | 3 × 8 |
| Square | 4 | 6 cm | 24 cm | 4 × 6 |
| Regular Pentagon | 5 | 7 cm | 35 cm | 5 × 7 |
| Regular Hexagon | 6 | 9 cm | 54 cm | 6 × 9 |
| Regular Octagon | 8 | 4.5 cm | 36 cm | 8 × 4.5 |
Frequently Asked Questions
1) What is the perimeter of a regular polygon?
It is the total distance around the polygon. Because a regular polygon has equal sides, perimeter equals the number of sides multiplied by one side length.
2) What makes a polygon regular?
A regular polygon has all sides equal and all interior angles equal. If either condition fails, these formulas no longer describe the shape correctly.
3) How do I calculate perimeter from side length?
Use P = n × s. Enter the number of sides and the side length. The calculator multiplies them and shows the full perimeter instantly.
4) Can I calculate perimeter from circumradius?
Yes. For a regular polygon, the side length comes from 2R sin(π/n). Then perimeter equals n times that side length.
5) Can the calculator use apothem instead?
Yes. It uses s = 2a tan(π/n), where a is the apothem. After finding side length, it multiplies by the number of sides.
6) Can perimeter be found from area?
Yes, for regular polygons. The calculator rearranges the area formula to get side length first, then uses perimeter equals side length times side count.
7) Why does the number of sides matter so much?
The same side length creates different perimeters when the side count changes. More sides mean more repeated lengths added into the total boundary.
8) Which units should I enter?
Use any consistent unit, such as centimeters, meters, feet, or inches. The result keeps the same unit label you provide in the form.