Calculator Form
Choose one known property, enter the polygon side count, and solve the matching side length instantly.
Example Data Table
| Method | Sides (n) | Input | Side Length |
|---|---|---|---|
| Perimeter | 6 | P = 48 units | 8.0000 units |
| Circumradius | 6 | R = 10 units | 10.0000 units |
| Apothem | 6 | a = 8.6603 units | 10.0000 units |
| Area | 4 | A = 25 square units | 5.0000 units |
| Chord | 8 | d = 10 units, k = 2 | 5.4119 units |
Formula Used
From perimeter: s = P / n
From circumradius: s = 2R sin(π / n)
From apothem: s = 2a tan(π / n)
From area: s = √[4A tan(π / n) / n]
From chord step k: s = d × sin(π / n) / sin(kπ / n)
Useful derived formulas
- Perimeter: P = ns
- Circumradius: R = s / [2 sin(π / n)]
- Apothem: a = s / [2 tan(π / n)]
- Area: A = ns² / [4 tan(π / n)]
- Interior angle: ((n − 2) × 180) / n
How to Use This Calculator
- Enter the number of sides for your regular polygon.
- Choose the property you already know, such as perimeter or area.
- Type the matching input value and adjust decimals or unit label.
- Press the calculate button to show the side length above the form.
- Review the summary table, graph, and steps, then export to CSV or PDF.
FAQs
1. What makes a regular polygon different?
A regular polygon has equal side lengths and equal interior angles. Because of that symmetry, one side length can determine many other measurements, including perimeter, area, apothem, and circumradius.
2. Can I solve the side using area?
Yes. The calculator rearranges the regular polygon area formula so the side length becomes the unknown. This is useful when only area and side count are available.
3. What is the apothem in this calculator?
The apothem is the perpendicular distance from the center of the polygon to the midpoint of any side. It helps connect area, radius, and side length neatly.
4. Why does the chord option need a step value?
Different chords connect vertices separated by different numbers of sides. The step value tells the calculator which chord is known, so it can scale that length back to a single side.
5. Does this work for a triangle and square?
Yes. Any regular polygon with at least three sides is supported. That includes equilateral triangles, squares, pentagons, hexagons, and larger regular n-gons.
6. What units should I use?
Use any consistent unit, such as millimeters, meters, inches, or feet. Area inputs should match that unit squared, and all derived results will remain consistent.
7. Why is the graph useful?
The graph shows how the solved side length changes as the selected known input changes while the number of sides stays fixed. It helps visualize sensitivity and scaling.
8. Can I export the result for reports?
Yes. After a calculation, use the CSV button for spreadsheet work or the PDF button for a cleaner report. Both exports capture the computed summary.