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Circumscribed Circle of a Regular Polygon Calculator — result sheet
Calculate the circumradius, diameter, and apothem of a regular polygon from its side length and side count.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Circumradius R=s/(2sin(π/n)); apothem a=s/(2tan(π/n)); diameter=2R.
Joining the polygon center to two adjacent vertices creates an isosceles triangle. Bisecting that triangle gives the sine and tangent relations used for the circumscribed circle and apothem.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Side length — length units; minimum 1.0E-6; maximum 1000000000
- Number of sides — minimum 3; maximum 100000
Worked example
| Input | Value |
|---|---|
| Side length | 2 |
| Number of sides | 6 |
Circumradius =2; apothem ≈1.7321; diameter =4.
Assumptions and limits
- The polygon is regular with n whole sides and equal positive side lengths.
- All lengths use one consistent unit.
- The result describes the ideal circumcircle and does not model a distorted or irregular polygon.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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