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Regular Polygon Calculator — result sheet
Calculate the perimeter, apothem, interior angle, and area of a regular polygon from its side count and side length.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: perimeter = ns; apothem = s/(2 tan(π/n)); area = perimeter × apothem/2; interior angle = 180°(n-2)/n.
A regular polygon has equal sides and equal angles. Its center-to-side apothem splits the shape into congruent triangles, making the area one half of perimeter times apothem.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Number of sides n — minimum 3; maximum 100000
- Side length — units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Number of sides n | 6 |
| Side length | 4 |
Perimeter: 24 units; apothem: 3.464 units; area: 41.57 square units; interior angle: 120°.
Assumptions and limits
- The polygon is convex, regular, and has at least three whole-number sides.
- The side length is measured along each edge and all dimensions use the same unit.
- The area and perimeter describe the ideal boundary; wall thickness and corner rounding are excluded.
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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