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Regular Dodecagon Area and Geometry — result sheet
Calculate the area, perimeter, apothem, circumradius, and interior angle of a regular dodecagon from its side length.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For n = 12, perimeter P = 12s; apothem a = s/(2 tan(π/12)); area A = ½aP; circumradius R = s/(2 sin(π/12)); each interior angle = 150°.
A regular dodecagon has twelve equal sides and twelve equal interior angles. The calculator derives the apothem and uses the center-triangle decomposition to report the area, while keeping perimeter and radius outputs separate so they are not confused with area.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Equal side length — length units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Equal side length | 4 |
Area ≈179.1384 square units; perimeter =48; apothem ≈7.4641; circumradius ≈7.7274; interior angle =150°.
Assumptions and limits
- The dodecagon is regular and convex.
- The side length is positive and all length inputs use one consistent unit.
- The geometry is planar and Euclidean.
- Area is expressed in square length units.
- The result does not model an irregular twelve-sided boundary or rounded corners.
- The circumradius runs from the center to a vertex and the apothem is perpendicular to a side.
- Rounding affects display only.
- Use measured vertex coordinates instead when the real shape is not regular.
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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