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Regular Pentagon Calculator — result sheet
Calculate the perimeter, apothem, circumradius, area, and interior angle of a regular pentagon from its side length.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: P = 5s; a = s/(2 tan(π/5)); R = s/(2 sin(π/5)); A = ½aP; each interior angle = 108°.
A regular pentagon has five equal sides and equal angles. The calculator makes the perimeter, apothem, circumradius, and area visible together, which helps a learner distinguish the distance to a side from the distance to a vertex.
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 1000000000000
Worked example
| Input | Value |
|---|---|
| Equal side length | 7 |
A regular pentagon with 7 length units per side has perimeter 35, apothem about 4.8173, circumradius about 5.9546, and area about 84.3034 square units.
Assumptions and limits
- The pentagon is regular: all five sides and all five interior angles are equal.
- The entered side length is positive and all outputs use the same length unit.
- The area is the flat two-dimensional area enclosed by the pentagon.
- This tool does not estimate material, cutting allowance, construction tolerance, or an irregular five-sided outline.
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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