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Regular Octagon Calculator — result sheet
Calculate the perimeter, apothem, circumradius, area, and interior angle of a regular octagon from its side length.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: P = 8s; a = s/(2 tan(π/8)); R = s/(2 sin(π/8)); A = ½aP = 2(1+√2)s²; each interior angle = 135°.
A regular octagon has eight equal sides and angles. The apothem-based area calculation is shown alongside the side-based closed form so a visitor can follow the geometry and reuse the result in a surface-area or layout problem.
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 | 13 |
A regular octagon with 13 length units per side has perimeter 104, apothem about 15.6924, circumradius about 16.9853, and area about 816.0042 square units.
Assumptions and limits
- The octagon is regular: all eight sides and all eight 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 octagon.
- This tool does not estimate material, cutting allowance, construction tolerance, or an irregular eight-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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