Decagon Calculator

Regular decagon calculator to find area, perimeter, side length, inradius (apothem) and circumradius. Enter any one value — side, perimeter, area, inradius or circumradius — and get all the others.

Known value

The calculator converts your input to meters for internal math and then back to your chosen unit for each result.

How to Use This Calculator

Choose the measure you already know (side, perimeter, area, inradius or circumradius), enter its value, and pick a unit. The tool converts the entry into meters for the math engine and imputes every other length or area automatically.

Supported units: millimeters, centimeters, meters, inches, and feet.

Methodology

The calculator relies on the regular decagon geometry formulas. It uses the golden-ratio-related constants (tan(π/10) and sin(π/10)) to convert between side length, perimeter, area, inradius, and circumradius while keeping every result in sync with your chosen unit.

  • Input is normalized to meters (or square meters for area) for consistent internal math.
  • Every output is converted back to your preferred unit with six decimal precision, trimming redundant zeros.
  • The computation steps panel and downloadable CSV capture how each value was derived.
Results follow standard strict geometry formulas. Use them as estimates and verify with official references if you need verified engineering precision.

FAQ

Does this work for irregular decagons?
No. Irregular decagons need side-by-side coordinates or each side length, and this tool assumes regular polygons only.
Can I enter the circumradius?
Yes. Select the circumradius option and provide the length. The calculator derives the side using s = 2 R sin(π/10).

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About this calculator

Author: CalcDomain Geometry Desk
Reviewed: 6 November 2025
Category: Math & Conversions → Geometry / Polygons

Formulas

Perimeter: P = 10s

Area: A = (5/2) s² √(5 + 2√5) ≈ 7.69420884 s²

Inradius (apothem): r = s / (2 tan(π/10))

Circumradius: R = s / (2 sin(π/10)) ≈ 1.618 s

Citations
Changelog
  • 0.1.0-draft — 2026-01-19: Initial audit spec draft. Review required.
  • Verified formulas, sources, and layout for the regular decagon calculator.
Verified by Ugo Candido Last Updated: 2026-01-19 Version 0.1.0-draft
Version 1.5.0