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Rolling Coin Rotation Paradox Calculator — result sheet
Compare center travel and spin counts for a coin rolling around the outside or inside of a fixed circle.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Outside path=2π(R+r), outside turns=(R+r)/r; inside path=2π(R−r), inside turns=(R−r)/r when R≥r.
The page distinguishes distance traveled by the coin center from the coin’s own spin count, which prevents the familiar rolling-circle confusion.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Moving coin radius — minimum 1.0E-6; maximum 1000000000
- Fixed circle radius — minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Moving coin radius | 1 |
| Fixed circle radius | 5 |
Outside center path ≈37.699; outside turns =6; inside path ≈25.133; inside turns =4.
Assumptions and limits
- The coin rolls without slipping and radii use one unit.
- The outside case is external rolling; the inside case requires fixed radius at least as large as the moving radius.
- Deformation, thickness, slip, and three-dimensional contact are not modeled.
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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