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Coin Rotation Paradox Calculator

Result

Calculated result 1 Based on the values entered.
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Coin Rotation Paradox Calculator Calculate how many times a rolling coin rotates as it moves around another coin of any radius — solving the famous coin rotation paradox. — free online calculator.

Formula

Absolute rotations = (r₁ + r₂) ÷ r₂; Relative = r₁ ÷ r₂
  • Coin Rotation Paradox Calculator calculates its result from Stationary Coin Radius, Rolling Coin Radius. It uses the formula Absolute rotations = (r₁ + r₂) ÷ r₂; Relative = r₁ ÷ r₂. Change any input to recalculate the result instantly.
  • The main inputs are Stationary Coin Radius, Rolling Coin Radius. Enter them in the units and format shown in the calculator.
  • Keep comparable quantities in compatible units whenever the formula combines or compares them.
  • Changing any input above recalculates the result with the same calculation engine used by this page.

Example: Coin Rotation Paradox

Inputs
  • Stationary Coin Radius: 25
  • Rolling Coin Radius: 25

Using Stationary Coin Radius = 25, Rolling Coin Radius = 25, the calculated result is 1.

Sample result: Calculating…

Frequently asked questions

What does the Coin Rotation Paradox calculate?

Coin Rotation Paradox Calculator Calculate how many times a rolling coin rotates as it moves around another coin of any radius — solving the famous coin rotation paradox. — free online calculator.

Which values should I enter?

Enter Stationary Coin Radius, Rolling Coin Radius using the units and format shown beside each field.

What formula does this calculator use?

The calculator uses the following relationship: Absolute rotations = (r₁ + r₂) ÷ r₂; Relative = r₁ ÷ r₂.

Why might my result differ from another source?

Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.

Does the result update automatically?

Yes. Changing an input updates the result using the same calculation engine shown on this page.

Page information

Updated: October 7, 2026