Free · Cycling calculators 🚴‍♀️

Bicycle Gearing and Cadence Speed

Estimate rolling speed from rim diameter, tire height, tooth counts and cadence, or solve a missing gearing quantity.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A 622 mm rim with tire radial height 25 mm, 50-tooth chainring, 20-tooth rear cog and cadence 90 RPM gives modeled rolling speed approximately 28.500529 km/h.

Speed = π(rim diameter + 2 × tire radial height) × (front teeth/rear teeth) × crank revolutions per second.

Worked example

Enter these known values and leave the other values blank.

Rim bead-seat diameter
622 mm
Modeled tire radial height
25 mm
Front chainring teeth
50 teeth
Rear sprocket teeth
20 teeth
Crank cadence
90 RPM
Front-to-rear tooth ratio
2.5 :1
Modeled rolling speed
28.5 km/h

Assumptions and limitations

  • This is rolling geometry for a direct chain drive without additional internal hub or planetary gearing. The tooth ratio counts rear-wheel revolutions per crank revolution.
  • Tire radial height is added on both sides of the rim diameter. A tire’s printed width need not equal its radial height; measured rollout is preferable for calibration.
  • Use bead-seat rim diameter, not a nominal marketing wheel-size label or complete tire outside diameter. Entering full outside diameter and adding the tire again overstates circumference.
  • Cadence is crank revolutions per minute. The local internal frequency is revolutions per second. Speed units preserve that conversion.
  • Front and rear tooth counts must be positive exact integers from 1 to 1,000,000. Other quantities must be positive. Tooth counts are discrete gearing choices, not continuous measurements.
  • The result assumes continuous pedaling and no wheel slip. It does not calculate required power, air resistance, grade, wind, tire deformation or coasting speed.
  • All seven controls and the captured inverse graph remain available. Gear ratio alone does not identify unique tooth counts; supply one tooth count to determine the other.
  • Only inferred tooth counts are recovered to the nearest integer when the arithmetic remainder is at most 10⁻⁵⁰ teeth. This narrow numerical rule does not round ordinary fractional gearing choices or provide a measurement-uncertainty allowance. Manually entered fractional teeth are rejected.

Common questions

Should I enter tire width?

The formula needs modeled radial tire height. Printed width can be an approximation but is not always the same dimension.

Does this predict my speed uphill?

No. It relates rolling geometry to a supplied cadence; it does not predict whether that cadence is achievable.

Why can an inverse tooth count be rejected?

A real sprocket needs a positive whole-number tooth count. Fractional inverse results are not a buildable gearing choice.

Why can an inferred whole tooth count be recovered?

Finite-precision arithmetic through circumference and speed can leave an extremely small remainder. The local inverse recovers the integer only within 10⁻⁵⁰ teeth; larger fractions remain invalid.

References

Preserve the rolling-speed and gear-ratio relationships, but recover an inferred whole tooth count when its computed value differs from the nearest integer by at most 10⁻⁵⁰ teeth. This repairs finite-precision residuals from the captured inverse graph. Larger fractional inverse results remain fractional and invalid; manually entered tooth counts still require exact integers. Use exact-sign positive tests for rim diameter, modeled tire radial height, speed, cadence and gear ratio. Tooth counts must be exact positive integers from 1 to 1,000,000; fractional manual values and inverse results outside the stated residual tolerance are rejected.

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