Enrichment · Passion Projects · Cycling

What each gear
does with one turn
of the pedals.

Choose the wheel and list the chainring and cog teeth. The calculator gives each gear's ratio, gear inches, distance per pedal turn and speed at your cadence.

Compare gearsWhat you get

The gear calculator

The worked example is a made-up road bike with 50 and 34 tooth chainrings and an 11 to 32 cassette. Nothing you type leaves this browser.

Loading the calculator. If nothing appears, turn on JavaScript.

What you get

Enrichment · Passion ProjectsFree

What you finish with
Ratio, gear inches, development and speed for each gear, with the hardest and easiest gears and the range. It prints as a summary and downloads as a spreadsheet.
Who it is for
Students who ride, physics and engineering classes studying gears and rotation, and bike clubs.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Up to 40 gears. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
Free. No account, no sign-in and nothing to install. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The Passion Projects space in Caveat Enrichment.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Choose the wheel size and type the tyre width.
  2. Set a comfortable cadence (80 to 95 rpm is common).
  3. Add each gear with its chainring and cog teeth.
  4. Read the gear inches and speeds.
  5. Print the table to plan a gearing change.

Compare gears

How the gears are compared

Teeth, wheel size and cadence.

The worked example: top gearRatio4.5550 ÷ 11 teethWheel678 mm622 + 2 × 28Gear inches121.34.545 × 26.69 inAt 90 rpm52.3 km/h9.68 m × 90 × 60The worked example: top gearRatio4.5550 ÷ 11 teethWheel678 mm622 + 2 × 28Gear inches121.34.545 × 26.69 inAt 90 rpm52.3 km/h9.68 m × 90 × 60
One turn of the pedals turns the cog, and the wheel, ratio times. A bigger wheel or a smaller cog goes further for each turn and is harder to push.

The arithmetic

The ratio is chainring teeth over cog teeth: how many times the rear wheel turns for each pedal turn. Gear inches multiply the ratio by the wheel diameter in inches, a number from the high-wheel era that still compares bikes with different wheels. Development multiplies the ratio by the wheel's circumference, the metres moved per pedal turn; times cadence it gives speed.

The wheel

The tyre's ISO size, such as 28-622, gives its width and the bead seat diameter of the rim in millimetres. The outside diameter is close to the bead seat diameter plus twice the width. Tyre pressure and load change it a little, so speeds are close estimates.

Sources

  1. International Organization for Standardization. ISO 5775-1, Bicycle tyres and rims: tyre designations and dimensions (iso.org).
  2. Brown, S. Gear inches and gain ratios, Sheldon Brown's bicycle technical information (sheldonbrown.com).
  3. National Institute of Standards and Technology. Handbook 44, appendix C: 1 inch = 25.4 mm (nist.gov).
  4. OpenStax. Physics, chapter on rotational motion: angular and linear speed (openstax.org).

The worked example is made up. Your gears stay in this browser. Support: team@caveatacademic.com.