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Bike Gear Ratio Calculator

Computes a bicycle gear's ratio, gear inches, metres of development and gain ratio from chainring and cog teeth and the wheel size (ISO rim diameter plus tyre width), and the speed that gear gives at a chosen cadence.

When to use

You want to compare gears or drivetrains (gear inches, development), or know how fast a given chainring/cog combination rolls at a cadence.

Do not use when: You already know the gear ratio and wheel circumference and only need speed (use cadence-to-speed), or you need engine or machine gearing rather than bicycle gearing.

Formula

wheel_diameter = rim_diameter_mm + 2 × tire_width_mm; gear_ratio = chainring_teeth / cog_teeth; gear_inches = wheel_diameter / 25.4 × gear_ratio; development_m = π × wheel_diameter / 1000 × gear_ratio; gain_ratio = (wheel_diameter / 2) / crank_length_mm × gear_ratio; speed_kmh = development_m × cadence_rpm × 60 / 1000

Wheel diameter from bead-seat diameter plus twice the nominal tyre width is the convention of Sheldon Brown's gear calculator; real rolling diameter differs by 1–2 % with tyre casing, pressure and load. Internally geared hubs would need their stage ratio applied to gear_ratio.

Inputs

ParameterTypeUnitRequiredDescription
chainring_teethintegerteethyesNumber of teeth on the front chainring. Range: ≥ 10, ≤ 90
cog_teethintegerteethyesNumber of teeth on the rear sprocket (cog). Range: ≥ 6, ≤ 60
rim_diameter_mmnumbermmdefault 622ISO 5775 bead-seat diameter: 622 for 700C / 29", 584 for 650B / 27.5", 559 for 26", 406 for 20" BMX. Range: ≥ 200, ≤ 700
tire_width_mmnumbermmdefault 25Nominal tyre width (e.g. 25 for 700×25C, 54 for 29×2.1"); wheel diameter = rim + 2 × tyre width. Range: ≥ 15, ≤ 130
cadence_rpmnumberrpmdefault 90Pedal revolutions per minute for the speed output. Range: ≥ 1, ≤ 250
crank_length_mmnumbermmdefault 170Crank arm length, used only for the gain ratio. Range: ≥ 100, ≤ 220

Outputs

OutputTypeUnitDescription
gear_rationumberchainring_teeth / cog_teeth: wheel revolutions per pedal revolution.
gear_inchesnumberinWheel diameter in inches × gear ratio (equivalent penny-farthing wheel diameter).
development_mnumbermDistance travelled per pedal revolution = π × wheel diameter × gear ratio.
gain_rationumberSheldon Brown's crank-independent measure: (wheel radius / crank length) × gear ratio.
wheel_diameter_mmnumbermmrim_diameter_mm + 2 × tire_width_mm.
wheel_circumference_mmnumbermmπ × wheel diameter (use as wheel_circumference_mm in cadence-to-speed).
speed_kmhnumberkm/hdevelopment_m × cadence_rpm × 60 / 1000.
speed_mphnumbermphSame speed in miles per hour.

Example

50 × 25 on 700×25C at 90 rpm: {"chainring_teeth":50,"cog_teeth":25,"rim_diameter_mm":622,"tire_width_mm":25,"cadence_rpm":90} → {"gear_ratio":2,"gear_inches":52.9,"development_m":4.222,"gain_ratio":3.953,"wheel_diameter_mm":672,"wheel_circumference_mm":2111,"speed_kmh":22.8,"speed_mph":14.17}

53 × 11 on 700×23C at 100 rpm: {"chainring_teeth":53,"cog_teeth":11,"tire_width_mm":23,"cadence_rpm":100} → {"gear_ratio":4.818,"gear_inches":126.7,"development_m":10.111,"gain_ratio":9.466,"speed_kmh":60.67,"speed_mph":37.7}

GET https://tttkmbb.com/api/v1/calculate/bike-gear-ratio?chainring_teeth=50&cog_teeth=25&rim_diameter_mm=622&tire_width_mm=25&cadence_rpm=90

Machine access

Sources

FAQ

What are typical gear-inch ranges?

Road bikes span roughly 30–130 gear inches; mountain bikes 18–100; a single-speed commuter is usually 65–75 gear inches.

Why gain ratio instead of gear inches?

Gear inches ignore crank length. Gain ratio (distance the bike moves per distance the pedal moves) compares bikes with different cranks fairly; a gain ratio of 4 means the bike travels 4 m per metre of pedal travel.

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