{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"bike-gear-ratio"},"result":{"entity_type":"calculator","id":"bike-gear-ratio","calculator_id":"bike-gear-ratio","canonical_url":"https://tttkmbb.com/fitness/bike-gear-ratio","name":"Bike Gear Ratio Calculator","title":"Bike Gear Ratio Calculator – Gear Inches, Development, Gain Ratio and Speed at Cadence","category":"fitness","category_name":"Sports & Fitness","tool_name":"calculate_bike_gear_ratio","featured_mcp_tool":false,"description":"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.","use_when":"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.","inputs":[{"name":"chainring_teeth","label":"Chainring teeth","type":"integer","unit":"teeth","required":true,"min":10,"max":90,"description":"Number of teeth on the front chainring.","example":50},{"name":"cog_teeth","label":"Rear cog teeth","type":"integer","unit":"teeth","required":true,"min":6,"max":60,"description":"Number of teeth on the rear sprocket (cog).","example":25},{"name":"rim_diameter_mm","label":"Rim bead-seat diameter","type":"number","unit":"mm","required":false,"default":622,"min":200,"max":700,"description":"ISO 5775 bead-seat diameter: 622 for 700C / 29\", 584 for 650B / 27.5\", 559 for 26\", 406 for 20\" BMX.","example":622},{"name":"tire_width_mm","label":"Tyre width","type":"number","unit":"mm","required":false,"default":25,"min":15,"max":130,"description":"Nominal tyre width (e.g. 25 for 700×25C, 54 for 29×2.1\"); wheel diameter = rim + 2 × tyre width.","example":25},{"name":"cadence_rpm","label":"Cadence","type":"number","unit":"rpm","required":false,"default":90,"min":1,"max":250,"description":"Pedal revolutions per minute for the speed output.","example":90},{"name":"crank_length_mm","label":"Crank length","type":"number","unit":"mm","required":false,"default":170,"min":100,"max":220,"description":"Crank arm length, used only for the gain ratio.","example":170}],"outputs":[{"name":"gear_ratio","label":"Gear ratio","type":"number","decimals":3,"description":"chainring_teeth / cog_teeth: wheel revolutions per pedal revolution."},{"name":"gear_inches","label":"Gear inches","type":"number","unit":"in","decimals":1,"description":"Wheel diameter in inches × gear ratio (equivalent penny-farthing wheel diameter)."},{"name":"development_m","label":"Development","type":"number","unit":"m","decimals":3,"description":"Distance travelled per pedal revolution = π × wheel diameter × gear ratio."},{"name":"gain_ratio","label":"Gain ratio","type":"number","decimals":3,"description":"Sheldon Brown's crank-independent measure: (wheel radius / crank length) × gear ratio."},{"name":"wheel_diameter_mm","label":"Wheel diameter","type":"number","unit":"mm","decimals":0,"description":"rim_diameter_mm + 2 × tire_width_mm."},{"name":"wheel_circumference_mm","label":"Wheel circumference","type":"number","unit":"mm","decimals":0,"description":"π × wheel diameter (use as wheel_circumference_mm in cadence-to-speed)."},{"name":"speed_kmh","label":"Speed at cadence","type":"number","unit":"km/h","decimals":2,"description":"development_m × cadence_rpm × 60 / 1000."},{"name":"speed_mph","label":"Speed at cadence","type":"number","unit":"mph","decimals":2,"description":"Same speed in miles per hour."}],"input_schema":{"type":"object","properties":{"chainring_teeth":{"description":"Number of teeth on the front chainring. Unit: teeth.","type":"integer","minimum":10,"maximum":90,"examples":[50],"x-unit":"teeth"},"cog_teeth":{"description":"Number of teeth on the rear sprocket (cog). Unit: teeth.","type":"integer","minimum":6,"maximum":60,"examples":[25],"x-unit":"teeth"},"rim_diameter_mm":{"description":"ISO 5775 bead-seat diameter: 622 for 700C / 29\", 584 for 650B / 27.5\", 559 for 26\", 406 for 20\" BMX. Unit: mm.","type":"number","minimum":200,"maximum":700,"default":622,"examples":[622],"x-unit":"mm"},"tire_width_mm":{"description":"Nominal tyre width (e.g. 25 for 700×25C, 54 for 29×2.1\"); wheel diameter = rim + 2 × tyre width. Unit: mm.","type":"number","minimum":15,"maximum":130,"default":25,"examples":[25],"x-unit":"mm"},"cadence_rpm":{"description":"Pedal revolutions per minute for the speed output. Unit: rpm.","type":"number","minimum":1,"maximum":250,"default":90,"examples":[90],"x-unit":"rpm"},"crank_length_mm":{"description":"Crank arm length, used only for the gain ratio. Unit: mm.","type":"number","minimum":100,"maximum":220,"default":170,"examples":[170],"x-unit":"mm"}},"additionalProperties":false,"required":["chainring_teeth","cog_teeth"]},"output_schema":{"type":"object","properties":{"gear_ratio":{"description":"chainring_teeth / cog_teeth: wheel revolutions per pedal revolution.","type":"number"},"gear_inches":{"description":"Wheel diameter in inches × gear ratio (equivalent penny-farthing wheel diameter). Unit: in.","type":"number","x-unit":"in"},"development_m":{"description":"Distance travelled per pedal revolution = π × wheel diameter × gear ratio. Unit: m.","type":"number","x-unit":"m"},"gain_ratio":{"description":"Sheldon Brown's crank-independent measure: (wheel radius / crank length) × gear ratio.","type":"number"},"wheel_diameter_mm":{"description":"rim_diameter_mm + 2 × tire_width_mm. Unit: mm.","type":"number","x-unit":"mm"},"wheel_circumference_mm":{"description":"π × wheel diameter (use as wheel_circumference_mm in cadence-to-speed). Unit: mm.","type":"number","x-unit":"mm"},"speed_kmh":{"description":"development_m × cadence_rpm × 60 / 1000. Unit: km/h.","type":"number","x-unit":"km/h"},"speed_mph":{"description":"Same speed in miles per hour. Unit: mph.","type":"number","x-unit":"mph"}}},"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","method":"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.","sources":[{"name":"Sheldon Brown – Bicycle Gear Calculator (gear inches, metres of development, gain ratio)","url":"https://www.sheldonbrown.com/gear-calc.html","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – ISO 5775 tyre and rim designations (bead seat 622 mm = 700C/29\", 584 mm = 650B/27.5\", 559 mm = 26\")","url":"https://en.wikipedia.org/wiki/ISO_5775","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"50 × 25 on 700×25C at 90 rpm","inputs":{"chainring_teeth":50,"cog_teeth":25,"rim_diameter_mm":622,"tire_width_mm":25,"cadence_rpm":90},"expected":{"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},"url":"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"},{"name":"53 × 11 on 700×23C at 100 rpm","inputs":{"chainring_teeth":53,"cog_teeth":11,"tire_width_mm":23,"cadence_rpm":100},"expected":{"gear_ratio":4.818,"gear_inches":126.7,"development_m":10.111,"gain_ratio":9.466,"speed_kmh":60.67,"speed_mph":37.7},"url":"https://tttkmbb.com/api/v1/calculate/bike-gear-ratio?chainring_teeth=53&cog_teeth=11&tire_width_mm=23&cadence_rpm=100"}],"faq":[{"q":"What are typical gear-inch ranges?","a":"Road bikes span roughly 30–130 gear inches; mountain bikes 18–100; a single-speed commuter is usually 65–75 gear inches."},{"q":"Why gain ratio instead of gear inches?","a":"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."}],"tags":["gear ratio","gear inches","bike gearing","development","gain ratio","chainring cog"],"related":[{"calculator_id":"cadence-to-speed","reason":"Speed from cadence when the ratio and wheel circumference are already known."},{"calculator_id":"ftp-power-zones","reason":"Power targets to pair with gearing choices."},{"calculator_id":"speed","reason":"Convert the resulting speed to other units."}],"links":{"html":"https://tttkmbb.com/fitness/bike-gear-ratio","markdown":"https://tttkmbb.com/fitness/bike-gear-ratio.md","json":"https://tttkmbb.com/fitness/bike-gear-ratio.json","api":"https://tttkmbb.com/api/v1/calculate/bike-gear-ratio","schema":"https://tttkmbb.com/api/v1/calculators/bike-gear-ratio","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:54:13Z"}