{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"cadence-to-speed"},"result":{"entity_type":"calculator","id":"cadence-to-speed","calculator_id":"cadence-to-speed","canonical_url":"https://tttkmbb.com/fitness/cadence-to-speed","name":"Cadence to Speed Calculator","title":"Cycling Cadence to Speed Calculator – km/h and mph from RPM, Gear Ratio and Wheel Circumference","category":"fitness","category_name":"Sports & Fitness","tool_name":"convert_cadence_to_speed","featured_mcp_tool":false,"description":"Converts pedalling cadence into road speed from the gear ratio (or chainring and cog teeth) and the wheel circumference, giving km/h, mph, m/s, metres per pedal revolution and wheel rpm.","use_when":"You want the speed a given cadence produces in a known gear, e.g. to plan cadence targets on a trainer or check a bike computer's wheel-size setting.","do_not_use_when":"You need to derive the gear ratio and wheel size from teeth counts and tyre dimensions first (use bike-gear-ratio), or you want running pace conversions (use pace-converter).","inputs":[{"name":"cadence_rpm","label":"Cadence","type":"number","unit":"rpm","required":true,"min":1,"max":250,"description":"Pedal revolutions per minute.","example":90},{"name":"gear_ratio","label":"Gear ratio","type":"number","required":false,"max":15,"exclusive_min":0,"description":"Chainring teeth divided by cog teeth (wheel turns per crank turn). Give this or chainring_teeth and cog_teeth.","example":2},{"name":"chainring_teeth","label":"Chainring teeth","type":"integer","unit":"teeth","required":false,"min":10,"max":90,"description":"Front chainring teeth, used with cog_teeth when gear_ratio is not given.","example":50},{"name":"cog_teeth","label":"Rear cog teeth","type":"integer","unit":"teeth","required":false,"min":6,"max":60,"description":"Rear sprocket teeth, used with chainring_teeth when gear_ratio is not given.","example":25},{"name":"wheel_circumference_mm","label":"Wheel circumference","type":"number","unit":"mm","required":false,"default":2111,"min":500,"max":3000,"description":"Rolling circumference of the wheel with tyre: about 2111 mm for 700×25C, 2096 for 700×23C, 2288 for 29×2.1\", 2055 for 26×2.0\".","example":2111}],"outputs":[{"name":"speed_kmh","label":"Speed","type":"number","unit":"km/h","decimals":2,"description":"cadence × gear ratio × circumference."},{"name":"speed_mph","label":"Speed","type":"number","unit":"mph","decimals":2,"description":"Same speed in miles per hour."},{"name":"speed_m_per_s","label":"Speed","type":"number","unit":"m/s","decimals":3,"description":"Same speed in metres per second."},{"name":"development_m","label":"Distance per pedal revolution","type":"number","unit":"m","decimals":3,"description":"gear_ratio × wheel_circumference_mm / 1000."},{"name":"wheel_rpm","label":"Wheel rpm","type":"number","unit":"rpm","decimals":1,"description":"cadence_rpm × gear_ratio."},{"name":"gear_ratio_used","label":"Gear ratio used","type":"number","decimals":3,"description":"Ratio applied (given directly or chainring_teeth / cog_teeth)."}],"input_schema":{"type":"object","properties":{"cadence_rpm":{"description":"Pedal revolutions per minute. Unit: rpm.","type":"number","minimum":1,"maximum":250,"examples":[90],"x-unit":"rpm"},"gear_ratio":{"description":"Chainring teeth divided by cog teeth (wheel turns per crank turn). Give this or chainring_teeth and cog_teeth.","type":"number","maximum":15,"exclusiveMinimum":0,"examples":[2]},"chainring_teeth":{"description":"Front chainring teeth, used with cog_teeth when gear_ratio is not given. Unit: teeth.","type":"integer","minimum":10,"maximum":90,"examples":[50],"x-unit":"teeth"},"cog_teeth":{"description":"Rear sprocket teeth, used with chainring_teeth when gear_ratio is not given. Unit: teeth.","type":"integer","minimum":6,"maximum":60,"examples":[25],"x-unit":"teeth"},"wheel_circumference_mm":{"description":"Rolling circumference of the wheel with tyre: about 2111 mm for 700×25C, 2096 for 700×23C, 2288 for 29×2.1\", 2055 for 26×2.0\". Unit: mm.","type":"number","minimum":500,"maximum":3000,"default":2111,"examples":[2111],"x-unit":"mm"}},"additionalProperties":false,"required":["cadence_rpm"]},"output_schema":{"type":"object","properties":{"speed_kmh":{"description":"cadence × gear ratio × circumference. 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"},"speed_m_per_s":{"description":"Same speed in metres per second. Unit: m/s.","type":"number","x-unit":"m/s"},"development_m":{"description":"gear_ratio × wheel_circumference_mm / 1000. Unit: m.","type":"number","x-unit":"m"},"wheel_rpm":{"description":"cadence_rpm × gear_ratio. Unit: rpm.","type":"number","x-unit":"rpm"},"gear_ratio_used":{"description":"Ratio applied (given directly or chainring_teeth / cog_teeth).","type":"number"}}},"formula":"gear_ratio = chainring_teeth / cog_teeth (if not given); development_m = gear_ratio × wheel_circumference_mm / 1000; speed_kmh = cadence_rpm × development_m × 60 / 1000; speed_mph = speed_kmh / 1.609344","method":"Assumes no wheel slip and a fixed ratio; for internally geared hubs multiply gear_ratio by the hub's stage ratio. Measured roll-out circumference (mark the tyre, roll one revolution under rider weight) is more accurate than tabulated values by 1–2 %.","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":"NIST Special Publication 811 – Guide for the Use of the SI (Appendix B: 1 mile = 1609.344 m, 1 yard = 0.9144 m)","url":"https://www.nist.gov/pml/special-publication-811","type":"standard","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":"90 rpm in a 2.0 ratio (50 × 25), 700×25C","inputs":{"cadence_rpm":90,"gear_ratio":2},"expected":{"speed_kmh":22.8,"speed_mph":14.17,"speed_m_per_s":6.333,"development_m":4.222,"wheel_rpm":180,"gear_ratio_used":2},"url":"https://tttkmbb.com/api/v1/calculate/cadence-to-speed?cadence_rpm=90&gear_ratio=2"},{"name":"100 rpm in 53 × 11, 700×23C","inputs":{"cadence_rpm":100,"chainring_teeth":53,"cog_teeth":11,"wheel_circumference_mm":2096},"expected":{"gear_ratio_used":4.818,"development_m":10.099,"speed_kmh":60.59,"speed_mph":37.65},"url":"https://tttkmbb.com/api/v1/calculate/cadence-to-speed?cadence_rpm=100&chainring_teeth=53&cog_teeth=11&wheel_circumference_mm=2096"}],"faq":[{"q":"Which input wins if I give both gear_ratio and teeth counts?","a":"gear_ratio is used and the teeth counts are ignored."},{"q":"What cadence is normal?","a":"Most trained road cyclists ride at 80–100 rpm; climbing is often 60–80 rpm. Speed scales linearly with cadence in a fixed gear."}],"tags":["cadence to speed","rpm to km/h","cycling speed calculator","gear ratio speed","wheel circumference"],"related":[{"calculator_id":"bike-gear-ratio","reason":"Derive the ratio and circumference from teeth counts, rim and tyre size."},{"calculator_id":"pace-converter","reason":"Convert speed to pace units."},{"calculator_id":"speed","reason":"General speed unit conversion."}],"links":{"html":"https://tttkmbb.com/fitness/cadence-to-speed","markdown":"https://tttkmbb.com/fitness/cadence-to-speed.md","json":"https://tttkmbb.com/fitness/cadence-to-speed.json","api":"https://tttkmbb.com/api/v1/calculate/cadence-to-speed","schema":"https://tttkmbb.com/api/v1/calculators/cadence-to-speed","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:53:52Z","next_actions":[{"tool":"run_calculator","calculator_id":"cadence-to-speed","reason":"Run Cadence to Speed Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/fitness/cadence-to-speed.md"}}