{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"horsepower-torque-rpm"},"result":{"entity_type":"calculator","id":"horsepower-torque-rpm","calculator_id":"horsepower-torque-rpm","canonical_url":"https://tttkmbb.com/engineering/horsepower-torque-rpm","name":"Horsepower, Torque and RPM Calculator","title":"Horsepower–Torque–RPM Calculator – Solve Power (hp/kW), Torque (lb·ft/N·m) or Engine Speed","category":"engineering","category_name":"Engineering & Automotive","tool_name":"solve_horsepower_torque_rpm","featured_mcp_tool":false,"description":"Solves the rotational power relation for whichever of power, torque or rotational speed is missing (HP = torque_lb_ft × rpm / 5252; kW = torque_nm × rpm / 9549) and reports the results in hp, PS, kW, lb·ft and N·m.","use_when":"You know two of engine/motor power, torque and rpm (from a dyno sheet or a datasheet) and need the third, or want to convert a torque-at-rpm figure to horsepower.","do_not_use_when":"You only need a unit conversion of power (use power) or torque (use torque) without rpm, or you need road speed from rpm (use gear-ratio-speed).","inputs":[{"name":"power_hp","label":"Power","type":"number","unit":"hp","required":false,"exclusive_min":0,"description":"Mechanical horsepower (1 hp = 745.7 W). Give power as power_hp or power_kw, not both."},{"name":"power_kw","label":"Power","type":"number","unit":"kW","required":false,"exclusive_min":0,"description":"Power in kilowatts. Give power as power_hp or power_kw, not both."},{"name":"torque_lb_ft","label":"Torque","type":"number","unit":"lb·ft","required":false,"exclusive_min":0,"description":"Torque in pound-feet (1 lb·ft = 1.3558 N·m). Give torque as torque_lb_ft or torque_nm, not both.","example":300},{"name":"torque_nm","label":"Torque","type":"number","unit":"N·m","required":false,"exclusive_min":0,"description":"Torque in newton-metres. Give torque as torque_lb_ft or torque_nm, not both."},{"name":"rpm","label":"Rotational speed","type":"number","unit":"rpm","required":false,"max":1000000,"exclusive_min":0,"description":"Revolutions per minute at which the torque or power applies. Omit to solve for it.","example":5252}],"outputs":[{"name":"solved_for","label":"Solved for","type":"string","decimals":4,"description":"power, torque or rpm."},{"name":"power_hp","label":"Power","type":"number","unit":"hp","decimals":2,"description":"Mechanical horsepower."},{"name":"power_ps","label":"Power","type":"number","unit":"PS","decimals":2,"description":"Metric horsepower (1 PS = 735.5 W)."},{"name":"power_kw","label":"Power","type":"number","unit":"kW","decimals":3,"description":"Power in kilowatts."},{"name":"torque_lb_ft","label":"Torque","type":"number","unit":"lb·ft","decimals":2,"description":"Torque in pound-feet."},{"name":"torque_nm","label":"Torque","type":"number","unit":"N·m","decimals":2,"description":"Torque in newton-metres."},{"name":"rpm","label":"Rotational speed","type":"number","unit":"rpm","decimals":1,"description":"Revolutions per minute."},{"name":"angular_speed_rad_s","label":"Angular speed","type":"number","unit":"rad/s","decimals":4,"description":"ω = 2π × rpm / 60."}],"input_schema":{"type":"object","properties":{"power_hp":{"description":"Mechanical horsepower (1 hp = 745.7 W). Give power as power_hp or power_kw, not both. Unit: hp.","type":"number","exclusiveMinimum":0,"x-unit":"hp"},"power_kw":{"description":"Power in kilowatts. Give power as power_hp or power_kw, not both. Unit: kW.","type":"number","exclusiveMinimum":0,"x-unit":"kW"},"torque_lb_ft":{"description":"Torque in pound-feet (1 lb·ft = 1.3558 N·m). Give torque as torque_lb_ft or torque_nm, not both. Unit: lb·ft.","type":"number","exclusiveMinimum":0,"examples":[300],"x-unit":"lb·ft"},"torque_nm":{"description":"Torque in newton-metres. Give torque as torque_lb_ft or torque_nm, not both. Unit: N·m.","type":"number","exclusiveMinimum":0,"x-unit":"N·m"},"rpm":{"description":"Revolutions per minute at which the torque or power applies. Omit to solve for it. Unit: rpm.","type":"number","maximum":1000000,"exclusiveMinimum":0,"examples":[5252],"x-unit":"rpm"}},"additionalProperties":false},"output_schema":{"type":"object","properties":{"solved_for":{"description":"power, torque or rpm.","type":"string"},"power_hp":{"description":"Mechanical horsepower. Unit: hp.","type":"number","x-unit":"hp"},"power_ps":{"description":"Metric horsepower (1 PS = 735.5 W). Unit: PS.","type":"number","x-unit":"PS"},"power_kw":{"description":"Power in kilowatts. Unit: kW.","type":"number","x-unit":"kW"},"torque_lb_ft":{"description":"Torque in pound-feet. Unit: lb·ft.","type":"number","x-unit":"lb·ft"},"torque_nm":{"description":"Torque in newton-metres. Unit: N·m.","type":"number","x-unit":"N·m"},"rpm":{"description":"Revolutions per minute. Unit: rpm.","type":"number","x-unit":"rpm"},"angular_speed_rad_s":{"description":"ω = 2π × rpm / 60. Unit: rad/s.","type":"number","x-unit":"rad/s"}}},"formula":"P_W = torque_nm × rpm × 2π / 60; power_hp = torque_lb_ft × rpm / 5252.113; power_kw = torque_nm × rpm / 9549.297; torque = P / ω; rpm = P × 60 / (2π × torque)","method":"Uses the exact constants 33,000 ft·lbf/min per hp (so 5252.113 = 33,000 / 2π) and 1 hp = 745.69987 W; the familiar rounded 5252 gives results within 0.003 %. Torque and power curves cross at 5252 rpm when plotted in lb·ft and hp.","sources":[{"name":"Wikipedia – Horsepower – relationship with torque","url":"https://en.wikipedia.org/wiki/Horsepower#Relationship_with_torque","type":"reference","retrieved_at":"2026-09-24"},{"name":"NIST Special Publication 811 – Guide for the Use of the SI, Appendix B (conversion factors)","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":"300 lb·ft at 5252 rpm","inputs":{"torque_lb_ft":300,"rpm":5252},"expected":{"solved_for":"power","power_hp":300,"power_kw":223.705,"torque_nm":406.75,"angular_speed_rad_s":549.9853},"url":"https://tttkmbb.com/api/v1/calculate/horsepower-torque-rpm?torque_lb_ft=300&rpm=5252"},{"name":"Torque of 100 kW at 3000 rpm","inputs":{"power_kw":100,"rpm":3000},"expected":{"solved_for":"torque","torque_nm":318.31,"torque_lb_ft":234.77,"power_hp":134.1,"power_ps":135.96},"url":"https://tttkmbb.com/api/v1/calculate/horsepower-torque-rpm?power_kw=100&rpm=3000"}],"faq":[{"q":"Why do horsepower and torque curves cross at 5252 rpm?","a":"Because hp = lb·ft × rpm / 5252: at exactly 5252 rpm the two numbers are equal. In metric units (kW and N·m) the crossing is at 9549 rpm."},{"q":"Which horsepower is this?","a":"Mechanical (imperial) horsepower, 745.7 W. Metric PS (735.5 W) is also reported; electrical (746 W) and boiler horsepower are different units."}],"tags":["horsepower","torque to horsepower","hp torque rpm","5252","kw to torque","engine power"],"related":[{"calculator_id":"torque","reason":"Convert torque between N·m, lb·ft and kgf·m."},{"calculator_id":"power","reason":"Convert power between W, kW, hp and PS."},{"calculator_id":"gear-ratio-speed","reason":"Road speed at a given engine rpm."}],"links":{"html":"https://tttkmbb.com/engineering/horsepower-torque-rpm","markdown":"https://tttkmbb.com/engineering/horsepower-torque-rpm.md","json":"https://tttkmbb.com/engineering/horsepower-torque-rpm.json","api":"https://tttkmbb.com/api/v1/calculate/horsepower-torque-rpm","schema":"https://tttkmbb.com/api/v1/calculators/horsepower-torque-rpm","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T02:03:06Z"}