Home › Engineering & Automotive › Horsepower, Torque and RPM Calculator

Horsepower, Torque and RPM Calculator

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.

When to use

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).

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)

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.

Inputs

Parameter	Type	Unit	Required	Description
`power_hp`	number	hp	no	Mechanical horsepower (1 hp = 745.7 W). Give power as power_hp or power_kw, not both. Range: > 0
`power_kw`	number	kW	no	Power in kilowatts. Give power as power_hp or power_kw, not both. Range: > 0
`torque_lb_ft`	number	lb·ft	no	Torque in pound-feet (1 lb·ft = 1.3558 N·m). Give torque as torque_lb_ft or torque_nm, not both. Range: > 0
`torque_nm`	number	N·m	no	Torque in newton-metres. Give torque as torque_lb_ft or torque_nm, not both. Range: > 0
`rpm`	number	rpm	no	Revolutions per minute at which the torque or power applies. Omit to solve for it. Range: > 0, ≤ 1000000

Outputs

Output	Type	Unit	Description
`solved_for`	string		power, torque or rpm.
`power_hp`	number	hp	Mechanical horsepower.
`power_ps`	number	PS	Metric horsepower (1 PS = 735.5 W).
`power_kw`	number	kW	Power in kilowatts.
`torque_lb_ft`	number	lb·ft	Torque in pound-feet.
`torque_nm`	number	N·m	Torque in newton-metres.
`rpm`	number	rpm	Revolutions per minute.
`angular_speed_rad_s`	number	rad/s	ω = 2π × rpm / 60.

Example

300 lb·ft at 5252 rpm: {"torque_lb_ft":300,"rpm":5252} → {"solved_for":"power","power_hp":300,"power_kw":223.705,"torque_nm":406.75,"angular_speed_rad_s":549.9853}

Torque of 100 kW at 3000 rpm: {"power_kw":100,"rpm":3000} → {"solved_for":"torque","torque_nm":318.31,"torque_lb_ft":234.77,"power_hp":134.1,"power_ps":135.96}

GET https://tttkmbb.com/api/v1/calculate/horsepower-torque-rpm?torque_lb_ft=300&rpm=5252

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/horsepower-torque-rpm (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/horsepower-torque-rpm · Markdown: https://tttkmbb.com/engineering/horsepower-torque-rpm.md · JSON definition: https://tttkmbb.com/engineering/horsepower-torque-rpm.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="horsepower-torque-rpm"
OpenAPI operationId: solve_horsepower_torque_rpm
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

FAQ

Why do horsepower and torque curves cross at 5252 rpm?

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.

Which horsepower is this?

Mechanical (imperial) horsepower, 745.7 W. Metric PS (735.5 W) is also reported; electrical (746 W) and boiler horsepower are different units.

Related calculators

Torque Converter — Convert torque between N·m, lb·ft and kgf·m.
Power Converter — Convert power between W, kW, hp and PS.
Gear Ratio and Speed Calculator — Road speed at a given engine rpm.