What is the formula for horsepower from foot-pounds and RPM?

Horsepower equals torque in foot-pounds times RPM divided by 5252. The constant 5252 comes from converting the rotational power formula: P = tau * omega, with omega in rad/s and the unit conversions between feet, pounds, and watts folded in. For example, 100 ft-lb at 3000 RPM gives 100 times 3000 divided by 5252, which is 57.14 hp.

What is the difference between torque and horsepower?

Torque is a rotational force, measured in foot-pounds or Newton-metres. Horsepower is a rate of doing work, a power unit. They are related by speed: a high-torque engine that spins slowly may produce less horsepower than a lower-torque engine that spins much faster. On a dyno chart, horsepower and torque curves always cross at 5252 RPM when torque is in ft-lb.

How do you convert foot-pounds to Newton-metres?

One foot-pound equals 1.35582 Newton-metres. To convert, multiply foot-pounds by 1.35582. For example, 100 ft-lb equals 100 times 1.35582, which is 135.58 N-m.

Torque to Horsepower Calculator

Torque and horsepower are the two key metrics used to describe an engine or motor's capability, and they are often confused because they are related but measure different things. Torque is the rotational force a shaft can exert, measured in foot-pounds (ft·lb) in imperial units or Newton-metres (N·m) in metric. Horsepower is the rate at which work is done, a power unit. The two are linked by rotational speed: the faster a shaft spins for a given torque, the more power it produces. That relationship is expressed in the formula horsepower equals torque in foot-pounds times RPM divided by 5252. The constant 5252 comes from the conversion factors between the various units in the power equation. In metric, the formula is simpler: power in watts equals torque in N·m times angular velocity in rad/s. This calculator accepts torque in foot-pounds or Newton-metres and the rotational speed in RPM, and returns the power in horsepower, kilowatts, watts, and metric PS. When you enter foot-pounds, it also shows the torque in N·m so you can cross-reference with metric specifications. The tool is useful for comparing engine dyno figures, sizing motors, and checking whether a drive system has enough power for a given load. The figures are for design reference; always consult manufacturer data for rated limits.

Torque unit

Torque

ft·lb

Speed

RPM

57.14 hp

mechanical horsepower

Power in kW42.60 kW

Power in watts42,598 W

Metric PS57.93 PS

Torque in N·m135.58 N·m

How it works

If torque is entered in foot-pounds, first convert to N·m by multiplying by 1.35582. Then power in watts = torque (N·m) times RPM times 2 pi divided by 60. Mechanical horsepower = watts divided by 745.7. The imperial shortcut is hp = torque (ft·lb) times RPM divided by 5252, which gives the same answer. Metric PS = watts divided by 735.5. kW = watts divided by 1000.

Worked example

An engine produces 100 ft·lb of torque at 3000 RPM. Converting: 100 times 1.35582 = 135.58 N·m. Power = 135.58 times 3000 times 2 pi divided by 60 = 135.58 times 314.16 = 42,598 W = 42.60 kW. Horsepower = 42598 divided by 745.7 = 57.14 hp. Metric PS = 42598 divided by 735.5 = 57.93 PS. Using the imperial shortcut: 100 times 3000 divided by 5252 = 57.14 hp, confirming the result.

Related calculators

Horsepower Calculator: calculate power from torque in N·m, or convert hp directly to kW.
RPM Calculator: find wheel or motor RPM from speed and diameter or frequency and poles.
Torque Converter: convert between N·m, ft·lb, in·lb, and kgf·m.
Energy Converter: convert between joules, kilowatt-hours, BTU, and other energy units.

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