Power from Torque and RPM: Formula and Calculator

Calculate rotational power by entering torque and rotational speed (RPM); the calculator returns power in horsepower and kilowatts. Use torque in pound-feet and RPM for the horsepower result, or enter torque in newton-metres to obtain kilowatts.

Formula

For torque in pound-feet and speed in revolutions per minute, power in mechanical horsepower is:

Horsepower = torque × RPM ÷ 5252.113

The calculator’s kilowatt output uses the equivalent conversion for the same pound-foot input:

Kilowatts = torque × RPM × 0.000142373

• Torque is the turning moment, entered here in pound-feet (lb-ft).
• RPM is rotational speed in revolutions per minute.
• Horsepower (hp) is mechanical horsepower, where 1 hp is approximately 745.7 watts.
• Kilowatts (kW) are metric units of power; 1 kW equals 1,000 watts.

The familiar constant 5,252.113 comes from the definitions of horsepower and a revolution: one revolution covers 2π radians, and one mechanical horsepower is 33,000 foot-pounds per minute. The formula therefore combines angular speed with torque and converts the resulting rate of work to horsepower.

Worked Example

Using the calculator’s default inputs, torque is 100 lb-ft and rotational speed is 3,000 rpm.

1. Multiply torque by speed: 100 × 3,000 = 300,000.
2. Divide by 5,252.113122: 300,000 ÷ 5,252.113122 ≈ 57.12 hp.
3. For kilowatts, multiply 100 × 3,000 × 0.000142373 ≈ 42.71 kW.

The results are 57.12 hp and 42.71 kW, rounded to two decimal places. The two values describe the same power in different units.

How Torque and RPM Produce Power

Torque describes how strongly a shaft twists; power describes how quickly that shaft can do work. A shaft can produce substantial torque while turning slowly, or less torque while turning much faster. Power depends on both, so neither torque nor RPM alone determines it.

In SI units, the relationship is especially direct:

Power in watts = torque in newton-metres × angular speed in radians per second

Since RPM is not radians per second, convert speed using angular speed = RPM × 2π ÷ 60. That gives power in watts as torque in N·m × RPM × 2π ÷ 60. To express that answer in kilowatts, divide by 1,000. For torque in N·m, a convenient form is:

Power (kW) = torque (N·m) × RPM ÷ 9,549.3

The calculator accepts lb-ft, not N·m, so convert before entering a metric torque value: 1 lb-ft is approximately 1.35582 N·m. For example, 100 lb-ft is about 135.58 N·m. Do not enter a number measured in N·m as if it were lb-ft; that would overstate torque and calculated power by about 35.6%.

When to Use the Calculator

This calculation is useful when comparing a motor, engine, or other rotating machine at a particular operating point. It also helps translate a torque-and-speed specification into a power figure, provided both measurements refer to the same shaft and operating condition.

• Use the torque and RPM measured at the same time. Combining peak torque from one speed with peak RPM from another does not give the machine’s actual peak power.
• Check whether a specification reports lb-ft, N·m, or another torque unit before entering it.
• Use the result as shaft power only when the torque is measured at that shaft. Power downstream of a gearbox or other transmission can differ because of losses and changed speed and torque.
• For a known power and RPM, torque can be rearranged from the same relationship: torque (lb-ft) = horsepower × 5,252.113 ÷ RPM. At zero RPM, that rearrangement cannot be used.

Vehicle and machine ratings may describe different measurement locations or testing conditions. A power figure at an engine shaft is not necessarily the same as power measured at the wheels or at a driven component. Measurement method, accessory loads, and transmission losses can all matter when interpreting published figures.

Reading Results and Common Mistakes

The result is a rate of energy transfer, not energy accumulated over a period. A machine producing 57.12 hp at a specified operating point is not necessarily producing that power continuously; the figure applies only while the stated torque and speed are present.

• Confusing lb-ft with N·m: these units are not numerically interchangeable. Convert one to the other, or use a formula matched to the entered unit.
• Mixing RPM and angular speed: the SI formula requires radians per second, not RPM. Use the RPM-specific formula or convert the speed first.
• Using mismatched values: torque and RPM must describe the same operating point. Multiplying independently listed maximums may produce a fictitious result.
• Over-interpreting rounding: displayed decimals do not make the inputs more precise. If torque or speed is approximate, the calculated power is approximate too.
• Assuming torque and power peak together: power may peak at a different RPM from peak torque because speed changes across the operating range.

The formula itself does not account for heat, friction, electrical efficiency, drivetrain losses, or measurement uncertainty. It simply converts torque and rotational speed into power. If the torque value is already a measured net output, do not subtract losses again unless you are specifically estimating power at a different point in the system.

Frequently Asked Questions

What is the formula for horsepower from torque and RPM?
With torque in lb-ft and speed in RPM, horsepower = torque × RPM ÷ 5,252.113. This gives mechanical horsepower.

Why is 5,252 used in the horsepower formula?
It is a conversion constant derived from the definitions of mechanical horsepower, foot-pounds, and revolutions per minute. The more precise value used here is 5,252.113.

How do I calculate power in kilowatts from N·m and RPM?
Use kW = torque in N·m × RPM ÷ 9,549.3. This SI-unit form avoids converting torque to pound-feet.

Can high torque mean high power at low RPM?
High torque contributes to power, but low speed limits the rate of work. Power depends on their product, so torque alone does not establish how much power is produced.

Is peak horsepower calculated from peak torque and peak RPM?
Not usually by multiplying those separate peak values. The torque and RPM must occur together at the same operating point; evaluate the formula across matching measurements to find peak power.

Limits of the Calculation

The calculator assumes a steady operating point and correctly specified torque and speed. It is a unit conversion and mechanical relationship, not a method for rating equipment or determining safe operating limits. Use appropriate measured data and consult qualified technical guidance when an application requires equipment selection, operating limits, or a safety decision.

Related

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in tq | Torque | lb-ft | 100 | 0
in rpm | Rotational speed | rpm | 3000 | 0
out hp | Power | hp | tq * rpm / 5252.113122 | 2
out kw | Power | kW | tq * rpm * 0.000142373 | 2