Torque Calculator From RPM: Formula and Examples

A torque calculator from rpm works out torque when you enter rotational speed and mechanical power. The result is torque in newton-metres (N·m) or pound-feet (lb·ft), depending on the units you use; rpm alone is not enough to determine torque.

Formula

The calculator uses the relationship between power, torque and rotational speed:

Torque (N·m) = Power (kW) × 9549.296596 ÷ Speed (rpm)

Equivalently, in SI units, P = τω, so τ = P ÷ ω. Here, τ is torque in newton-metres, P is mechanical power in watts, and ω is angular speed in radians per second. Since one revolution is 2π radians and one minute is 60 seconds, rpm converts to radians per second by multiplying by 2π/60. Combining that conversion with watts-to-kilowatts gives the calculator’s constant.

• Power: entered in kilowatts (kW); the second output converts it to mechanical horsepower (hp).
• Speed: entered in revolutions per minute (rpm).
• Torque: reported in N·m, then converted to lb·ft. One N·m is approximately 0.737562 lb·ft.

The calculator requires positive speed because torque at zero rpm cannot be calculated from this power-and-speed equation: dividing by zero is undefined. The input limits are broad mathematical bounds, not a claim that every combination describes a real machine.

Worked Example

Using the default values, power is 10 kW and speed is 1,500 rpm.

1. Convert power to watts: 10 kW × 1,000 = 10,000 W.
2. Convert speed to radians per second: 1,500 × 2π ÷ 60 ≈ 157.0796 rad/s.
3. Divide power by angular speed: 10,000 ÷ 157.0796 ≈ 63.66 N·m.
4. Convert that torque: 63.66 × 0.737562149 ≈ 46.96 lb·ft.
5. Convert power: 10 × 1.34102209 ≈ 13.41 mechanical hp.

The calculator therefore returns 63.66 N·m as its headline result, along with 13.41 hp and 46.96 lb·ft. Small differences in the last decimal can occur if intermediate values are rounded.

Why RPM Alone Cannot Give Torque

RPM tells you how quickly a shaft turns, not how strongly it twists. A freely spinning shaft and a loaded shaft can turn at the same speed while transmitting very different torque. To calculate torque, you also need power, or an independent measurement of torque itself.

For example, at 1,500 rpm, 10 kW corresponds to about 63.66 N·m. If power were 20 kW at the same speed, torque would be about 127.32 N·m. Conversely, the same power at twice the speed produces half the torque. This inverse relationship applies when power is held constant.

Power in this equation must be power transmitted at the shaft under consideration. A motor’s electrical input power is not necessarily its mechanical output power: losses in the motor mean the output is lower. If you use input power without accounting for losses, the calculated torque will be too high.

When to Use the Calculator

Use this calculation when a machine specification gives shaft power and rotational speed but omits torque, or when you want to compare operating points. It is useful for motors, engines, gearboxes and rotating equipment, provided power and rpm refer to the same shaft and the same operating condition.

• Use mechanical output power for a motor or engine shaft, not an unrelated electrical supply rating.
• For a gearbox, distinguish input-shaft values from output-shaft values. A speed change usually means a torque change too.
• For a measured operating point, use simultaneous power and speed readings. Combining a peak power figure with rpm from a different condition can mislead.
• For US customary power, the equivalent shortcut is Torque (lb·ft) = Power (mechanical hp) × 5252.113 ÷ rpm.

The familiar value 5,252 is a conversion constant, not a universal engine characteristic. It follows from the definitions of horsepower, foot-pounds and revolutions per minute. The kW-to-N·m expression used by this calculator is the same physical relationship expressed in metric units.

Interpreting Results and Limits

Torque measures a turning effect: force multiplied by its perpendicular distance from the axis. A value of 1 N·m means a force of 1 newton acting at a perpendicular distance of 1 metre. In US customary units, lb·ft expresses the corresponding force-distance product using pounds-force and feet.

The result is an operating-point calculation, not necessarily a machine’s maximum or continuous torque rating. Real equipment may have torque curves that vary with speed, control settings, temperature and load. The equation also does not account for efficiency, acceleration, vibration, changing loads or transmission losses. If power is specified as a time-varying peak, the calculated torque represents that power only at the rpm paired with it.

At zero speed, a stationary motor may still produce holding torque, but this formula cannot find it from shaft power: mechanical power at zero rotational speed is zero even when torque is present. Use a torque measurement or a manufacturer’s torque data for that condition. Do not treat a calculated value as a safe load rating or use it alone to select components; equipment ratings and operating limits require appropriate engineering information.

Common Mistakes

• Using rpm without power: speed alone cannot determine torque.
• Mixing units: the calculator expects kW and rpm. Entering watts as though they were kW makes the answer 1,000 times too large; entering hp as kW also gives the wrong result.
• Using the wrong horsepower: the output is mechanical horsepower, not metric horsepower or electrical input power. Horsepower definitions differ slightly, so identify the unit in the source data.
• Pairing unrelated values: power and speed must describe the same shaft and operating moment.
• Overinterpreting decimals: two displayed decimal places do not make uncertain input data precise. Round only after the calculation, and keep sensible significant figures.

Frequently Asked Questions

Can you calculate torque from rpm alone?
No. You need power as well, or a direct torque measurement. RPM describes rotational speed, while torque describes turning effect.

What is the torque formula using rpm and kW?
Torque in N·m equals power in kW multiplied by 9,549.296596 and divided by rpm. The speed must be greater than zero.

How do I calculate lb·ft from horsepower and rpm?
For mechanical horsepower, use lb·ft = hp × 5,252.113 ÷ rpm. Keep the horsepower and speed values from the same operating point.

Does higher rpm mean higher torque?
Not by itself. At constant power, torque decreases as rpm increases. In a real machine, power can change with speed, so its torque curve depends on its design and operating conditions.

Why can a motor have torque at zero rpm?
A motor can exert holding or starting torque while stationary, but shaft power is torque multiplied by rotational speed. At zero speed, that mechanical power is zero, so the power-and-rpm formula cannot recover the torque.

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in p | Power | kW | 10 | 0 | 1000000
in r | Speed | rpm | 1500 | 0.000001 | 1000000
out t | Torque | N·m | p * 9549.296596 / r | 2
out hp | Power | mechanical hp | p * 1.34102209 | 2
out lbft | Torque | lb·ft | t * 0.737562149 | 2