Power RPM Calculator: Convert Torque and Speed

A power rpm calculator determines mechanical power from torque and rotational speed, or calculates the torque or rpm needed when the other two values are known. Enter torque and rpm to get power; use consistent units, because torque may be entered in newton-metres or pound-feet and power reported in kilowatts, horsepower, or both.

Formula

For torque in newton-metres (N·m) and rotational speed in revolutions per minute (rpm), power in kilowatts is:

Power (kW) = torque (N·m) × rpm × 2π ÷ 60,000

The same relationship in watts is power = torque × angular speed, where angular speed in radians per second is rpm × 2π ÷ 60. Mechanical horsepower can be calculated as:

Power (hp) = torque (N·m) × rpm ÷ 7,121.4

Here, torque is the turning moment applied to a shaft, measured in N·m; rpm is rotations per minute; kW is kilowatts; hp is mechanical horsepower. The calculator’s horsepower output uses 1 mechanical hp = 745.7 watts, so it is not the same unit as metric horsepower (often written PS or CV).

Worked Example

With the calculator’s default values, torque is 100 N·m and speed is 3,000 rpm.

• Convert speed to radians per second: 3,000 × 2π ÷ 60 = 100π, or about 314.16 rad/s.
• Calculate power: 100 N·m × 314.16 rad/s = about 31,416 watts.
• Convert watts to kilowatts: 31,416 ÷ 1,000 = 31.42 kW.
• Convert to mechanical horsepower: 31,416 ÷ 745.7 = 42.13 hp.

The calculator rounds both displayed results to two decimal places. Small differences can arise if you calculate using a rounded value of π or a rounded conversion factor.

What the Calculator Measures

Power describes how quickly work is done or energy is transferred. Torque describes rotational force, while rpm describes how fast a shaft turns. A larger torque or a higher rotational speed increases power, provided the other value stays the same. Doubling torque at the same rpm doubles power; doubling rpm at the same torque does too.

This relationship applies to rotating machinery such as engines, electric motors, pumps, fans, and shafts. It describes mechanical power at the point where the torque and speed are measured. It does not automatically give electrical input power, fuel energy, or useful power delivered after losses.

Using Other Units

Keep torque units consistent with the formula. The calculator takes N·m. If your torque is in pound-feet (lb·ft), convert it first: 1 lb·ft is approximately 1.35582 N·m. Alternatively, a formula designed for lb·ft is:

Power (hp) = torque (lb·ft) × rpm ÷ 5,252

That approximation gives mechanical horsepower. For example, 100 lb·ft at 3,000 rpm is about 57.1 hp. Do not enter the number 100 as though lb·ft were N·m; the resulting answer would be too low because the units differ.

Metric power is usually stated in watts or kilowatts; customary measurements often use horsepower. One mechanical horsepower is about 0.7457 kW, and one kW is about 1.341 mechanical hp. Metric horsepower is slightly different: one metric horsepower is about 0.7355 kW. Check which definition a specification uses before comparing figures.

When to Use the Relationship

Use the calculator when torque and rotational speed are known at the same shaft and operating condition, and you want their corresponding mechanical power. The equation can also be rearranged to find a missing value:

• Torque (N·m) = power (kW) × 60,000 ÷ (2π × rpm)
• rpm = power (kW) × 60,000 ÷ (2π × torque in N·m)

These rearrangements require a nonzero rpm or torque, respectively. If you know only a motor’s rated power, you cannot determine its torque without also knowing the rpm at which that power is produced. Likewise, torque alone does not specify power.

Reading Results and Common Mistakes

Power figures are meaningful only when their conditions and measurement points are clear. An engine’s torque changes with rpm, so its maximum torque and maximum power usually occur at different speeds. Multiplying a peak torque figure by a peak power rpm may produce a value that the machine never actually reaches, because those peaks may not happen together.

• Mixing units: N·m and lb·ft are not interchangeable numbers. Convert before using a formula.
• Confusing power and torque: Torque is a turning moment; power combines torque with rotational speed.
• Comparing different horsepower definitions: Mechanical and metric horsepower are close but not identical.
• Ignoring measurement location: Power at an engine crankshaft differs from power measured at a wheel or after a gearbox, because components can absorb energy.
• Overinterpreting precision: Two decimal places are a display choice, not a guarantee that input measurements are accurate to that level.

Limits of the Calculation

The formula gives ideal mechanical power from the torque and rpm supplied. It does not account for changing torque, fluctuating speed, friction, heat, electrical efficiency, transmission losses, or measurement uncertainty. For a varying operating cycle, one pair of values is only a snapshot; calculating average energy use or output requires measurements over time.

Also distinguish shaft torque from a force measured at a distance. Torque equals force multiplied by the perpendicular distance from the axis, but that relation alone does not determine rpm or power. For equipment selection or engineering decisions, use the machine’s complete specifications and appropriate professional guidance rather than treating a calculator result as a rating.

Frequently Asked Questions

How do you calculate power from torque and rpm?
With torque in N·m, multiply torque by rpm and by 2π, then divide by 60,000 for kilowatts. For mechanical horsepower, divide torque × rpm by about 7,121.4.

Can I calculate rpm from horsepower and torque?
Yes. Convert horsepower to kW if needed, then use rpm = power (kW) × 60,000 ÷ (2π × torque in N·m). Make sure both values refer to the same operating point.

Is torque the same as power?
No. Torque is rotational turning moment; power is the rate of doing work. At a given torque, a faster rotation means greater power.

Why does horsepower change with rpm?
Power depends on both torque and rotational speed. If torque varies as an engine or motor speeds up, power changes according to the product of those values.

Is kW the same as hp?
No. Kilowatt is a metric unit of power and mechanical horsepower is a customary unit. One mechanical hp is approximately 0.7457 kW.

Related

• Ton to HP Conversion Calculator: What It Really Means
• Work Formula: How to Calculate Work in Physics
• HP vs Torque Calculator: Convert and Compare

in tq | Torque | N·m | 100 | 0
in rpm | Rotational speed | rpm | 3000 | 0
out kw | Power | kW | tq * rpm * 2 * pi / 60000 | 2
out hp | Mechanical horsepower | hp | tq * rpm / 7121.4 | 2