Power From Torque and Speed Calculator
Enter any two of power (W), torque (Nm) and speed (RPM) to calculate the third
(2 π) / 60
Quick answer
Mechanical power equals torque multiplied by angular speed. In SI units, P (W) = T (Nm) × ω (rad/s). With speed in RPM: P (W) = T × RPM × 2π ÷ 60, or in kilowatts, P (kW) = T × RPM ÷ 9,549. Enter any two values above and the calculator returns the third.
Unfamiliar with a term? Check the electric motor glossary.
| Speed (RPM) | Torque (N-m) | Power (Watts) |
|---|---|---|
| 1000 | 9.55 | 1000 |
| 2000 | 4.77 | 1000 |
| 3000 | 3.18 | 1000 |
| 4000 | 2.39 | 1000 |
| 5000 | 1.91 | 1000 |
| 6000 | 1.59 | 1000 |
| 7000 | 1.36 | 1000 |
| 8000 | 1.19 | 1000 |
| 9000 | 1.06 | 1000 |
| 10000 | 0.95 | 1000 |
Torque vs. Speed Chart Generating 1000Watts Power
The Formula in Three Forms
1. P = T × ω (ω in rad/s)
2. P = T × 2π × RPM ÷ 60
3. P (kW) = T × RPM ÷ 9,549
All three give the same answer. Form 3 is the shortcut used on most datasheets: 9,549 is 60,000 ÷ 2π, which combines the RPM-to-rad/s conversion (× 2π ÷ 60) with watts to kilowatts (÷ 1,000). Rearranged for torque: T = P × 9,549 ÷ RPM, with P in kW.
Table of Torque and Speed Pairs
| Torque (Nm) | Speed (RPM) | Power (W) | Power (kW) |
|---|---|---|---|
| 1 | 1,000 | 104.7 | 0.105 |
| 5 | 1,000 | 523.6 | 0.524 |
| 10 | 3,000 | 3,141.6 | 3.14 |
| 20 | 200 | 418.9 | 0.419 |
| 20 | 60 | 125.7 | 0.126 |
| 35 | 500 | 1,832.6 | 1.83 |
Worked Examples
- A robot joint. 20 Nm at 200 RPM: ω = 200 × 2π ÷ 60 = 20.94 rad/s, so P = 20 × 20.94 = 418.9 W.
- The same joint, slower. 20 Nm at 60 RPM: P = 20 × 2π × 60 ÷ 60 = 125.7 W. The torque the motor makes is the same; only the power changes.
- A faster motor. 10 Nm at 3,000 RPM: P = 10 × 3,000 ÷ 9,549 = 3.14 kW.
- Torque from power. 3 kW at 1,500 RPM: T = 3 × 9,549 ÷ 1,500 = 19.1 Nm.
Why Power Changes With Speed
At a given torque, power is proportional to speed: double the speed and the power doubles. That is why a drive is rated for the power at the top of its operating range, not the average, and why a slow direct-drive motor and a fast geared motor can deliver the same power with very different torque. The torque and power density guide explains why that distinction matters when comparing motors.
Checking a Datasheet
A datasheet often gives torque and speed at a single rated point. Use the formula to check the power at that point, then check the power at the speeds you actually run: a motor that meets the torque at one speed may not meet it at another, and continuous and peak ratings are different points. The calculated figure is mechanical output power; electrical input power is higher by the losses, which is what motor efficiency describes.
Unit Conversions
- 1 Nm = 0.7376 lbf·ft (torque converter)
- 1 hp (mechanical) = 745.7 W; 1 metric horsepower (PS) = 735.5 W (horsepower to watts)
- 1 rad/s = 9.549 RPM (rad/s to RPM converter)
Frequently Asked Questions
What is the formula for power from torque?
P = T × ω, with torque in Nm and angular speed in rad/s, gives power in watts. With speed in RPM: P (kW) = T × RPM ÷ 9,549.
Why is 9,549 in the formula?
9,549 is 60,000 ÷ 2π, rounded. It combines the conversion from RPM to rad/s (multiply by 2π ÷ 60) with the conversion from watts to kilowatts (divide by 1,000).
How do I calculate torque from power and speed?
T = P × 9,549 ÷ RPM, with P in kW. For example, 3 kW at 1,500 RPM gives 3 × 9,549 ÷ 1,500 = 19.1 Nm.
Is power the same as torque?
No. Torque is a turning force; power is the rate at which work is done. Two motors with the same torque deliver very different power if their speeds differ.
Does the calculator work in lbf·ft or horsepower?
It works in Nm, RPM and watts. Convert first: 1 Nm = 0.7376 lbf·ft and 1 hp = 745.7 W.
Why is my calculated power different from the datasheet?
Common causes are a different torque basis (continuous or peak), a different speed point, or a datasheet that quotes electrical input power rather than mechanical output power.