Calculator
Example Data Table
Sample values below assume 100% efficiency and a ratio of 1.
| Power | Speed | Angular Speed (rad/s) | Torque (N·m) |
|---|---|---|---|
| 0.75 kW | 1500 RPM | 157.080 | 4.775 |
| 2.20 kW | 1450 RPM | 151.844 | 14.489 |
| 5.00 kW | 3000 RPM | 314.159 | 15.915 |
| 10.00 kW | 960 RPM | 100.531 | 99.472 |
Formula Used
The core relationship between mechanical power, torque, and angular speed is:
- P = T × ω
- T = P / ω
- ω = 2π × RPM / 60
With a gear reduction ratio R = input_speed / output_speed and efficiency η:
- P_out = P_in × η
- ω_out = ω_in / R
- T_out = (P_in / ω_in) × R × η
How to Use
- Enter the driving power and choose its unit.
- Enter the rotational speed and select the unit.
- If using a gearbox, set the input/output ratio.
- Set efficiency to reflect real power losses.
- Pick your preferred torque unit and decimals.
- Press Submit to see results and download options.
Power to Torque Guide
1) Why Convert Power to Torque
Motors are often rated by power, while shafts and couplings are sized by torque. Converting power to torque helps you estimate twisting load at a given speed, compare motor options, and spot conditions that may overload a gearbox.
2) The Core Relationship
Mechanical power equals torque multiplied by angular speed: P = T × ω. When speed falls, the same power produces higher torque. That is why slow gear outputs can deliver large turning force.
3) RPM and Angular Speed
Torque calculations use ω in rad/s. The conversion is ω = 2π × RPM / 60. If you enter rps, deg/s, or rad/s, the calculator converts them consistently before solving for torque.
4) Gear Ratio Effects
This calculator treats gear ratio as input_speed / output_speed. A ratio of 4 means the output speed is one-quarter, and ideal torque multiplies by about four. The output speed shown helps you validate the ratio you typed.
5) Efficiency and Real Losses
Real systems lose power through friction, windage, and heat. Using efficiency reduces output power and output torque. For example, 90% efficiency means only 0.9 × P reaches the load. This is useful for belts, reducers, and pumps.
6) Unit Choices That Matter
Engineers may prefer N·m, while technicians may use lbf·ft or lbf·in. Horsepower and kilowatts are both supported. Consistent units prevent mistakes when comparing datasheets and torque limits.
7) Practical Checks
After calculating, compare output torque to coupling ratings, keyway limits, and gearbox service factors. If torque is high, verify starting conditions and transient loads. For quick estimates at steady RPM, the rule T(N·m) ≈ 9550 × P(kW) / RPM is handy.
FAQs
1) What if I only know power in horsepower?
Choose hp as the power unit, enter the value, and provide the speed. The calculator converts horsepower to watts internally and returns torque in your selected unit.
2) Why does torque increase when RPM decreases?
Because power is P = T × ω. If power stays constant and speed drops, torque must rise to keep the product the same.
3) How should I enter gear ratio?
Use input_speed divided by output_speed. If the motor turns 3000 RPM and the output turns 750 RPM, enter 4.
4) Does efficiency change torque or only power?
It changes both at the output. Lower efficiency means less power reaches the load, so output torque is reduced compared with an ideal, lossless drive.
5) Can I calculate torque at the motor shaft only?
Yes. Set gear ratio to 1 and efficiency to 100%. The “Input torque” lines will match the output torque values.
6) Why are there two torque outputs shown?
N·m is shown for a universal reference, while the “selected unit” line converts the same torque into the unit you prefer for reporting or comparison.