Calculator
Example data table
These sample values illustrate typical motor ranges and expected torque. Actual torque depends on load, slip, drive settings, and mechanical losses.
| Case | Method | Power | Speed | Estimated Torque (N·m) | Notes |
|---|---|---|---|---|---|
| 1 | Power & RPM | 2.2 kW | 1450 RPM | ≈ 14.50 | Small induction motor under rated load. |
| 2 | Power & RPM | 7.5 kW | 2900 RPM | ≈ 24.71 | Two-pole motor, higher speed reduces torque. |
| 3 | Electrical → Torque | 400 V, 12 A, PF 0.85, η 90% | 1450 RPM | ≈ 23.10 | Three-phase; computed from input power and efficiency. |
| 4 | Power & ω | 1.0 HP | 180 rad/s | ≈ 4.14 | Useful for drives reporting angular speed directly. |
Formula used
- Angular speed: ω = 2πN/60 where N is RPM and ω is rad/s.
- Torque from power: T = P/ω where P is mechanical power (W) and T is torque (N·m).
- Convenient form: T(N·m) = 9550 × P(kW) / N(RPM).
- Single-phase input power: P_in = V × I × PF.
- Three-phase input power: P_in = √3 × V × I × PF (V is line-to-line).
- Mechanical output from efficiency: P_out = P_in × η where η is efficiency as a fraction.
How to use this calculator
- Select a calculation method that matches your available data.
- Enter power and speed, or electrical inputs with efficiency and RPM.
- Pick the torque display unit and the required decimal precision.
- Click Calculate Torque to show results above the form.
- Use the export buttons to download CSV or PDF for records.
Notes and tips
- Measured RPM under load is better than nameplate RPM.
- For drives, ensure speed is the shaft speed, not electrical frequency.
- Efficiency and power factor vary with load; use real measurements when possible.
- Calculated torque is average shaft torque, not peak transient torque.
Electric Motor Torque Basics
Motor torque is the turning force at the shaft. It is expressed in N·m or lb·ft and depends on power and speed. Higher torque helps starts and heavy loads. This calculator normalizes units and reports consistent results.
Power–Speed–Torque Relationship
Mechanical power links torque and angular speed: P = T·ω. With speed in rpm, ω = 2πN/60. Rearranging gives T = P/ω. A handy shortcut is T(N·m) = 9550 × P(kW) / N(rpm) for quick checks.
Using Electrical Inputs Carefully
Electrical input is not shaft output. For AC motors, compute Pin using phase and power factor, then apply efficiency: Pout = Pin·η. Rated values are fine for sizing, while measured values improve accuracy.
Torque from Current for DC and Servo Motors
Many DC and servo motors provide a torque constant: T = Kt·I, where Kt is in N·m/A. In SI units, Kt is closely related to the back‑EMF constant. This method is useful for low-speed control, stall torque estimates, and verifying drive sizing. Always respect continuous and peak current limits to avoid overheating.
Rated, Continuous, and Peak Torque
Continuous torque is sustainable without exceeding temperature limits. Peak torque is allowed for short durations and depends on thermal mass and cooling. Duty cycle and airflow can change the safe continuous torque. Compare continuous torque to steady loads and peak torque to starts and shocks.
Units and Conversions You’ll See
Common conversions include 1 hp = 745.7 W and 1 N·m = 0.7376 lb·ft. Also, 1 N·m ≈ 141.6 oz·in for small motors. Torque rises when speed drops in constant-power systems. For example, a 2.2 kW motor at 1450 rpm delivers about 14.5 N·m using 9550×2.2/1450.
Practical Tips for Accurate Results
Use operating rpm under load. Include gearbox ratio and efficiency if torque is needed at the driven load. Confirm whether power is electrical input or mechanical output. Compare results with the datasheet torque-speed curve near limits.
FAQs
1) What inputs give the most reliable torque estimate?
Shaft output power and actual rpm are best. Nameplate kW and measured speed typically work well with T = 9550×P/N. Electrical inputs need efficiency to avoid overestimating shaft torque.
2) Why does torque change when rpm changes?
For constant power, torque is inversely proportional to speed. If power stays constant and rpm drops, torque rises. If the motor or drive is current-limited, torque can cap even as speed decreases.
3) How do I include gearbox effects?
Multiply motor torque by the gear ratio, then multiply by gearbox efficiency. Output torque ≈ Tmotor × ratio × ηgear. Output speed decreases by the same ratio: Nout ≈ Nmotor/ratio.
4) What’s the difference between stall and rated torque?
Stall torque is the torque at zero speed and is usually time-limited by heating. Rated torque is continuous torque the motor can deliver at rated conditions without exceeding temperature limits.
5) Can I estimate torque from voltage and current alone?
Only approximately. Compute input power using phase and power factor, apply efficiency for output power, then convert to torque with speed. For DC/servo motors, Kt·I is often more direct and accurate.
6) What units should I use for consistent results?
Use kW and rpm to apply T(N·m) = 9550×P/N directly. If using watts, use T = P/ω with ω in rad/s. Convert to lb·ft when needed for reporting or comparison.