Find the shaft torque an electric motor delivers from its power rating and rotational speed, using the standard T = 9549 × P(kW) / N(rpm) relationship.
Quick Facts
Method
T (N·m) = 9549 × P(kW) / N(rpm) = P(W) / ω
Equivalent imperial shortcut: T (lb-ft) = 5252 × P(hp) / N(rpm). Torque is directly proportional to power and inversely proportional to speed.
Results
Calculated
Full-Load Torque
—
At rated power & speed, in N·m
Full-Load Torque
—
At rated power & speed, in lb-ft
Torque at Load Factor
—
Scaled by your load factor, in N·m
Angular Velocity
—
Shaft speed in radians per second
Ready
Enter power, speed, and load factor, then press Calculate.
Add this calculator to your website
How to use this calculator
Enter the motor's rated power (in kilowatts or horsepower), its rated speed in RPM, and the load factor — the percent of rated power it's actually delivering. Click Calculate to get the full-load torque, the torque at your specified load, and the shaft's angular velocity. Click Reset to restore the default example values.
The formula
Torque, power, and rotational speed are related by T = P / ω, where ω (omega) is the angular velocity in radians per second. Since ω = 2πN/60 for a speed N in RPM, this simplifies to the standard motor-sizing shortcuts:
Metric: T (N·m) = 9549 × P (kW) / N (RPM)
Imperial: T (lb-ft) = 5252 × P (hp) / N (RPM)
Both forms come from the same physics: mechanical power equals torque times angular velocity. The rated (nameplate) power of a motor is its output shaft power, so no efficiency adjustment is needed to get full-load torque — efficiency only matters when converting electrical input power to mechanical output power, which is a separate calculation.
Understanding the inputs
Motor Power Rating and Power Unit describe the nameplate rating (for example, 5 kW or 7.5 hp). Motor Speed (RPM) is the rated full-load speed shown on the nameplate — not the no-load synchronous speed, which is always somewhat higher due to slip in AC induction motors. Load Factor lets you scale the result to a partial load: since torque is proportional to power at constant speed, running at 75% of rated power delivers 75% of rated torque (at the same speed).
Interpreting the results
Full-Load Torque is the torque available when the motor is delivering its full rated power at its rated speed, shown in both N·m and lb-ft. Torque at Load Factor scales that figure by the load percentage you entered. Angular Velocity converts the rated RPM into radians per second, the unit the underlying physics equation uses directly.
Frequently Asked Questions
What is the formula for electric motor torque?
Torque equals power divided by angular velocity: T = P / ω. For a motor rated in kilowatts at a known RPM, this becomes the shortcut T (N·m) = 9549 × P (kW) / N (RPM). For horsepower, T (lb-ft) = 5252 × P (hp) / N (RPM). Both are the same relationship expressed in different unit systems.
Why does higher RPM mean lower torque for the same power?
Power is the rate at which torque does rotational work: P = T × ω. For a fixed power output, torque and angular velocity are inversely proportional — spin the shaft faster and it can only exert proportionally less twisting force. This is why high-RPM motors are typically paired with reduction gearboxes when high torque is needed.
Should I use rated (nameplate) power or electrical input power?
Use the rated shaft (output) power printed on the motor's nameplate — that is what the standard torque formula expects. Electrical input power is higher than shaft output power by the motor's efficiency (input × efficiency = output), so plugging in input power without adjusting for efficiency will overstate the torque.
What is the difference between full-load torque and starting torque?
Full-load torque, calculated here, is the steady-state torque a motor produces while running at its rated speed and power. Starting (locked-rotor) torque is a separate, typically higher, value produced the instant an induction motor is energized from a standstill, and it is not derived from the P/ω formula used for running torque.