The calculation, without hidden assumptions
Solve the shaft relationship between torque, mechanical power and rotational speed without mixing electrical input power into shaft output. Choose the unknown, enter the other two values, and MAXScanner shows the SI derivation plus practical N·m, lb·ft, kW and mechanical-horsepower equivalents.
How to use this calculator
Choose whether torque, shaft power or speed is unknown.
Enter the two known shaft quantities using mechanical output power, not electrical input kW.
Read the solved value plus equivalent torque/power units and angular speed.
Use the substituted working to verify the exact operating point.
For induction motors, continue to Motor Slip when you need synchronous-versus-shaft-speed analysis.
Where people use it
- •Checking rated shaft torque from motor kW and nameplate RPM.
- •Converting dynamometer torque and RPM to mechanical shaft power.
- •Finding required RPM for a known power and torque operating point.
- •Comparing gearmotor operating points before detailed gearbox sizing.
Example: 7.5 kW at 1,450 rpm
Angular speed is about 151.844 rad/s. Torque = 7,500 ÷ 151.844 = 49.393 N·m, about 36.43 lb·ft. This is running shaft torque at that operating point, not starting torque.
What the result does not assume
- •Use mechanical shaft output power. Electrical input power is higher when motor losses are present; use Motor Efficiency when converting between electrical input and shaft output.
- •The relationship describes one steady operating point. It does not predict starting, locked-rotor, pull-up or breakdown torque.
- •Real motors have speed-torque curves; constant-power comparisons across speed are scenarios, not proof that a particular motor can operate at every point.
- •Zero RPM with nonzero shaft power is physically incompatible with P=Tω, so torque from power at zero speed is rejected.
- •Gearbox output torque also depends on ratio and drivetrain efficiency; this owner does not invent those values.
Frequently asked questions
What is the motor torque formula from kW and RPM?+
T = 60,000×P(kW)/(2π×RPM), commonly approximated as 9549.3×kW/RPM.
Is motor kW electrical input or shaft output?+
For this torque relationship use mechanical shaft power. Electrical input must be adjusted for motor efficiency before treating it as shaft output.
How do I calculate motor power from torque and RPM?+
P(kW)=T(N·m)×2π×RPM/60,000.
Can this calculate starting torque?+
No. Starting and breakdown torque require motor-specific speed-torque data or manufacturer values.
Why does torque rise when RPM falls at the same power?+
Because P=Tω. Holding power constant means torque is inversely proportional to angular speed.
Can I solve RPM from torque and power?+
Yes. With positive torque, RPM=60,000×P(kW)/(2π×T).
Semantic next steps
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