Induction Motor Calculator: Torque, Slip, Starting Torque, Efficiency and Torque-Speed Curve
Analyse a three-phase induction motor from its equivalent circuit values and get the torque, slip, starting and maximum torque and efficiency.
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How this calculator works
Enter the supply voltage and connection, the frequency, the number of poles and the stator and rotor resistance and leakage reactance per phase (referred to the stator). Enter the slip you want to analyse.
The calculator finds the synchronous speed and rotor speed, the phase current and power factor, the air-gap power, the mechanical power developed, the rotor copper loss, the torque and the efficiency.
It then gives the starting current and torque, the slip and the maximum (pull-out) torque, and draws the torque-speed curve with the operating, starting and maximum torque points marked.
Formulas used
- N_s = \frac{120f}{p}
- P_{ag} = \frac{3I^2R_2}{s}
- T = \frac{P_{ag}}{\omega_s}
- s_m = \frac{R_2}{\sqrt{R_1^2 + (X_1+X_2)^2}}
- T_{max} = \frac{3V^2}{2\omega_s\left(R_1 + \sqrt{R_1^2 + (X_1+X_2)^2}\right)}
Worked example
With the default numbers in the calculator above:
- Synchronous speed: 1500.00 rev/min
- Rotor speed at this slip: 1440.00 rev/min
- Phase voltage and current (magnetising branch neglected): 22.42 A at power factor 0.98 lagging
- Air-gap power (power crossing to the rotor): 15.07 kW
- Mechanical power developed and rotor copper loss: 14.47 kW and 0.60 kW
- Torque at this slip: 95.97 N m
- Shaft output and efficiency (stator copper loss included, iron loss neglected): 14.17 kW out, efficiency 89.53 %
- Starting current and torque (slip = 1): 109.25 A (4.87 times the running current) and 91.18 N m
- Slip and speed at maximum torque: 19.40 % slip, 1208.96 rev/min
- Maximum (pull-out) torque: 214.01 N m (2.23 times the torque at this slip)
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
What is slip?
The difference between the synchronous speed and the rotor speed as a fraction of the synchronous speed. It is about 2 to 6 percent at full load.
Does rotor resistance change the maximum torque?
No. It changes the slip at which the maximum torque occurs, so more rotor resistance gives more starting torque. It does not change the maximum value.
How does supply voltage affect torque?
Torque goes as the square of the voltage, so a 10 percent drop in voltage gives about 19 percent less torque.
Why is the power factor so high?
This approximate circuit ignores the magnetising current, which is what makes a real motor power factor lower. The torque and slip results are still good.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Fitzgerald, Kingsley and Umans, Electric Machinery (induction machines); Chapman, Electric Machinery Fundamentals.
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