Motor Torque, Synchronous Speed and Slip Calculator

Find the shaft torque from the power and speed (or the power from the torque), the synchronous speed and slip of an induction motor, and the running cost.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Power is torque times angular speed. With the power in kilowatts and the speed in rev/min, the torque in newton metres is about 9549 times the power divided by the speed.

The rotating field of an induction motor runs at 120 times the frequency divided by the number of poles. The shaft turns a little slower. The difference as a share of the field speed is the slip.

Formulas used

  • T = \dfrac{60\,000\,P}{2\pi N}
  • N_s = \dfrac{120 f}{p}
  • s = \dfrac{N_s - N}{N_s}

Worked example

With the default numbers in the calculator above:

  1. Shaft torque: 99.47 N·m
  2. Shaft power: 15.00 kW
  3. Synchronous speed of the rotating field: 1500.00 rev/min
  4. Slip: 4.00 %
  5. Electrical input at the motor efficiency: 16.67 kW
  6. Energy used in a year: 66666.67 kWh
  7. Running cost per year at the assumed price: $20000.00

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Why do some sheets use 9.55?

With the power in kilowatts the factor is 9549. The 9.55 figure gives kilonewton metres for a power in kilowatts, which is a thousand times smaller than the torque in newton metres.

Is this the starting torque?

No. It is the rated full-load torque. The starting torque is a multiple of it and comes from the motor curve.

Related calculators

Further reading: Standard electrical and mechanical engineering texts (motor torque, power and speed).

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