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Induction Motor & Linear Induction Motors Formulas & Equations

Formulas and Equations for Linear and Induction Motors

The following equations and formulas related to linear and induction motors can be used to calculate the basic parameters while analyzing and designing a single phase and three phase induction motor.

Linear and Induction Motor Formulas and Equations

Formula and Equations for Induction Motor:

Induced EMF:

eind = vBl


  • eind = induced EMF
  • v = velocity of the rotor
  • B = magnetic flux density
  • l = length of conductors inside magnetic field

Rotor Current:

The rotor current is given by:
Rotor current of induction motor

Torque Induced:

Terms used in Motor Torque Equations and formulas.

  • Ns = Synchronous speed
  • s = slip of the motor
  • s= breakdown or pull-out slip
  • E1 = stator voltage or input voltage
  • E2 = Rotor EMF per phase at a standstill
  • R2 = Rotor Resistance Per Phase
  • X2 = Rotor Reactance Per Phase
  • V = supply voltage
  • K = rotor/stator turn ration per Phase

Starting Torque

Starting torque of induction motor

  • Maximum Starting Torque Condition

R= X2

  • Starting Torque Relation With Supply Voltage

Tst  α  V2

  • Torque In Running Condition

Torque in running condition of induction motorGross torque of induction motor

  • Gross Torque

Gross torque of induction motor

  • Maximum Running Torque Condition

R= sX2

  • Maximum Running Torque

Maximum running torque of induction motor

  • Breakdown Slip

Breakdown slip of induction motor

  • Torque Relation With Max Torque

Torque relation with max torque of induction motor

Slip Speed & Slip of Induction Motor:

Slip speed is the difference between synchronous speed and rotor speed;

  • Nslip = N­– N­                         (Speed in RPM)
  • ωslip = ω– ω­                        (Angular speed in Rad/sec)


  • N­­slip = Slip speed
  • Ns ­= Synchronous speed = 120f/P
  • N­­ = Rotor speed of motor

The slip of induction motor is a relative term expressed in percentage. It is given by:

Slip of Induction motor


Rotor Speed:

The rotor speed of induction motor is given by

  • N = (1-s)N               (Speed in RPM)
  • ω = (1-s) ω s             (Angular speed in Rad/sec)

Electrical Frequency on the Rotor: 

Electrical frequency on the rotor of induction motor


  • f = Rotor Frequency
  • f  = Line Frequency
  • P = Number of Poles

Power of Induction Motor:

Related terms used in Motor Power Formulas and Equation.

  • P1 = Stator input Power
  • P2 = Rotor Input power
  • Pm = Rotor Gross Output Power
  • Pout = Output Power
  • Tg = gross torque
  • Tsh = shaft torque

Rotor Input Power:

P2 = Tgωs

  • Rotor Gross Output Power:

Pm = Tgω

  • Output Power:

Pout = Tshω

P1 = P2 + stator Losses = P+ Rotor Copper Losses = Pout + Windage & friction Losses

Rotor Input Power: Output Mechanical Power: Rotor Cu loss ratio:

Power loss relation in induction motor


  • Pcr = I2R = rotor Copper loss

Synchronous Watt:

The torque at which the machine at synchronous speed will generate one watt;

Synchronous watt

Efficiency of Induction Motor:

  • Rotor Efficiency:

Rotor Efficiency of induction motor

  • Overall Efficiency

Overall Efficiency of induction motor

Formula & Equations for Linear Induction Motor:

Synchronous Speed:

Synchronous speed of linear induction motor

  • v = linear synchronous speed
  • w = width of one pole-pitch
  • f = line frequency


Slip of linear induction motor


  • v= linear synchronous speed
  • v = Actual speed

Thrust or Force:

Thrust Or Force of linear induction motor


P2 = Rotor input Power

Rotor Cu Loss:

Rotor Cu loss of linear induction motor

Gross Mechanical Power:Gross Mechanical Power of linear induction motor

Related Formulas and Equations Posts:

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One Comment

  1. In the article “Voltage And Power Equations of a DC Motor” the iron losses are also important. Those losses can not be neglected in real cases instead of ideal cases. By the way, it is interesting to use these equations to simplify the circuit analysis and calculations.

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