### Motor efficiency formula:

Motor efficiency η is equal to the ratio between the output power P_{(o)} in watts to input power P_{(i)} in watts.

η = P_{o} / P_{i}

Efficiency is always mentioned in percentage %

η = P_{o} x 100 / P_{i}

P_{i} in watts is equal to the product of input voltage V_{i} in volts input current I_{i} in amps

P_{i }= V_{i} x I_{i}

This is the basic formula for motor efficiency calculation.

### DC motor efficiency:

Let us take Motor Output = V x I

Motor Input = motor output + Loss

DC motor has three losses such as copper losses, iron losses and mechanical losses.

Hence the motor output = Input – (Copper loss + iron loss + Mechanical loss)

The motor efficiency formula become,

η = Output / (Input – (Copper loss + iron loss + Mechanical loss))

η = (V*I) / (VI – ((I^{2}*R) + W_{e} + W_{m}))

### Efficiency for 3 phase AC motors:

AC motor efficiency is equal to the net output at the shaft to net electrical input to the motor

% η = Net output of the shaft / net electrical input.

Here the net input P_{(input)} in watts is equal to the 1.732 to times of the current and voltage and power factor.

P_{(input)} = 1.732 x V_{L} x I_{L} x pf

The mechanical power is equal to net input electrical power P_{(input) }minus total losses including stator copper loss, rotor copper loss and mechanical friction losses.

P_{(mechanical)} = P_{(input) }– (Stator loss + Rotor copper loss + mechanical loss)

Here starter copper loss = 3 x I_{L}^{2} x R_{stator}

Here RStator is the stator resistance of the coil.

Rotor Copper loss = 3 x I_{2r}^{2} x R_{(rotor)}

Here the 3 phase motor efficiency formula can be written as,

I2r is the rotor input current in amps.

R_{(rotor)} is the rotor resistance in ohms.

R_{(stator)} stator coil resistance in ohms

Also, note that the maximum efficiency of the motor can be archived when the variable loss is equal to the constant loss of the motor

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