# 3 Phase Motor Efficiency Formula & DC motor Efficiency Calculation

### 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 = Po / Pi

Efficiency is always mentioned in percentage %

η = Po x 100 / Pi

Pi in watts is equal to the product of input voltage Vi in volts input current Ii in amps

Pi = Vi x Ii

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 – ((I2*R) + We + Wm))

### 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.

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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 VL x IL 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 IL2 x Rstator

Here RStator is the stator resistance of the coil.

Rotor Copper loss = 3 x I2r2 x R(rotor)

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