# Motor Efficiency

on . Posted in Rotating Equipment

Motor efficiency, abbreviated as $$\eta_m$$ (Greek symbol eta), a dimensionless number, is the ratio of useful mechanical power output to the electrical power input in an electric motor.  It measures how effectively an electric motor converts electrical energy into mechanical work or output power.  Motor efficiency is important to consider when evaluating the performance and energy consumption of electric motors.

In an ideal situation, where there are no losses, the efficiency would be 100%.  However, real world motors always have some level of losses due to factors such as resistance in the windings, friction, and other mechanical losses.  These losses result in a reduction of the overall efficiency of the motor.

Efficiency matters because more efficient motors consume less energy to achieve the same level of mechanical output, leading to reduced energy costs and lower environmental impact.  When selecting a motor for a specific application, choosing a motor with higher efficiency can result in long term energy savings and improved overall system performance.

## Motor Efficiency formula

$$\large{ \eta_m = \frac{ P_{out} }{ P_{in} } }$$     (Motor Efficiency)

$$\large{ P_{out} = \eta_m \; P_{in} }$$

$$\large{ P_{in} = \frac{ P_{out} }{ \eta_m } }$$

Symbol English Metric
$$\large{ \eta_m }$$  (Greek symbol eta) = motor efficiency   $$\large{dimensionless}$$
$$\large{ P_{out} }$$ = output power $$\large{\frac{ft-lbf}{sec}}$$  $$\large{kg\;m^2\;s^{-3}}$$
$$\large{ P_{in} }$$ = input power $$\large{\frac{ft-lbf}{sec}}$$  $$\large{kg\;m^2\;s^{-3}}$$

## One Phase Motor Efficiency formula

$$\large{ \eta_m = \frac{ 746 \; P_{out} }{ I \; V \; PF } }$$     (One Phase Motor Efficiency)

$$\large{ P_{out} = \frac{ \eta_m \; I \; V \; PF }{ 746 } }$$

$$\large{ I = \frac{ 746 \; P_{out} }{ \eta_m \; V \; PF } }$$

$$\large{ V = \frac{ 746 \; P_{out} }{ \eta_m \; I \; PF } }$$

$$\large{ PF = \frac{ 746 \; P_{out} }{ \eta_m \; I \; V } }$$

Symbol English Metric
$$\large{ \eta_m }$$  (Greek symbol eta) = motor efficiency   $$\large{dimensionless}$$
$$\large{ P_{out} }$$ = output power $$\large{\frac{ft-lbf}{sec}}$$  $$\large{kg\;m^2\;s^{-3}}$$
$$\large{ I }$$ = current $$\large{A}$$ $$\large{\frac{C}{s}}$$
$$\large{ V }$$ = voltage $$\large{V}$$ $$\large{\frac{kg-m^2}{s^3-A}}$$
$$\large{ PF }$$ = power factor $$\large{dimensionless}$$

## Three Phase Motor Efficiency formula

$$\large{ \eta_m = \frac{ 746 \; P_{out} }{ 1.732 \; I \; V \; PF } }$$     (Three Phase Motor Efficiency)

$$\large{ P_{out} = \frac{ \eta_m \; 1.732 \; I \; V \; PF }{ 746 } }$$

$$\large{ I = \frac{ 746 \; P_{out} }{ \eta_m \; 1.732 \; V \; PF } }$$

$$\large{ V = \frac{ 746 \; P_{out} }{ \eta_m \; 1.732 \; I \; PF } }$$

$$\large{ PF = \frac{ \eta_m \; 1.732 \; I \; V }{ 746 \; P_{out} } }$$

Symbol English Metric
$$\large{ \eta_m }$$  (Greek symbol eta) = motor efficiency   $$\large{dimensionless}$$
$$\large{ P_{out} }$$ = output power $$\large{\frac{ft-lbf}{sec}}$$  $$\large{kg\;m^2\;s^{-3}}$$
$$\large{ I }$$ = current $$\large{A}$$ $$\large{\frac{C}{s}}$$
$$\large{ V }$$ = voltage $$\large{V}$$ $$\large{\frac{kg-m^2}{s^3-A}}$$
$$\large{ PF }$$ = power factor $$\large{dimensionless}$$ Tags: Efficiency Motor