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Motor Efficiency

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

\eta_m \;=\; \dfrac{ P_{out} }{ P_{in} } \cdot 100      (Motor Efficiency)

 P_{out} \;=\; \dfrac{ \eta_m \cdot P_{in} }{ 100 }

 P_{in} \;=\;  \dfrac{ P_{out} \cdot 100 }{ \eta_m }
Symbol English Metric
\eta_m  (Greek symbol eta) = Motor Efficiency dimensionless dimensionless
P_{out} = Output Power W kg-m^2 \;/\; s^3
P_{in} = Input Power W kg-m^2 \;/\; s^3

 

Single Phase Motor Efficiency Formula

  • Single phase motor efficiency is the measure of how effectively a single phase motor converts electrical energy into mechanical energy.

\eta_m \;=\; \dfrac{ 746 \cdot P_{out}  }{ I \cdot V \cdot PF }     (Single Phase Motor Efficiency)

P_{out} \;=\; \dfrac{ \eta_m \cdot I \cdot V \cdot PF }{ 746 }

I \;=\; \dfrac{ 746 \cdot P_{out}  }{ \eta_m \cdot V \cdot PF }

V \;=\; \dfrac{ 746 \cdot P_{out}  }{ \eta_m \cdot I \cdot PF }

PF \;=\; \dfrac{ 746 \cdot P_{out}  }{ \eta_m \cdot I \cdot V } 
Symbol English Metric
\eta_m  (Greek symbol eta) = Motor Efficiency dimensionless dimensionless
P_{out} = Output Power W kg-m^2 \;/\; s^3
I = Current A C \;/\; s
V = Voltage V kg-m^2 \;/\; s^3-A
PF = Power Factor dimensionless dimensionless

 

 Three Phase Motor Efficiency Formula

  • Three phase motor efficiency is the percentage of input electrical power that a three phase motor converts into usable mechanical power.

\eta_m \;=\; \dfrac{ 746 \cdot P_{out}  }{ 1.732 \cdot I \cdot V \cdot PF}      (Three Phase Motor Efficiency)

P_{out} \;=\; \dfrac{ \eta_m \cdot 1.732 \cdot I \cdot V \cdot PF }{ 746 }

I \;=\; \dfrac{ 746 \cdot P_{out} }{ \eta_m \cdot 1.732 \cdot V \cdot PF }

V \;=\; \dfrac{ 746 \cdot P_{out} }{ \eta_m \cdot 1.732 \cdot I \cdot PF }

PF \;=\; \dfrac{ \eta_m \cdot 1.732 \cdot I \cdot V }{ 746 \cdot P_{out} }
Symbol English Metric
\eta_m  (Greek symbol eta) = Motor Efficiency dimensionless dimensionless
P_{out} = Output Power W kg-m^2 \;/\; s^3
I = Current A C \;/\; s
V = Voltage V kg-m^2 \;/\; s^3-A
PF = Power Factor dimensionless dimensionless

   

Motor Efficiency Formulas

V = Voltage  -  I = Amps  -  PF = Power Factor  -  \eta = Efficiency  -  HP = Horsepower
To Find Direct Curren Alternating Current
Single Phase Two Phase Four Wire Three Phase
Efficienty \large{\frac{ 746 \; HP }{ V \; I } } \large{\frac{ 746 \; HP }{ V \; I  \; PF} } - \large{\frac{ 746 \; HP }{ 1.732 \; V \; I  \; PF} }

 

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