# Power and Horsepower in Electrical Motors

## Electrical power is rated in Horsepower or Watts

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Electrical power is in general rated in watt (W) or horsepower (HP). A horsepower is a unit of power equal to *746 watts* or *33,000 lb.ft per minute* (or *550 lb.ft per second*).

A watt is equal to the power produced by a current of *1 amp* across the potential difference of *1 volt*. A watt is *1/746* of *1 horsepower*.

Even if the watt is the base unit of electrical power, it is common to rate motor power in either horsepower or kilowatts.

### Power in Watts

#### Direct Current

Electric power supply to a direct current (DC) motor can be expressed as:

*P _{kW} = η_{m} U I*

*/ 1000 (1)*

*where*

*P _{kW} =*

*power (kW)*

*η _{m}*

*= motor efficiency*

*U** = voltage (V)*

*I** = current (A, amps)*

Electric power supply to a alternating current (AC) motor can be expressed as:

#### Single Phase

*P _{kW}* = η

_{m}U I

*PF / 1000 (1b)*

*where *

*PF = Power Factor*

#### Two Phase Four Wire

*P _{kW}* = η

_{m}2 U I

*PF / 1000 (1c)*

#### Three Phase

*P _{kW}* = η

_{m}1.73 U I

*PF / 1000 (1d)*

### Power in Horsepower

Horse power can be expressed as:

P_{hp}=P/ 0.746_{kW}(2)

or

P_{hp}= (η_{m}U I / 1000) / 0.746

=η(2b)_{m}U I / 746

where

P_{hp}=horsepower (hp)

#### Example - Power and Horsepower of Electric Motor

The power consumption of a *230 V* electrical direct current motor with *85%* efficiency, pulling *10 amps* can be calculated as

P_{kW}= 0.85 (230 V) (10 amps) / 1000

= 1.96 kW

The horse power can be calculated as

P_{hp}= 0.85 (230 V) (10 amps) / 746

= 2.62 hp

*Standard Horsepower Ratings*

Standard horsepower ratings of electrical motors - 1 to 4000 hp are indicated below:

- 1, 1 1/2, 2, 3, 5, 7 1/2, 10, 15, 20, 25, 30, 40, 50, 60, 75, 100, 125, 150, 200, 250, 300, 350, 400, 450, 500, 600, 700, 800, 900, 1000, 1250, 1500, 1750, 2000, 2250, 2500, 3000, 3500, 4000

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