# Shaft Power from Electrical Motors

## Electrical motors are rated in horsepower or watts

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Power is in general rated in *watt (W)* or *horsepower (hp)*. The old imperial unit *horsepower* is equal to *746 watts (0.745 kW)* or *33000 lb ft per minute* (or *550 lb ft per second*).

The unit of electric power - *1 watt* - is equal to the power produced by an electrical current of *1 amp* at a potential difference of *1 volt*.

*1 watt = 1/746 hp**1 hp = 746 watts = 0.76 kW*

### Shaft Power in watts

#### Direct Current - DC

Shaft power produced from a *direct current (DC)* electrical motor:

*P _{shaft_kW} = η_{m} U I*

*/ 1000 (1)*

*where*

*P _{shaft_kW}* =

*shaft power (kW)*

*η _{m}*

*= motor efficiency*

*U** = voltage (V)*

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

#### Alternating Current - AC

Shaft power produced from an *alternating current (AC)* electrical motor:

##### Single Phase

*P _{shaft_kW}* = η

_{m}U I

*PF / 1000 (1b)*

*where *

*PF = Power Factor*

##### Two Phase Four Wire

* P_{shaft_kW}* = η

_{m}2 U I

*PF / 1000 (1c)*

##### Three Phase

* P_{shaft_kW}* = η

_{m}1.73 U I

*PF / 1000 (1d)*

### Shaft Power in hp

Shaft power as horse power:

P_{shaft_hp}=/ 0.746P_{shaft_kW}(2)

or for a DC motor

P= (η_{shaft_hp}_{m}U I / 1000) / 0.746

=η(2b)_{m}U I / 746

where

P=_{shaft_hp}shaft power (hp)

#### Example - Shaft Power Electric Motor

The shaft power produced by an electric direct current motor with *230 V, **85%* efficiency and *10 amps* - can be calculated in *watts* as

P= 0.85 (230 V) (10 amps) / 1000_{shaft_kW}

= 1.96 kW

The shaft power as *hp*

P= (1.96 kW) / 746_{shaft_hp}

= 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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