# Horsepower

on . Posted in Fluid Dynamics

Horsepower, abbreviated as HP, is a measure of power or the rate of doing work.  It is typically used to describe the work of an engine or machine and is the equivalent of moving 33,000 pounds through the distance of one foot in one minute.  In the context of engines, horsepower is used to measure the power output of an engine.  It is calculated by measuring the torque (rotational force) produced by the engine and multiplying it by the engine's rotational speed.

### Horsepower Index

Horsepower is commonly used to compare the performance of different engines and vehicles.  A higher horsepower rating generally indicates a more powerful engine, which can result in better acceleration, higher top speed, and greater towing or hauling capacity.  However, horsepower alone does not tell the whole story of an engine's performance, as factors such as torque, fuel efficiency, and emissions must also be considered.

### Horsepower formula

$$HP = F \; d \;/\; t$$     (Horsepower)

$$F = HP \; t \;/\; d$$

$$d = HP \; t \;/\; F$$

$$t = F \; d \;/\; HP$$

Symbol English Metric
$$HP$$ = horsepower $$lbf-ft\;/\;sec$$ $$J\;/\;s$$
$$F$$ = force $$lbf$$ $$kg-m^2\;/\;s^2$$
$$d$$ = distance $$ft$$ $$m$$
$$t$$ = time $$sec$$ $$s$$

### Amps to Horsepower formula

$$HP = I \; V \; \eta \; PF \;/\; 746$$     (Amps to Horsepower)

$$I = HP \; 746 \;/\; V \; \eta \; PF$$

$$V = HP \; 746 \;/\; I \; \eta \; PF$$

$$\eta = HP \; 746 \;/\; I \; V \; PF$$

$$PF = HP \; 746 \;/\; I \; V \; \eta$$

Symbol English Metric
$$HP$$ = horsepower $$lbf-ft\;/\;sec$$ $$C\;/\;s$$
$$I$$ = amps $$I$$ $$kg-m^2\;/\;s^2$$
$$V$$ = voltage $$V$$ $$kg-m^2 \;/\; s^3-A$$
$$\eta$$ (Greek symbol eta) = efficiency $$dimensionless$$
$$PF$$ = power factor $$dimensionless$$

### Motor Horsepower Formulas

$$V$$ = Voltage  -  $$I$$ = Amps  -  $$PF$$ = Power Factor  -  $$\eta$$ = Efficiency  -  $$HP$$ = Horsepower

To Find Direct Current Alternating Current
Single Phase Two Phase Four Wire Three Phase
Horsepower $$\large{\frac{ V \; I \; \%\eta }{ 746 } }$$ $$\large{\frac{ V \; I \; \%\eta \; PF }{ 746 } }$$ $$\large{\frac{ V \; I \; \%\eta \; PF \; 2 }{ 746 } }$$ $$\large{\frac{ V \; I \; \%\eta \; PF \; 1.73 }{ 746 } }$$

### horsepower conversion Factor

• 1 boiler horsepower = 9,809.5 W
• 1 horsepower = 745.699872 or 746 W
• 1 horsepower = 0.746 kW
• 1 Metric horsepower = 735.49875 W
• 1 horsepower = 33,000 lb-ft/min
• 1 horsepower = 550 lb-ft/s
• 1 horsepower = 2544.434187 or 2545 BTU
• 1 horsepower = 3960 gal/min/foot
• 1.341 horsepower = 1 kW
• 1 cu-ft/sec = 448 GPM
• 1 PSI = a head of 2.309 ft (water weight)
• 1 horsepower = 5252 RPM  -  When charting torque and horsepower, the math always cross at 5252 RPM.

### horsepower conversion

Multiply By To Get
2545.45766 BTU per hour, BTU/hr
42.42429433 BTU per minute, BTU/min
0.707071572 BTU per second, BTU/sec
1980796.979 foot pound-force per hour
33013.28298 foot pound-force per minute
550.221383 foot pound-force per second
1 horsepower, hp
17702.8489 pound square foot per cubic second
0.212121472 ton of refrigeration, ton
2.6856E+13 dyne centimeter per hour
4.476E+11 dyne centimeter per minute
7460000000 dyne centimeter per second
2685600 joule per hour
44760 joule per minute
746 joule per second
746 watt, W
0.746 kilowatt, kW
0.000746 megawatt, MW
0.000000746 gigawatt, GW
2685600 newton meter per hour
44760 newton meter per minute
746 newton meter per second

Tags: Torque Horsepower