Physics Formulas

Horsepower Formula

Horsepower is like any other unit of power. It is simply a rate at which work is being done. This horsepower unit originates from an experiment. This experiment was set out to measure the power of a single horse. It was determined that a horse is capable of doing 33,000 ft-lbf of work per minute. We will address to this number later in the explanation. To represent the efficiency of a person or a machine for performing some task, horsepower is used as a reliable unit. In this article, we will discuss the horsepower formula. Let us begin learning!

Horsepower Formula

What is horsepower?

Horsepower is a popular imperial unit of power of an engine. It is defined as the work done by a person or machine per unit amount of time. This term of Horsepower was invented by James Watt. It is a unit of power that compares the power of a machine to the muscle power of the horse.

In earlier days it was used to measure steam engine power output compared to the power of draft horses. But later on, its usage was expanded to different types of piston engines, electric motors, turbines, and other machinery.

Horsepower Formula

The formula for Horsepower calculation:

First, we will see some equations to help in calculating the horsepower:

Power = \( \frac{work}{time} \)

For the electric motors, we can calculate the power or horsepower from the torque and speed. For example, if we have a motor with 3,000 rpm and 6 in-lbf then the horsepower can be calculated below.

Horsepower =  \( \frac{300 × 6}{63025} \)

i.e. horsepower = 0.286

Here, 63025 is a constant when using rpm for speed and in-lbf for torque units. 5252 is another common constant if the speed is in rpm and torque is in ft-lbf. If the units are different then first we have to make the unit conversion.

Get the huge list of Physics Formulas here

The derivation of these constants is as follows:

33,000 ft-lbf /min = 1 horsepower.

Though horsepower units is a derivative of the 33,000 ft-lbf / min, it is not critical to understanding how to calculate motor horsepower for speed and torque.

Another common but popular unit of power that motors are rated in is watts. The conversion from watts to horsepower is:

745.7 watts = 1 horsepower

Or 1 hp =746 watt.

Also, One Horsepower equals to 33,000 lb. ft/min.

Horsepower formula is:

Horsepower = \( \frac{Torque × speed}{5252} \)

With another computation,

Horsepower = weight ×  \( \frac{velocity}{(234)^2} \)

Solved Examples on Horsepower Formula

Q.1: Determine the horsepower of a vehicle which moves with a speed of 500 revolutions per minute and has a torque of 100 pound-foot.


Given parameters in the problem are:

Torque = 100 pound foot

Speed = 500 revolutions per minute

Now we may apply the Horsepower formula as below:

Horsepower =  \( \frac {Torque × Speed }{ 5252 } \)

Substituting the known values, we get

Horsepower =  \( \frac { 100 × 500 }{ 5252 }\)

= \( \frac{ 50000 } { 5252 }\)

Horsepower = 9.52 HP

Therefore the horsepower of the engine of the vehicle will be 9.52 HP.

Share with friends

Customize your course in 30 seconds

Which class are you in?
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
Ashhar Firdausi
IIT Roorkee
Dr. Nazma Shaik
Gaurav Tiwari
Get Started

Leave a Reply

5 Comment threads
0 Thread replies
Most reacted comment
Hottest comment thread
5 Comment authors
Yashdeep tiwariKwame DavidumerMalek safrinRoger Carmichael Recent comment authors
newest oldest most voted
Notify of
Roger Carmichael

Typo Error>
Speed of Light, C = 299,792,458 m/s in vacuum
So U s/b C = 3 x 10^8 m/s
Not that C = 3 x 108 m/s
to imply C = 324 m/s
A bullet is faster than 324m/s

Malek safrin

I have realy intrested to to this topic


m=f/a correct this

B. Akshaya
B. Akshaya


Kwame David

Interesting studies

Yashdeep tiwari
Yashdeep tiwari

It is already correct f= ma by second newton formula…

Customize your course in 30 seconds

Which class are you in?
No thanks.