Horsepower Versus Torque

Since this discussion happens so often, as it has, again, on the previous post, it's about time we explain horsepower and torque and how they relate. There are a lot of misconceptions, but there doesn't have to be because both are straightforward terms used everyday when motor vehicles (and a lot of other things) are discussed.
Please read this entire article carefully before commenting. You'll see where that 5252 number comes from and you'll see why you can't talk about horsepower and disregard torque anymore than you can discuss an omelet and ignore the eggs.

You gotta start somewhere, this is a good place.

Every motorhead wants more horsepower, but what exactly IS horsepower? What does it measure? Horsepower is an arbitrary unit created from a common reference point that everyone can understand. In today's world of advanced scientific instruments, horsepower hangs on, even though it is a little imprecise. Those keepers of the units and standards that quantify everything with precision would rather toss out this well known measure and substitute kilowatts. That Corvette has 298.28 kilowatts, hmm... 400hp just sounds better.

Where did horsepower come from?

James Watt, who did quite a bit of work on steam engines back in the 1700's, needed a way to measure their output. Watt used a common reference, the horse, as the basis for his calculations (like the inch was based on the width of a man's thumb). The exact process he followed to find out what a horse could do is open to speculation, everyone seems to have their own favorite story, but the end result was: 1 horsepower = 550 foot-pounds per second, which means, in Watt's calculations, a horse can lift 550 pounds one foot in one second.

Important note: There are only seven base units of measurement: length, time, mass, temperature, electric current, amount of substance and luminous intensity. Each unit can be determined by scientifically reproducible results (no more horses and thumbs!) and all units and standards used today can be derived from those basic seven. An international system, SI, maintains the agreed upon standards for all of these basic units.

Horsepower conversion formulas

The neat thing about defining a reference point with numbers is how easy it is to convert that reference to some other unit of measure.
1 horsepower = 550 foot-pounds/second
1 horsepower = 33,000 foot-pounds/minute
1 horsepower = .7456999 * kilowatts
1 kilowatt = 1.34102 * horsepower

Horsepower is one measure of power

All of those formulas and conversions are different ways of saying how much work is being done, which is exactly what power is. Power is work done over time.
P = W / t
where P is power, W is the work done and t is time.
Watts are the more common term for measuring power which is why the conversion to and from horsepower is good to know. One watt is 1 joule/second. And that can be converted to ... well, you'll have to do the rest of that research yourself because we could go on forever.

Torque - what is it?

Now, remember that figure of 550 foot-pounds? We said that 1 horsepower was equal to 550 foot-pounds "per second." It's important to see that "per second" because horsepower is a calculation not a measurement. Think about that. It means you don't actually measure horsepower, you measure that force exerted through a distance over a period of time and make a calculation that results in a number, the number is horsepower. That force being measured is torque.
Cars, motorcycles and most everything we are interested in here have engines that turn wheels. The twisting force necessary to turn them is torque. Torque can be measured in several different units but, because it's more familiar here in the US, we'll stick to foot-pounds . If you were to attach a one foot long wrench to a bolt and apply one pound of pressure to the end of the wrench, you would be applying one foot-pound of torque to the bolt. So,... torque is a twisting force measured (in our examples) in foot-pounds.

Torque to horsepower conversion

Now we need just a little math, it's easy but you will have to pay attention. Suppose we attach that one foot wrench to the end of a crankshaft and the engine rotates one revolution against that one pound of resistance. The end of the wrench will move 6.2832 feet (Pi * a two foot diameter circle) against a one pound weight. The end result is 6.2832 foot-pounds of work done at one foot-pound of torque.

Remember Pi? That's the ratio of the circumference of a circle to its diameter. Pi is a constant equal to 3.14159 carried for as many decimal points as you wish.

OK, here we go:
1 horsepower = 550 foot-pounds/second = 33,000 foot-pounds/minute
33,000 foot-pounds / 6.2832 foot-pounds = 5252  (Here's where 5252 comes from!)
So, if the engine rotates against the one pound resistance at 5252 rpm:
6.2832 X 5252 = 33,000 foot-pounds/minute = 1 horsepower
because the one pound of resistance was moved 33,000 feet in one minute
(1 foot-pound X 5252) / 5252 = 1

Therefore, to convert torque to horsepower:

(Torque X RPM) / 5252 = Horsepower
Example: 100 foot-pounds * 4000 rpm / 5252 = 76.16 horsepower
Example: 200 foot-pounds * 8000 rpm / 5252 = 304.65 horsepower
If you understand the above relationship, you'll quickly see there is a lot of misunderstanding floating around. Both terms are important but they represent different things. Torque measures a force being applied while horsepower is a measure of how much work the force can do.

by Paul Crowe on 4/21/2013
Original Story can be seen HERE