A Staff Report from the Straight Dope Science Advisory Board

What's the difference between horsepower and torque?

July 19, 2005

Dear Straight Dope:

There is a question on the table that I would like to be able to answer before my friend can so that I can seem like the smart guy: What is the difference between an engine's horsepower and torque? Apparently, this is a question that neither reference manuals or mechanics can give a satisfactory answer to. If any genius in the world can get this straight, you can.

Dear Straight Dope:

I was looking to buy my first car and had a question come to mind. What is "horsepower"? How is it measured? I'm sure it has something to do with how much a horse could pull, not how many horses could be pulled. But what horse breed do they use, and what's it pulling?

Measures of engine performance such as torque and horsepower are relatively simple, yet are often badly misunderstood by the public. Some of this misunderstanding is due to automobile advertising, some to people having just enough knowledge to be dangerous, and some to the continuing death-spiral of science education in America. I'll begin by explaining power vs. horsepower, then torque and how it is related to power. Finally I'll give examples of why knowing something about these concepts is important when comparing automobile engines.

First, let’s note that horsepower is a unit of measurement for power, in the scientific sense of the term, just as the foot is a unit of measurement for length. Horsepower measures the same thing that the watt does--the power that a device can create or consume. Just as the wattage of a light bulb tells you how much power it will use, the horsepower specification for an engine tells you how much power the engine can produce. 

Power is measured in many other units besides horsepower, depending on location and application. Watts (W) and kilowatts (kW) are in common use worldwide. Less common measures include British thermal units per hour (Btu/hr) and foot-pound force per minute (ft-lbf/min). Since any or all of these could be valid performance measures, technically it's more correct to talk about an engine's power than its horsepower. However, in practice most people in the United States use the two words synonymously. 

Standard mechanical horsepower is defined as about 33,000 ft-lbf/min, or 745.7 watts. However, there are many different official and unofficial definitions of horsepower. Some of these definitions refer to different ways of measuring power for a specific application. For example:

  • “Brake horsepower” generally means that the power was measured on a type of dynamometer called a “prony brake" (sometimes incorrectly called a “pony brake”--prony refers to the inventor, Gaspard de Prony)
  • “Drawbar horsepower,” used in railroad applications
  • “Air horsepower,” used in fan calculations.

Some types of horsepower define power at different magnitudes. Listing them in terms of relationship to the standard horsepower, we see:

Definition Watts ft-lbf/min
Horsepower (also called “standard” or “mechanical”) 745.7 33,000
Boiler horsepower 9,809.5 434,107
Electric horsepower 746 33,013.3
Metric horsepower 735.499 32,548.6
Water horsepower 746.043 33,015.2

How did we end up with the “horse” in horsepower? The term was coined by James Watt (1736-1819), the British inventor best known for his improved steam engines, who used the term to relate steam engine performance to that of horses. At the time horses were the primary energy source for applications ranging from pumping water from mines and turning grinding mill wheels to pulling carts and loads. Although sources differ on exactly how Watt arrived at the number, it’s generally thought that in 1782, he noted how quickly a brewery horse could turn a mill wheel of a certain radius, estimated the amount of force the horse needed to exert to turn the wheel, did the math, and came up with a value of 32,400 ft-lbf/min, later rounded to 33,000 ft-lbf/min. Comparing the power output of a steam engine to an equivalent number of horses was an easy way for prospective engine purchasers to compare power ratings, so the term stuck. 

What type of horse was a brewery horse? In England at the time a work horse most likely would have been one of the three British "heavy breeds" – the Suffolk punch, the shire horse, and the Clydesdale. The Clydesdale is said to have originated in the latter 1700s, perhaps too late to be a common work horse at the time Watt was doing his horsepower calculations. So it seems likely the horse in question was either a Suffolk punch or a shire horse.

Now let’s talk torque. Torque is turning force, which for automotive applications is most often measured in either foot-pounds (ft-lbf) or Newton-meters (N-m). Sometimes these are written as lbf-ft or m-N, a convention some use to differentiate torque from work, since they involve the same units . . . but I digress.

Here's a simple way to visualize torque: Imagine holding a 1-pound weight straight out, with your arm parallel to the ground. My arm measures about two feet from shoulder to wrist. If I hold a 1-pound weight straight out, the torque my shoulder experiences is roughly 2 foot-pounds (2 feet times 1 pound). If I were to hold a 10 pound weight in my hand, then the torque on my shoulder would be roughly 20 foot-pounds (2 feet times 10 pounds).

Now think of this turning force applied to a wheel, such as if a lever was attached to the center of an automobile wheel. The more force you apply on that lever, the more torque you apply to the wheel, the more readily the wheel turns, and the faster the car starts moving. See where I’m going with this? Torque is a measure of the ability of an engine to do work. It's a component of, but not the same as, the (horse) power of the engine, which is the rate at which work can be done. In an automotive engine, power and torque are related by a simple equation that considers torque, engine speed (in revolutions per minute), and a conversion factor:
equation

In this equation, torque is expressed in terms of ft-lbf, the engine speed is given in revolutions per minute, and 5252 is a conversion constant. An engine's horsepower, then, isn't constant, but rather varies with its speed. The numbers you see quoted in brochures and so on indicate peak horsepower. Such figures can be misleading, as we shall now see.

Let’s say we're trying to decide between Engine A and Engine B for a high-performance car. Here's a chart showing the peak power and torque for each engine:

Power, hp Torque, ft-lbf
Engine A 224 300
Engine B 247 210

At first glance, Engine B looks like the better choice – it has 23 more peak horsepower! However, now let's look at a graph of the power curves of these two engines, showing their power as a function of engine speed.

graph

Notice that although Engine B has more peak horsepower, Engine A has more power at speeds up to 5500 rpm. What's more, it has significantly more power in the 1500-4000 rpm range (highlighted area), the range of engine speeds in which you'd typically operate a car. 

Now let's look at the torque curves of the two engines:

graph

We see that Engine A puts out much greater torque, especially over the typical engine speed range, indicating that under normal conditions Engine A will give you much more “oomph” than Engine B. Peak numbers are nice to brag about but often don't mean much, since few people operate their engines at peak conditions (which would generally be full throttle) in a typical day. 

I'm oversimplifying things with this example, as many other factors come into play when selecting an engine, such as fuel efficiency, emissions, weight, cost, etc.  Depending on circumstances, a performance enthusiast or racer might opt for Engine B, especially if she can mate it with transmission gearing that will take advantage of the power available at high engine speeds. But how many of us are shopping for that kind of performance when we head down to the dealership for the ritual shakedown known as buying a new car?

References

Adler, U., editor, Bosch Automotive Handbook, 1986.

Weast, Robert C., editor, CRC Handbook of Chemistry and Physics, 1976-1977, p. F-313.

Heywood, John B., Internal Combustion Engineering Fundamentals, 1988.

Kirby, Richard S.; Withington, Sidney; Darling, Arthur B.; and Kilgour, Frederick G., Engineering in History, 1990, pp. 167-172.

Skelton, Betty, Purnell's Pictorial Encyclopedia of Horses and Riding, 1977, pp. 30-31.

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