Doing the Twist: Horsepower, Torque, and Automotive Performance

One of the most confusing (and frequently contentious) questions in the automotive realm is the difference between horsepower and torque. You may have heard any number of pithy expressions, like “horsepower sells cars, but torque wins races,” or fans of big-engine muscle cars complaining that 200-horsepower four-cylinder engines are “gutless.” Surprisingly few of the worthies who throw around comments like that, though, are actually able to define the difference. What IS the difference between horsepower and torque, and what effect do they have on how a car performs?

UNDERSTANDING TORQUE

If you stayed awake through high school physics, you may dimly recall that torque is twisting force — that is, a force that tries to cause an object to rotate around a particular axis. For example, if you turn a doorknob or spin a roulette wheel, you are applying torque to it.

If we were in physics class, we’d say that torque is the cross product of the vectors for force and distance. The force vector is the direction in which the force is applied. The distance vector is (at its simplest) the distance between the point where the force is applied and the axis of rotation. For example, imagine you’re using a wrench to loosen a bolt. The distance vector in that case is the distance between the axis of rotation (the center of the bolt) and the point where force is applied to the wrench. The force vector is which direction you move the wrench.

If the distance between the center of the bolt and the point where you grip the wrench (and thereby apply force to it) is 1 foot (305 mm) and you apply 10 pounds (about 4.5 N) of force, you are applying 10 pounds-feet (about 13.6 N-m) of torque. If the bolt won’t turn, you might try picking up a bigger 2-foot (610 mm) wrench. If you apply the same 10 pounds-feet (4.5 N) of force, the torque generated would be 20 pounds-feet (27.1 N-m).

What is engine torque? As you probably know, an internal combustion engine works by burning air and fuel. The energy of that combustion moves one or more pistons (or rotors), which act on the engine’s crankshaft, causing it to rotate. In a car, the rotation of the crankshaft turns the gears in the transmission, which turn the wheels. An engine’s torque is the amount of twisting force the pistons (or rotors) can exert on the crankshaft.

UNDERSTANDING HORSEPOWER

Now, what is horsepower? Again recalling that long-ago physics class, power is work performed over time. Mechanical work represents force exerted over distance — for example, moving a 10-pound weight a distance of one foot represents 10 foot-pounds of work. Power is the rate at which that work is performed.

One mechanical horsepower represents the ability to do 550 foot-pounds of work per second or 33,000 foot-pounds of work per minute. (One metric horsepower represents a rate of 75 kilogram-meters per second; a metric horsepower is about 735 watts, whereas a mechanical horsepower is equivalent to about 746 watts.)

The brighter students among us may have noticed the similarity between the units for work — foot-pounds (ft-lb) — and the units for torque — pounds-feet (lb-ft). The units are actually the same, but are typically written differently to avoid confusion. For an engine with a rotating crankshaft, then, one horsepower is equivalent to exerting 550 pounds-feet of torque per second.

Remember that torque is a twisting force; that means that if applying torque to an object will tend to cause the object to rotate, rather than move in a straight line. Therefore, if torque produces any work, we have to measure how much rotation it imparts (angular speed) rather than how far it cause the object to move.

Angular speed is usually expressed in terms of radians per second or radians per minute — one radian is 180 degrees divided by π (pi), or about 57.3 degrees) — but we usually measure engine speed in terms of revolutions per minute (rpm), so it’s more useful to think of it that way. One revolution is 360 degrees, which is equal to 2π radians. If 1 horsepower equals 33,000 lb-ft of work per minute, then we can calculate an engine’s power based on its torque (in lb-ft) and its engine speed (in rpm):

Power (hp) = Torque (lb-ft) x 2π x Rotational Speed (rpm) / 33,000

or

Power (hp) = Torque (lb-ft) x Rotational Speed / 5,252.113

For example, if an engine produces 200 lb-ft of torque at 4,000 rpm, it is producing 152.3 horsepower (200 x 4,000 / 5,252.113) at that speed.

The upshot: Horsepower depends on torque and engine speed. If your engine produces more torque, it also makes more power; if you run the engine at a higher speed, it also makes more power. It is entirely possible for engine A to make more power than engine B, even if engine B makes more torque — engine A must simply rev higher to make up for its torque deficiency.

TORQUE AND POWER CURVES

Engines used for stationary applications (generators, for example) or in aircraft spend most of their lives running at a constant engine speed. As a result, they produce their full, rated horsepower most of the time. Engines used in cars, trucks, or motorcycles operate over a broad range of engine speeds, from a few hundred rpm at idle to 10,000 rpm or more at redline. Since horsepower depends in part on engine speed, the amount of power the engine produces varies quite a bit at different points in its rev range. Engineers describe the relationship between an engine’s power and rpm as the power curve.

If an engine produced its maximum torque at all engine speeds, the power curve would be a straight line: that is, increasing rpm by 50% would also increase horsepower by 50% (as long as it didn’t rev the engine beyond its redline, which risks serious mechanical failure). That is true of electric motors, but it isn’t true of internal combustion engines. We will discuss the reasons for this in more detail in a future article, but for now, we’ll just say that an engine’s torque output also varies with engine speed.

All internal combustion engines produce their maximum torque at one particular engine speed; this is called the torque peak. Above or below the torque peak, the engine produces somewhat less torque than that maximum value. Just as an engine has a power curve describing how much power the engine produces at different points in its rev range, the engine also has a torque curve, describing how much torque it generates at different speeds.

The engine’s design determines at what speed the engine’s torque peak occurs as well as the shape of the torque curve. If an engine produces a fairly constant level of torque throughout its rev range, its torque curve is said to be flat. Electric motors, which usually produce close to their full torque output from zero rpm all the way to their maximum safe operating speed, have extremely flat torque curves. (Contrary to popular belief, the shape of the torque curve is not directly related to how much torque the engine produces. Two engines can have very similarly shaped torque curves even if one has far more maximum torque than the other does.)

An engine can be tuned to produce its maximum torque at the low end of its rev range, in the mid-range, or at high rpm. Modern engine designers have various tricks available to “flatten” the torque curve of an engine (that is, to keep engine torque close to its maximum through a broad range of engine speeds), but any given engine will be notably stronger in one range than in others.

Since power is a function of torque and rpm, the shape of the torque curve also determines the shape of the power curve. The horsepower curve will always peak later than the torque curve, but if the engine’s torque curve is strongest at low rpm, the power peak will also be relatively low. If the torque peak is at high rpm, horsepower will also peak at lofty engine speeds.

If you’ve ever driven a car with a tachometer, you’ve probably noticed that the engine spends much of its time at speeds well under 4,000 rpm. Since the horsepower peak of almost every modern engine is higher than 4,000 rpm, that means the engine rarely has a chance to develop its rated maximum power. Therefore, in normal driving, the shape of the torque curve is often more important than maximum power.

THE REAL WORLD (SORT OF)

To see how this works in practice, let’s consider a couple of real engines: Ford’s 3,996 cc (244 cu. in.) “Cologne” V6 (which powered the Ford Ranger and Explorer for many years) and Volkswagen’s turbocharged, four-cylinder, 1,781cc (109 cu. in.) 1.8T engine (used in several different configurations in a wide range of Volkswagen and Audi models).

The Ford Cologne V6 was an engine of venerable design dating back to the early 1960s. The 4.0-liter version was intended for truck use, so it was tuned for strong low-end torque. Its peak torque was 220 lb-ft (298 N-m) at only 2,400 rpm; maximum horsepower was 160 hp (119 kW) at a modest 4,200 rpm.

Volkswagen’s 1.8T was a more modern and far more technically sophisticated engine with dual overhead camshafts, five valves per cylinder, and an intercooled turbocharger. Turbocharged engines tend to be “peaky,” putting out more power at high rpm, but Volkswagen designed it to have as flat a torque curve as possible. In fact, Volkswagen claimed that the engine produced its full maximum torque from 1,950 rpm to 5,000 rpm. VW offered it in several states of tune, but the one we’ll use for our discussion is the version found in later Mk 4 Golfs, Jetta/Bora sedans, and the SEAT Leon, which was advertised at 180 hp (134 kW) at 5,500 rpm and 173 lb-ft (235 N-m) of torque.

The best way to judge an engine’s torque curve is to hook it up to a dynamometer and see exactly how much torque it actually puts out at various rpm. We aren’t in a position to do that, but we can make some educated guesses about the torque curves for both engines based on their rated torque and horsepower peaks.

As we mentioned above, the Ford engine’s rated torque peak is at 2,400 rpm. Using the equation we derived earlier, we can calculate its power output at that speed: 101 horsepower (220 lb-ft x 2,400 rpm / 5,252), or about 75 kW. The V6’s horsepower peak comes at 4,200 rpm. Using the same equation, we calculate that it has 200 lb-ft (271 N-m) of torque at that speed (160 hp x 5,252 / 4,200 rpm). We can see from those numbers that between 2,400 and 4,200 rpm, the engine probably produces between 200 and 220 lb-ft (271 and 298 N-m) of torque.

What about at higher speeds? We know that the engine never produces more than 160 horsepower (119 kW). Even if it still produced 160 horsepower at 5,000 rpm (which is unlikely), torque would have dropped to 168 lb-ft (228 N-m) at that speed. If it produced 140 horsepower (104 kW) at 5,000 rpm, that would mean that its torque output was down to 147 lb-ft (199 N-m). In short, the Ford engine’s torque and power both start dropping off very rapidly after the 4,200-rpm horsepower peak — the V6 was designed for low-end grunt, not high-rpm power.

What about the Volkswagen engine? The 1.8T’s peak torque begins at 1,950 rpm. At that speed, it’s making only 64 hp (48 kW) (173 lb-ft x 1,950 rpm / 5,252). By 2,400 rpm (the Ford’s torque peak), the VW engine’s power has risen to 79 hp (59 kW). At 4,200 rpm, the 1.8T’s power output has risen to 138 hp (103 kW), still well behind the Ford. The VW’s power doesn’t start to exceed that of the Ford engine until after the Ford hits its peak power. When the VW hits its peak horsepower at 5,500 rpm, torque is still about 172 lb-ft (233 N-m) — torque has tapered off, but only very slightly. That means the engine continues to make useful power even past its power peak; its redline is 6,500 rpm, which it doesn’t have much trouble reaching.

Horsepower and torque curve chart
These torque and horsepower curves are estimates based on published power and torque figures, but they illustrate the difference between the engines. Note that even though the VW’s torque curve (light green) is far flatter than the Ford’s, the Ford’s is higher over much of the rev range.

What does this mean in practical terms? Even though the VW’s torque curve is very flat, it has significantly less torque than the Ford until well over 4,200 rpm, which means that the 1.8T also has less power at lower speeds. It ultimately produces more power than the Ford engine, but not until over 5,000 rpm.

Imagine that we installed these engines in two otherwise identical cars, with the same transmissions, same gearing, and identical weights. We would discover the following:

  • In normal, street driving, the car with the Ford engine would almost always be quicker than the VW-powered car. That shouldn’t be surprising — the Ford’s greater torque gives it almost 30% more power than the VW engine at low rpm even though the VW is stronger at higher speeds.
  • In a drag race over a standing quarter mile or standing kilometer, the Ford-powered car would take an early lead and would stay ahead until both cars were well down the strip. The 1.8T car would begin to catch up as it hit higher engine speeds and it would eventually pull ahead. It would win by a narrow margin and its trap speed (its speed at the finish line) would be slightly higher than the Ford-powered car’s.
  • In a road race or on a big oval track, the VW-powered car would be ahead most of the time. As long as both cars were driven flat out, the VW engine’s greater horsepower would be more important than the Ford’s low-speed torque. The only place the Ford-powered car would have an advantage would be in slow corners, where its higher torque would again give it more power than the VW engine.

This assumes everything else is equal, which in the real world isn’t necessarily the case. For example, we could help the VW-engined car by changing its gear ratios so that the engine is always running at higher rpm. This would give it more power in low-speed driving, although it would also mean more engine noise, greater fuel consumption, and somewhat higher engine wear.

In a future article, we’ll look at what makes some engines produce more torque and/or more horsepower than others do.

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14 Comments

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  1. As someone who spends a lot of time explaining this concept to others, I’d say this article dearly needs a graph or two.

    Additionally, an emphasis on the effects of drivetrain (gearing, mostly) would go a long way to set straight the pseudo-experts.

    A major point I like to make is that sure, a 200hp 4-banger is making an honest 200hp with a smaller displacement than a 200 hp 4L V6. But when that 4cyl is making that 200 hp, it’s consuming at least as much fuel as the bigger engine.

    Hence: bigger engines can actually net better mileage as they can lope along at lower RPM while producing enough torque to keep things moving.

  2. I agree, some charts would be helpful. I will see about creating some to
    add.

    I decided that a discussion of gearing and fuel economy was beyond the scope of this segment, which is already a tricky concept to grasp. (Note the proviso in the example about "all else being equal.)

    To say a 4.0L six will usually produce better fuel economy than a 2.0L turbo four of the same output is awfully simplistic, and not necessarily true. All else being equal, a 4-liter engine will burn more fuel than a 2-liter engine; a six-cylinder engine will burn more fuel than a four-cylinder engine; a turbocharged engine will burn more fuel than a normally aspirated engine; and an engine hooked to a transmission giving 20 mph/1,000 rpm in top gear will burn more fuel than one whose transmission is geared for 25 mph/1,000 rpm. Any car is fuelish if you drive it like you stole it; and if all we cared about was specific fuel consumption at full-throttle cruising, we’d be all be driving gas turbines. It’s certainly possible for a turbo four car to be just as thirsty as a normally aspirated V6 (the Mazda CX-7 springs to mind) or even thirstier (as many a Subaru WRX owner will attest), but to say it’s always (or even usually) so is kind of disingenuous.

    The point is not to get into a pissing match about the moral rectitude of different configurations, which is what tends to happen in these discussions. ANY engine configuration has advantages and disadvantages — whether the pros are enough to outweigh the cons depends greatly on what you want the engine to do, and what your priorities are.

    1. Yeah, not so much trying to claim that bigger engines always get better mileage, just that they can…and can more easily than one might expect.

      As a WRX owner, I [i]can[/i]tell you just how thirsty my 4cyl compact can get if you get too zealous with the right foot. A full tank of highway at 80ish mph = 27mpg. Throw in a few choice on- and offramps, and it’s more like 23.something. On premium.

      Most of all, I’d like manufacturers to publish the power and torque curves for their engines. A lot of seemingly under-performing engines might look a lot better if you could see the area under the curve from 1500-4500 rpm.

  3. Interesting torque article. A good example of “advertise horsepower, drive torque” (one of those pithy comments) is the Corvette transition from the L98 to the LT1 engine. Simply put the L98 was a low rpm torque monster at a seemingly modest 245HP in 1990. The LT1 jumped to 300 HP by moving torque peak to a higher rpm (oversimplified). Interestingly enough the quarter mile times for similarly optioned L98 and LT1 Vettes is almost identical.
    I do enjoy a high revving engine, but I must admit the “immediate” low end response of the often derided L98 is a pleasure during everyday driving. Not to mention that the L98’s “stop light Grand Prix advantage”. I’ve had a few “oh just a L98” folks drive the car and they were amazed that just 245HP performed so well.
    Good mention on the turbo car. Yes a turbo can (if done correctly) increase HP by increasing torque throughout the entire rpm range using modern engine management (turbo’s with carbs were never able to accomplish this – another topic perhaps).

    1. I’ve never studied the torque curves of L98 and LT1 engines, but that makes a lot of sense. I think Chevy was responding to the new crop of Japanese supercars — the 300 hp Nissan 300ZX Twin Turbo and Mitsubishi GTO/3000GT VR4/Dodge Stealth that appeared at the same time, which made them feel like they had to offer at least 300 hp.

      Since the L98 and LT1 cars weigh about the same, if they had the same gearing, I would expect a drag race to look something like the hypothetical V6 vs 1.8T race alluded to in the article — the L98 would take the LT1 off the line and stay with it much of the way down the strip. The LT1 would ultimately pull ahead, but their ETs through the quarter mile would probably be pretty similar (I could dig up some numbers, but I think the point is made). I would expect the LT1 to have a higher trap speed, though, since trap speed is more a function of peak power than torque.

      1. It’s all hypothetical, but…

        Your race depends on what RPM you launch at. In a race situation, you adjust your driving/shifting to stay in the peak-HP RPM range.

        Thus, you might launch the LT-1 at a higher RPM and take advantage of the higher HP output.

        This gets complicated as you accelerate through multiple gears…but I think you get the point.

        In normal driving (accelerating from idle to some shift point), the car with more low-end torque is going to “feel” quicker.

  4. [quote]In normal driving (accelerating from idle to some shift point), the car with more low-end torque is going to “feel” quicker.[/quote]

    Well, more to the point, it’s going to [i]be[/i] quicker, because at those lower engine speeds, it makes more power.

  5. This is an excellent – and quite possibly the best description of torque vs. horsepower I’ve read.

    Looking at the other comments, while a turbo can increase overall efficiency by scavenging energy from the exhaust stream, typically a turbo is there to generate extra power with a given engine displacement – and in a VERY fundamental way, power = fuel consumption. Plus, a gasoline engine must run fairly close to 13 to 1 mix ratio – or the combustion just doesn’t proceed correctly (overheat and other problems). So a larger displacement engine – under virtually all circumstances would burn more gas – even if the power loads are similar.

    1. Turbocharged engines have a number of pros and cons when it comes to fuel economy. Against them is levied the decrease in compression ratio that’s typically necessary to avoid detonation, along with the increased back pressure caused by the turbo itself and the extra fuel necessary at high boost to maintain something approximating stoichiometry. All of those things increase specific fuel consumption. The major pro, compared to a larger, normally aspirated engine, is that small displacement is beneficial to fuel economy. All else being equal, a 2.0 liter engine will burn less fuel than a 4.0 liter engine because of lower frictional losses from the smaller displacement, and a four-cylinder engine will burn less fuel than a five, six, or eight because of lower pumping losses, reduced friction, and lower reciprocating mass.

      You can pretty much balance these trade-offs in any way you can afford, biasing towards either fuel economy or power. There is no free lunch…

  6. One of the best articles illustrating that more low to mid-RPM torque output means more low to mid-RPM horsepower. So the question is do want more horsepower at normal engine speeds or more horsepower only at 6000 RPM. Unfortunately, most people use the peak horsepower figure to judge how powerful the car will feel not realizing that 99% of the time they will be experiencing less power for all those times they are below 4500 RPM in a low displacement highly strung buzz box. They will keep needing to downshift to keep up or have the engine scream to achieve decent 0-60 times. The smaller displacement however does have the potential for better fuel economy when driven lightly compared to its larger counterpart, as it’s more likely to be under load in lighter power demands. See BSFC.

    1. It’s important to note that modern engine technology — in particular variable valve timing and the combination of turbocharging and direct injection — has done much to flatten and fatten engine torque curves. Consequently, there are now engines of 1 liter or less metric displacement with as much real power and torque as a workaday 2-liter four of the ’90s and turbocharged 2-liter engines that have the muscle of an early ’90s 4-liter V-8. Of course, when you do that, real world fuel economy is more commensurate with power extracted than displacement, and that technology isn’t cheap, but the traditional distinction between stump-pullers and screamers is increasingly becoming obsolete.

  7. So my 3.5 V-6 EcoBoost with 365 hp at 5500 and 420 lb-ft torque at 2250 put in a Vette would stuff both the V-8’s? Right? No that wouldn’t be right. It would be just plain wrong to have a Vette with anything but a V-8. Super glad Chase Moresey stuck to his gut feeling.

    1. Well, the current Corvette has another 95 hp and 45 lb-ft beyond that, but your engine is a good deal more powerful than most classic Corvette engines.

      Simply from a marketing standpoint, I do think a non-V8 Corvette would be calamitous — not because it wouldn’t perform, but tradition, etc. From a weight and cost standpoint, or even specific fuel consumption, the latter-day Corvette pushrod V8s really do pretty well. They aren’t exceptional in terms of specific output, but that’s not the point, and there is something to be said for variety in a class of cars that are sort of by definition indulgence purchases.

  8. I drive a ’92 Chevy 1500 with a 4.3 v6. It’s my first full-sized pickup, and I have every intention of keeping this truck indefinitely, v6 and all. I have two questions. First, I’m considering increasing the bore and stroke. I know this will increase my overall power output, but what will it do to my towing capacity? Second, and also in regards to towing capacity, would it be better to install a supercharger or a turbocharger?

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