# What is the difference between torque and horsepower?

A very basic question - what is the difference between torque and horsepower? Its all over Google, but I am really confused and can't get any satisfactory answers. I'll tell you my confusion:

Torque is an indication of acceleration, right? So, to find the pickup of a car from 0-60 mph torque curve should be used. Then why is a horsepower curve used for that. What does horsepower denote?

If I say to shift gears (say from 1-2) for best mileage, shift at 10 kmph, while for extracting max power, shift at 22 kmph. Which one should a user use and why?

I am really confused at where to use a torque curve and where a power curve? What is their significance? What is their contribution to a car for a user?

## Power <-> torque relation

In general, the relation between power an torque is a simple formula:

``````Power[kW] = Torque[Nm] * RPM * π / 30,000
``````

which means that you can always calculate the one curve from the other in torque/power diagrams (That's also what the dynamometer does)

## So, why are always both curves plotted, if they are more or less the same?

This diagram shows a few curves of five theoretical motors: Each motor has a torque of 350Nm at 8000RPM (and so the same peak power at that RPM), and each motor has a peak torque of 450Nm.

A normal driver uses the range up to 3000RPM on the street, so his best choice is motor #2 followed by #1. Those would give best acceleration at moderate RPM.

In a race where the motor runs at very high RPM, you'd better chose #5.

This evaluation can be done with both curves - power and torque, because they show more or less the same quantity. BUT the torque curves show the differences much clearer than the power curves!

However, the power curves (can) show some interesting details. The power of #4 decreases between 4000 and 5000RPM. Another point is that usually, max power is not at max RPM, and you want to know at what RPM it is, and how it behaves around that RPM.

## Why does the power still increase though the torque already decreases with RPM at some point?

Imagine you have a 50kg weight which you lift by pulling a rope which runs over a pulley at the ceiling. The force you have to effort is just the gravitational force of the weight when you pull it with constant speed. Since 50kg is quite heavy, you'll lift it very slowly. If the weight is lighter, you need less force, and can lift it faster. Let's say you lift 25kg in 1/3 of the time. This means, in the same time you lift the heavy 50kg weight, you can also lift a total of 3x25kg=75kg. Since power is work done per time and you can lift 75kg instead of 50kg in the same time, the power is 50% higher - though you put in only half the force.

It's about the same for a motor: At high RPM, it may have less torque (force) during a rev, but since it does more revs in the same time, it can deliver more power.

## What happens in the gear box(es)?

As said, power is work done per time. Since power is conserved, the power at the motor shaft equals the power at the wheels. From the formula above one can calculate what happens when the ratio of motor an wheel ratio is different (neglecting any losses):

``````Wheel_torque = Motor_torque * Motor_RPM / Wheel_RPM
``````

In my next diagram, I've plotted the wheel torque vs. motor RPM for the six gears of a BMW M3 (365Nm@4900RPM; 252Kw@7900RPM): But it's also possible to draw power and torque vs. speed: Yes, the 365Nm of the motor is transformed to almost 6000Nm (4400lb ft) in first gear. This shows the massive impact of gear ratios as well as wheel dimensions. On the other side, power is always the same at a given RPM.

Note that when you shift into second gear at or around 4900RPM (max torque), you reduce the wheel torque by about 50%. (And when you shift into 3rd later, you loose again about 50%).

This means, in a race you will shift as late as possible, even if also power already falls, because shifting means a heavy loss in power / torque. (The red area in my plot just marks the RPM range from 4900 to max in first gear to make this clear). However, in an acceleration contest where you start from zero, high torque at low RPM will help, because it's important to get to high speed as fast as possible, and it doesn't matter that much if you still accelerate a little on the last meters.

Of course, in reality there is drag and so which increases with speed, and the only way to overcome it is even more power. Thus, power of course defines top speed, but this example shows that power already plays a role in the range of 50km/h / 30mph, which is not really fast.

## So compare different cars by power or torque?

You have seen the massive impact of RPM ratios due to the transmission, and wheel circumference also plays a role. So it's impossible to compare two cars by just looking at their motor torque curve. This only works for a car with several motor options, but same transmission. Power is a little (!) better. Note that the BMW M3 delivers more or less constant max power above 125km/h in 3rd gear, when you shift late.

## Fuel economy

Torque is also a measure of the work the motor does during a single rev. More precisely:

``````Work_per_rev[J]= torque[Nm] * 2π
``````

If we consider that the motor burns always the same amount of fuel per rev (not fully realistic, but OK), i.e. the same chemical energy (work) is released, the ratio of chemical / mechanical work is best when torque is at it's maximum. So, the machine runs most efficient when torque is high.

But keep in mind, best fuel efficiency is not equal to best mileage! In case of the BMW M3: Driving at 2000RPM instead of 4000RPM means reducing torque from 340Nm to 290Nm, which is a loss of only 15%, but fuel consumption is reduced by 50%.
This is why it is recommended to drive at very low RPM for best mileage, though fuel efficiency isn't the best there. However: High torque at lower RPM for sure means better mileage.

## Conclusion

In general, power and torque are two measures of the same thing: The strength of the motor. If you have one curve, you can calculate the other.

Power determines the racing capability and max speed of the car, but also acceleration capability once the motor has reached a higher RPM

Torque shows much clearer what acceleration capability the motor has at low RPM, but the torque at the wheel depends on gear ratios and wheel dimension, so it's not that easy to compare. A normal driver would like to have high torque at low RPM.

I got the motor curves from BMWs press site. And this (unfortunately German) site takes tire dimension, a set of RPM and a BMW model for gear ratios (or custom ratios), and calculates speed at the RPMs in the gears. In my case, the circumference of the wheel is ~2m and the speed is 7.5; 12.9; 19.3; 25.6; 30.1 and 35.1km/h in gears 1-6. This allows to calculate wheel RPM for given motor RPM in a given gear.

• This is a great answer.
– Zaid
Feb 7 '16 at 17:26
• Indeed. Great answer. Feb 9 '16 at 6:48
• @sweber Could you elaborate on what you mean by "racing", "racing capability", "acceleration contest", etc.? Is "getting to speed" not important in "racing"? I'm really confused by the terms you are using, when is high top end power and when is high low end torque important? Feb 17 '16 at 13:22

Horsepower is how much power the engine can produce (how much work is done in a given time), wheras torque is the amount of turning force it can make (how much work is done). The two are quite intricately linked, so you can't have one without the other.

You'll need to think of a few physics equations:

Force = Mass x Acceleration

Power = Work Done (Torque) / Time

To calculate one from the other, you can use some substitution with some rotary motion equations:

HP = (2 x pi x Torque x RPM)/33000 = (Torque*RPM)/5252

In general, an engine will be most efficient when it is running at peak torque (hence why industrial diesels run very slowly), and Torque has more of an effect on how quickly the car accelerates, particularly at lower speeds. HP is of more use at higher speeds, where it gives you an indication of how much ability the car has to attain and maintain a higher speed.

As an example, compare the engine in a ship, which will generate huge amounts of torque (to move a very heavy thing slowly) at very low RPM (only a few hundred), with that in a racing motorbike, which will generate a lot of power (to move a light thing very quickly) at a high RPM (10-12 thousand)

• So, referring to the original question, why is horsepower instead of torque is usually mentioned when talking about 0-60/0-100 times? Jan 28 '16 at 13:37
• I think to a certain extent it's mostly force of habit. Both are important for that - the car with more torque will get off the line quicker, but the one with more HP will go faster before it 'runs out of steam' and has to change gear...
– Nick C
Jan 28 '16 at 13:40
• This kind of clears a bit of dust: The ability to accelerate (i.e. your "pick up") depends on the torque, and you will see that a diesel has much better torque at low revs, which is useful in city driving, where you frequently accelerate from a standing start. However, top speed is determined by power, which is maximal in both petrol and diesel vehicles at a higher engine speed than the max torque. So, what I can make out is torque is needed when referred to city driving and horsepower when referred to highway driving. Jan 28 '16 at 13:57
• 0-60 pickup is done as if in a highway, hence power curve, while gear shift for best mileage/comfort is done for city driving, hence torque curve. For highway gear shift, we should use power curve. Read:in.answers.yahoo.com/question/index?qid=20100817103621AAiC2FH Jan 28 '16 at 14:00
• Well it had to start somewhere. And it can't be about torque only, otherwise all racing would be done in diesels. Jan 28 '16 at 16:17

## Torque is work, horsepower is work rate

In the context of engines:

• Torque indicates how much load an engine can carry for a certain distance in a certain amount of time.

• Power indicates how fast the engine can move that load over that distance.

Some other things that may help to explain the difference between the two:

• Torque is what accelerates a vehicle from standstill

``````▲ Torque = ▲ Acceleration
``````

The word standstill is very important here, because it is the only time where the aerodynamic drag forces will not limit a vehicle's straight-line acceleration. This is also why torque has a dominant effect at lower speeds - the drag forces are relatively small.

• Torque does work; it pulls loads

Say you have two identical vehicles in a tug-of-war competition with two different engines that develop the same maximum horsepower, but at different engine speeds. The vehicle with the lower engine speed will have more torque at the wheels than the other. This will also be the engine that wins the tug-of-war competition.

• Peak horsepower will govern top speed

``````Power = Resistive Forces x Vehicle Speed
``````

Horsepower is just a unit of measure for power, or work rate, so:

``````▲ Horsepower = ▲ Top Speed
``````
• Your example about engine speeds, - you completely neglect gearing. The fact that 2 engines create the same horsepower means that they can, theoretically , accelerate at the same rate. To analyse, if the second engine were to be geared down to produce the same torque at the wheels, and produces it for the same rev range (after gearing down !) then what'l be the difference? Feb 3 '16 at 5:26
• @chilljeet I thought torque depends on the gear? Feb 4 '16 at 8:03
• @IhavenoideawhatI'mdoing if you're talking about the wheel, then yes. Feb 4 '16 at 8:04
• @chilljeet I thought you said gearing down will produce the same torque at the wheels? Feb 4 '16 at 8:05
• Anyways, Zaid, so why is horsepower important, how does it describe how quick the car is? Nobody cares about the top speed, no one drives at top speed. Acceleration is where it is, so what's the purpose of horsepower? Feb 4 '16 at 8:06

Torque is the amount of force exerted by your engine at a particular RPM. In two cars with equal gearing and in the same gear, a car making twice as much torque will accelerate exactly twice as fast.

Horsepower is calculated from torque and RPM. A given amount of torque at a low RPM equals less horsepower than the same amount of torque at a higher RPM.

Horsepower is important because the amount of force that reaches the rear wheels to accelerate the vehicle is a combination of torque and gearing. Generally speaking, the higher a car revs, the more tightly it can be geared. The more tightly you gear a car, the faster it accelerates for a given amount of torque. Since horsepower represents a combination of torque and RPM, it's actually a pretty good indication of how most cars with well chosen transmission ratios will accelerate.

To take an extreme example, let's say we have an extremely high revving engine (like a formula 1 engine). It makes 250 ft lbs of torque, but it maintains that torque until a peak horsepower of 20k RPM, making nearly 800 hp. On the other hand, we have an engine with lots of displacement but a relatively low redline. Let's say that this hypothetical torquey car makes peak torque of 600 ft lbs and revs to 6k rpm, making just over 600 hp. Note that the car with more hp is making significantly less torque. In first gear, let's say that the high-revving car is geared three times as tightly as the torquey car- the high revving car will be at 60mph and 18000 rpm while the torquey car will be at 6000 rpms at 60mph. This makes the high revving car actually put down more wheel torque in this gear, so it will accelerate faster. And since it still has another 2000 rpm of engine speed left when the torquey car runs out of rpm, it will continue to accelerate past 60mph in first gear while the other car is shifting. And the same drama will be repeated in the higher gears as well- the higher HP car will generally be accelerating faster because it can afford to stay in lower gears which can afford to be geared more tightly.

Gearing- that's why horsepower is important. Tight gearing means that a car has to rev higher to achieve a given road speed. Long gearing means that the car doesn't have to rev as high to go a certain speed. The tradeoff is acceleration. So first gear in most cars is very tight, ending before 30 mph in many small cars. On the other hand, the overdrive gear is meant to offer very poor acceleration but it allows the car to maintain nearly idle RPM at highway speeds, saving gas. Also, otherwise identical cars can have different final drive ratios, which will affect their overall acceleration and top speed. So a car with a 3.00 rear ratio will accelerate more slowly to a higher top speed than the same car with a 4.10 rear ratio.

• Could you please elaborate what you mean by "tight gearing"? Feb 2 '16 at 7:40
• Tight gearing means that the car is going less fast for a given engine speed. For example, take an engine that revs up to 7000 rpms. If the car with that engine reaches 50mph in 1st gear, that car is more loosely geared than if the car reached 30mph in 1st gear at the same RPM. Feb 2 '16 at 14:41
• Basically the spacing of the transmission's gear ratios is governed by the shape of the car's power curve while the final drive represents a tradeoff between top speed and acceleration. Sometimes the top gear of the transmission will be exceptionally long to allow for a low RPM highway cruising gear. Feb 2 '16 at 14:49
• Surely final drive diff ratio will be a factor here? Feb 2 '16 at 15:15
• So, higher transmission gear ratios? Feb 2 '16 at 15:21

In the simplest terms possible:

Torque = Lbs/Ft. A concrete, real measurement of the twisting force produced by the engine.

Horsepower = An arbitrary, made up unit of work. A unit of horsepower is predicated on the assumption that a horse can pull with a force of just over 180 lbs.

The mistake most people make when engaging in this debate is considering horsepower and torque independently. Almost everyone argues as if they are separate, unrelated values. They aren’t.

Horsepower = (Torque x RPMs) / 5252

This equation is the second most important thing on this page, and it’s the reason that anyone telling you that horsepower and torque should be considered equally and separately is significantly off-base. The fact of the matter is that horsepower is the product of torque and another value — RPMs (divided by 5252). It’s not unrelated, separate, or different.

In fact, there’s not a single machine in existence that measures a car’s horsepower. It’s a man-made number. When a car’s performance is tested, it’s torque is measured using a dynamometer. The measure of an engine’s performance is torque. Horsepower is an additional number that’s attained by multiplying the torque by the RPMs.

The Relationship Between Horsepower, Torque, and Acceleration

• The link you provided is a gold mine. You may want to expound your answer to cover some of the different things besides the relationship between HP & TQ which the OP is asking about. This is a good start to a great answer. Feb 4 '16 at 22:28
• -1: While it's indeed torque what's measured, your second sentence about horse power doesn't address the question. Of course, it's an odd unit basing on odd assumptions - but Lbs * Ft (yes, `*`, not `/`) sound very very odd for me, too. Just because it's an arbitrary unit doesn't mean it doesn't make sense. Feb 5 '16 at 12:59

Typical analogy: Potential Energy:Torque::Kinetic Energy:Horse power

Torque can exist without motion.It is a capacity to do work.
Horsepower can exist only in motion. It is rate of doing work.

Power of engine = Torque * Speed;

To refer an engine running at constant load, Power reference is used to extract maximum power.
. To refer an engine running at variable loads(shift of gears,for eg), Torque is more appropriate.

Curves:
Torque curve:Torque produced by engine vs engine rpm, at various load on engine.
Power curve:Power produced by engine vs engine rpm, at various load on engine. This will be obtained by multiplying torque curve by speed.So this will be a shifted + elongated version on torque curve. Refer Power torque curve example
Fuel economy curve will be overlapped on above curves for better understanding.

You are getting confused between power curve/torque curve and fuel economy curve.

Given a power curve, we can obtain torque curve and vice-versa.
Fuel economy curve must be provided explicitly as an overlapping graph.

Now it must be obvious when to use what.
To get best mileage,follow mileage curve.
To get max power, refer power curve.

Torque curve will be generally used as a reference for transmission control systems,to know which is next best gear to shift.

Still not clear? Check a real-world example

Note: The curves are specified only at certain load conditions.So the actual behavior of engine depends on current load on engine as well as various limitations imposed due to legislative/emission norms/damage protection.