# What is the relationship and difference between BHP and Torque?

I've recently been looking into performance figures for various auto mobiles, and I see the terms BHP and Torque used quite often, but I can't say I really understand the terms, or how they relate to engine size.

Take for example the following specifications:

Ford Focus Zetec 1.6 (Petrol): BHP = 100, Torque = 110 lbs/ft

Ford Focus Zetec 1.6 (Diesel): BHP = 113, Torque = 210 lbs/ft

Subaru Impreza 2.0RX (Petrol): BHP = 148, Torque = 145 lbs/ft

Subaru Impreza 2.0RC (Diesel): BHP = 148, Torque = 258 lbs/ft

Subaru Impreza 2.5WRX(Petrol): BHP = 227, Torque = 236 lbs/ft

Can someone shed some light (in layman's terms) what is the difference between BHP and Torque, and how they relate to one another?

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The units of torque are lb.ft not lb/ft –  John Rennie Jun 28 at 9:58
@JohnRennie, I copied these figures directly from www.pistonheads.com Please feel free to edit if yo so wish. –  series0ne Jun 28 at 10:09
You are missing the @rpm values which are critical to understanding how an engine behaves. –  ja72 Jun 28 at 13:35
@ja72 why is RPM critical? –  Tushar Mathur Dec 15 at 20:51
Taking a single point from what actually is a curve (Torque vs. Rpm) requires both the x and y values of the point. –  ja72 Dec 16 at 13:42

$$\text{bhp} \propto \text{torque} \times \text{engine speed}$$

To start with a simple example consider linear motion. If we have some force, $F$, the as the force moves a distance $d$ the work done is force times distance, $Fd$. The power is the work done divided by the time, $Fd/t$, but $d/t$ is just the velocity (distance divided by time) so the power is simply $Fv$:

$$W = Fv$$

Now go back to the engine. At some distance $r$ from the axle the force is torque divided by distance, $\tau /r$, and the velocity is the angular velocity multiplied by the radius, $\omega r$. So when you multiply force times velocity the distance $r$ cancels and we get:

$$W = \tau \omega$$

That's why the power is torque times engine speed. There are a few conversion factors in there, e.g. engine speed is normally given as rpm and you need to convert to radians per second, and bhp needs converting to watts (and note that US and UK bhp are different!).

The figures car manufacturs quote are normally the maximum power and torque, and those maximum values are normally at different engine speeds. Because power is related to engine speed maximum power is usually generated at maxium engine speeds, while maximum torque is usually around medium engine speeds or a bit above. The reason the diesel models have greater torque for the same power is that diesels are lower revving than the petrol versions. Since torque is bhp divided by engine speed, for a given bhp a lower engine speed means a larger torque.

The acceleration of the car is proportional to the torque (divided by the car mass), so in terms of how hard you feel the car accelerate the torque is more important. However bear in mind that the torque at the wheels is the engine torque divided by the gearbox (and differential) ratio. The diesel won't accelerate twice as fast as the petrol because for any given speed it's gearing will be different.

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So is that right that "torque" in this car terminology isn't really a torque (moment of force) but force itself? Why are the units written above lbs/ft and not just pound-force? lbs/ft seems correct neither for force nor for torque. –  Luboš Motl Jun 28 at 9:39
No, torque is force times distance just as usual. I've just been a bit loose in my phrasing to try and keep the answer simple. –  John Rennie Jun 28 at 9:41
OK, could you please add a part of the answer that actually does it right? By engine speed, you meant the angular velocity, too, right? See en.wikipedia.org/wiki/… I am still confused by the units. They should be pound times foot, right? en.wikipedia.org/wiki/Pound-foot_(torque) –  Luboš Motl Jun 28 at 9:43
Yes, that's a fair criticism. I'll revisit my answer to make it more rigorous. I've only just noticed the units of torque in the question are given as lb/ft. That's wrong. It should be lb.ft as you say. –  John Rennie Jun 28 at 9:46

Here is how you quickly make sense of the numbers without any equations. Know also that what is shown is maximums only, and those values vary with rpm and throttle.

Caution Generalizations Below

Torque is the ability to accelerate at any instant, and power is the ability to accelerate over time (actually speed). At any given gear the peak acceleration occurs at the peak torque rpm, and at any given speed the peak acceleration occurs at the gear which brings the engine closets to the peak power rpm.

You cannot compare torque across cars or models because the gearing is different, but you can compare power. With Ford example if gas and diesel weight about the same and have roughly the same peak power, then at $100 {\rm km/hr}$ they will both have similar ability to accelerate. Why? Even though the diesel has double as much torque, this occurs at about half the engine rpm and so the higher gearing needed dilutes the torque to produce the same acceleration as the gas engine.

Oh an equation

This is why power is great for comparisons. Because if you know the mass $m$, the speed $v$ the drag force $F_D$ and the engine power $P$ you can calculate the acceleration at that instant as

$$a = \frac{P}{m v} - \frac{F_D}{m}$$

No need for torque, rpm and gears to be considered. It all washes away.

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Can someone shed some light (in layman's terms) what is the difference between BHP and Torque, and how they relate to one another?

In layman's terms:

(1) BHP is a measure of power which is the rate at which work is done.

Imagine a weight lifted to a certain height. The amount of work required to lift the weight to that height is the same regardless of the amount of time taken.

However, to lift the weight in a shorter time requires greater power. The more powerful a motor, the more work it can do in a given time.

(2) Torque, in this context, is a measure of rotational force which means that net torque is proportional to rate of change in rpm. Where the tire hits the road, more torque means greater (instantaneous) acceleration.

Now, it turns out that these are related - power is proportional to the product of torque and rpm - and it is sometimes difficult to disentangle these terms from each other.

However, in the case of a DC electric motor, the differences are stark.

A DC electric motor produces maximum torque when there is zero shaft rotation, i.e., 0 rpm. Zero shaft rotation implies zero power so the acceleration is greatest when there is zero power developed by the motor!

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As mentioned by others BHp $\propto$ Torque x (r.p.m.). The torque of the automobiles varies with speed hence it is important to specify it at a particular r.p.m. Normally manufactures specify the maximum torque along with the r.p.m. value. This means that this is the maximum torque which the engine can produce and it produces this value at the specified r.p.m. So if you want to get maximum torque out of your vehicle, you have to use gears appropriately so that the engine is running close to this specified r.p.m.