# The Relationship Between Horsepower, Torque, and Acceleration

I purchased a new car recently and in doing so became (for the first time) moderately curious about vehicle performance. I set about to see how it compared to my previous car performance-wise and was immediately struck by a pivotal question:

What matters more for acceleration — horsepower or torque?

My first approach was to ask those immediately around me and call some friends that were into cars and/or racing. The results were not satisfactory. I got a few decent responses, but nobody could explain the relationship to me in a way that I could understand.

All this did was confuse and intrigue me. One thing I did figure out is that none of the people arguing were using hard science as the foundation for their argument; they were invoking science, but were doing so very sloppily. Well, that wasn’t enough for me so I set out to find the real answers.

## The Basics

So to start with I naturally consulted Google. Most of the top hits for “torque vs. horsepower” are excellent pieces; they break down the math in a very methodical way, so I won’t repeat that excellent work here. Instead I’ll just summarize the basics that are accepted as fact by everyone:

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• Horsepower:

James Watt came up with the concept of horsepower — which is a measure of, interestingly enough, power. 1 HP is the equivalent of 33,000 ft/lbfs per minute. The reason for the complex unit is that we’re accounting for three things with this number: the amount of weight involved, the distance it’s being moved, and how long it takes to do it (that last one is important).

• Torque:

Torque is nothing more than a measurement of twisting, or rotational, force. The easiest way to think of this is to imagine a long shaft — like a car’s axle — and imagine it’s in a room suspended in mid air. Hanging on the bottom of one end is a rope with a weight attached — a very heavy weight.

Now imagine someone trying to, using their hands, twist the shaft so as to lift the weight. Think of them as essentially trying to act like a wench and reel it up. The amount of force they are able to generate to lift the weight in this manner is the torque that they’re able to produce. One unit for measurement of this is the foot-pound. A foot-pound is the rotational ‘force’ generated by hanging a one-pound weight at the end of a 1-foot wrench.

## The Common Mistake

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 Physics of Acceleration

<

p>So now for the most important thing on the page. What determines true acceleration for a vehicle isn’t really debatable — it’s force divided by mass. The formula for acceleration is seen below.

```f = ma
```

Which means…

```a = f/m
```

The confusion only comes in determining which force we’re actually talking about.

So we are solving for acceleration and we have a constant mass. We’ve already established that torque is the amount of rotational force being generated at the engine, but we aren’t concerned with the force at the engine. What we’re interested in is the force at the wheels. The force at the wheels is the `f` in `f = ma` (actually, it includes the radius of the wheel as well, but we’re simplifying).

But remember, the transmission ultimately gives the force to the wheels, not the engine.

And that’s the trick to this whole mess. Gearing magnifies torque. The torque at the wheels is the torque at the engine combined with the torque magnification given by the transmission through gearing. So the transmission only sees what’s coming off the engine, while the wheels see the resulting force combination of the engine plus the transmission.

That’s what horsepower represents. Horsepower is the combination of the benefits of the engine’s raw abilities combined with RPMs. And RPMs are what allow us to use gearing effectively, which gives us more torque at the wheels.

## Conclusion

So yes, the answer to the question is torque, but torque at the wheels, not at the engine. And since we’re talking about torque at the wheels and not at the engine, the actual complete answer is horsepower because horsepower encompasses not only the engines torque but the total torque that gets put to the ground to accelerate the vehicle.

For any comments, corrections, flames, or other types of input, feel free to contact me. I’m game for anything that’ll help me better understand this interesting subject. ::

### Notes and References

• Gearing is extremely important because it controls RPMs (and therefore horsepower).
• Gears magnify torque — hence the acceleration available in first gear.
• Another excellent explanation of the topics at allpar.com.
• Racecars have high horsepower due to high RPMs, not due to high torque (see gearing).
• “Below 5252 RPMs any engine’s torque will always be higher than its horsepower, and above 5252 RPMs any engine’s horsepower will always be higher than its torque. At 5252 RPMs the horsepower and torque will be exactly the same.” — revsearch.com
• “It is better to make torque at high rpm than at low rpm, because you can take advantage of gearing.” — vettenet.org