Horsepower Calculator

What the horsepower calculator does

Horsepower, torque, and engine speed are locked together by one tidy equation, and if you know two of them, the third is fixed. This tool works that equation in whichever direction you need. Know the torque and the rpm and want the power? It finds the power. Have a power figure and an rpm and want to know the torque behind it? It works backwards. Same for finding the rpm.

It is the tool for making sense of a dyno sheet or an engine spec, where these three numbers are quoted and you want to see how they fit together.

How to use it

1. Choose a calculation. Find Power, Find Torque, or Find Speed, depending on which value you are missing.
2. Enter the other two. Torque is in pound-feet, and engine speed is in revolutions per minute. The boxes change to ask for exactly what each calculation needs.

Press Calculate for the answer, or Reset to start over.

The formula, and what 5252 is doing there

The relationship between the three is this:

Horsepower = (torque × rpm) ÷ 5252

Rearranged, that gives you the other two. Torque is power times 5252 divided by rpm, and rpm is power times 5252 divided by torque. So where does that oddly specific 5252 come from? It is not a fudge factor. One horsepower was defined long ago as 33,000 foot-pounds of work per minute. When you convert torque and rotational speed into that unit of work, the maths leaves behind 33,000 divided by two times pi, which comes out to about 5252. So the number is just the bookkeeping that ties pound-feet and rpm to the old definition of a horsepower.

A worked example of each

Finding power

An engine makes 300 lb-ft of torque at 6,000 rpm. Power = (300 × 6000) ÷ 5252 = about 343 hp.

Finding torque

An engine is rated 200 hp at 4,000 rpm. Torque = (200 × 5252) ÷ 4000 = about 263 lb-ft.

Finding speed

You have 250 hp and 280 lb-ft and want the rpm where that happens. Speed = (250 × 5252) ÷ 280 = about 4,689 rpm.

One equation, read three ways. The only thing that changes is which value you start without.

Torque and horsepower are not the same thing

People use the two words almost interchangeably, but they describe different things. Torque is the twisting force the engine produces, the shove you feel. Horsepower is the rate at which that force does work, which folds in how fast the engine is spinning. That is why a big diesel can have huge torque but modest horsepower, while a small high-revving engine can make strong horsepower from modest torque by simply spinning faster. The formula is what connects the shove to the speed, and this calculator lets you move between them.

Why the two lines always cross at 5252 rpm

Here is a fact that surprises people the first time they meet it. On any dyno graph, the torque curve and the horsepower curve always cross at exactly 5,252 rpm. Every engine, no exceptions. It falls straight out of the formula. At 5,252 rpm the rpm term and the 5252 cancel, so horsepower and torque come out to the same number. Below that speed the torque figure is the higher of the two, and above it the horsepower figure pulls ahead. If you ever see a dyno chart where the two lines cross somewhere else, the graph is drawn wrong.

Questions people ask

What is the horsepower formula?

Horsepower equals torque in pound-feet times engine speed in rpm, divided by 5252. Rearrange it to solve for torque or rpm instead.

Why 5252?

It comes from the definition of one horsepower as 33,000 foot-pounds per minute. Converting torque and rpm into that unit leaves 33,000 divided by two pi, which is about 5252.

What is the difference between torque and horsepower?

Torque is the turning force the engine makes. Horsepower is how quickly that force does work, so it also depends on rpm. The same torque at higher rpm is more horsepower.

Can I get horsepower from my quarter-mile run instead?

Yes, but that is a different approach. This tool uses the torque and rpm relationship from a spec or dyno. To estimate power from your weight and quarter-mile time or trap speed, the engine horsepower calculator does that.

References

1. National Institute of Standards and Technology (NIST), Special Publication 811: Guide for the Use of the International System of Units (SI), on units of power and the horsepower to watt relationship. https://www.nist.gov/pml/special-publication-811