## Torque-Horsepower relationship

**by John Vandergrift**

May 20, 2003

**This is a file contributed by the RV Forum resident "gearhead" that describes the relationship between torque and horsepower for an engine. It explaines the differences in power output between gasoline and diesel engines. It also gives the mathematical formula of the relationship between torque and horsepower. The file originated as a forum message responding to a message from Lou Schneider "Horsepower = Torque * RPM (times a constant I can't remember). Diesel horsepower peaks at a lower RPM than gas engines, so they have correspondingly higher torque per horsepower."**

With my being the resident "gearhead", I hope I can shed a little light in this discussion. I went through a *lot* of education in this arena when I selected the components for the hotrodded engine in my Jeep. (I ended up with a Chevy 400 engine that ran 410 hp @ 5200 RPM and 473 lb-ft at about 3500 RPM when measured on a flywheel dynamometer, so I did a *lot* of figuring and research to select components to get me to those levels. I learned quite a bit about this argument in the process!)

The formula you are looking for is:

**hp = (torque x rpm)/5252**

Basically, at 5252 RPM, torque and hp are the same. Torque is an actual measurement, whereas hp is a calculated value. Because of the mathematics of the equation, hp always peaks higher than torque. Diesel engines have lower torque peaks (typically 1100-1500 RPM) than gasoline engines (usually 2500 and higher, depending upon camshaft, valve size and ignition system as well as other internal engine factors such as bore and stroke ratios). This is why the gasoline engines with lower overall torque outputs have relatively higher horsepower outputs--it's the multiplication factor of the higher RPMs. You will note that it is really easy to increase the horsepower output of an engine simply by raising the torque peak to a little higher RPM level.

For example, the current Dodge Magnum 5.9L engine is rated at 245 hp at about 4200 RPM, whereas the new 5.7L Hemi is rated at 345 hp at about 5400 RPM. The big increase in hp is from spinning the engine faster, which is done with roller rockers, roller camshaft and a different camshaft grind. The torque output is 335 for the 5.9L engine and 37 for the 5.7, but the peak RPM is higher for the higher output. Thus, the power output at a given lower RPM is similar between the two engines. The 5.7 puts out more power simply because it spins faster and the mathematics give a higher calculated hp.

Similarly, the diesel engines have huge torque at low RPMs, but can't spin very fast. Thus, the hp peak that is calculated is relatively much lower because of the lower RPM. Check the stats of the new diesel engines--for the most part they make greater hp by spinning faster--just like the gas engines!

Diesel engines are designed to be low speed engines, thus they can run at peak hp all day long and not complain. Gasoline engines operated at peak hp for extended periods will die an early death--they just aren't constructed heavily enough to tolerate that kind of abuse. Diesels *are*.

With any of these engines, there is a "sweet spot" for power output, generally between peak torque and peak hp. If you stay in that range, your performance and economy will be optimized. Too low and you'll lug the engine. Too high and you'll over-rev and actually see decreased performance. The best situation is to know the torque and hp peaks for your engine, and use your tachometer to keep the engine in that "sweet spot" for your engine if the transmission doesn't keep it there, and you will optimize your performance.

Both types of engines work well in their intended applications. You just have to use the right tool for the job and use it in the right way!