If you’ve seen a dyno graph more than once in your life, you’ve likely noticed that horsepower and torque always seem to cross around 5,200 rpm, regardless of combination or engine type. That’s not some fluke, because horsepower and torque do, in fact, cross at exactly 5,252 rpm. It’s not magic or witchcraft, but rather simple math. We’ll explain.
Where The Lines Cross And Why
The mathematical equation for horsepower is torque times RPM, divided by 5,252. If you are familiar with algebraic expressions, you have probably already picked up why the lines of the dyno graph cross at 5,252 rpm. In the horsepower equation, when RPM equals 5,252, dividing it by the constant gives us a value of 1. So simplifying that equation for that specific RPM means that at 5,252 rpm, horsepower equals torque. (If you’re a pedantic math nerd, it actually means that horsepower equals torque, times 1, divided by one.)
So, we’ve answered why they always cross, but you might have picked up on something else… why is there an equation for horsepower? Aren’t we measuring it on the dyno? The answer to that question might surprise you. No, we aren’t directly measuring horsepower on the dyno. We are directly measuring torque, and then calculating horsepower using the torque measurement and engine RPM.
That leads us further down the mathematical rabbit hole. If all that is true, then below 5,252 rpm torque will always be greater than horsepower, and above 5,252 rpm, horsepower will always be greater than torque. But, again, why? That all comes down to the variable of time.
Torque Ove Time
You might have heard horsepower referred to as “torque over time.” While that isn’t quite correct mathematically, grammatically it is a fair description of horsepower. Let’s take a look at a make-believe dyno graph for a minute. For ease of discussion, let;s say the engine is perfectly efficient across a 5,000-rpm range, and it makes the same 500 lb-ft of torque at 2,500 rpm as it does at 5,000 and 7,500 rpm – a perfectly flat torque curve.
At 2,500 rpm, it is making that torque 42 times per second, which works out to 238 horsepower. At 5,000 It is making that same torque 83 times per second, which equates to 478 horsepower, or exactly double. It’s making the same 500 lb-ft of torque, but doing it twice as often in the same amount of time. Now, moving to the 7,500 rpm calculation, we can guess, based on the trend we’re seeing that it will make 1.5 times the horsepower as it does at 5,000 rpm since that torque is now happening 125 times per second instead of 83.
That guesstimate says 478 x 1.5 = 714 horsepower. Running the actual equation of 500 lb-ft times 7,500 rpm, divided by 5,252 gives us 714.014 horsepower. You can see how the same torque at different engine speeds makes for a linear graph. Now, it’s very uncommon to see a graph that is that straight, as an engine is more or less efficient at different engine speeds. But, what is common to all dyno graphs is that torque and horsepower will always cross at 5,252 rpm.
Now, if you want to really get into the physics definition of horsepower (and have a good old argument about lb-ft versus ft-lbf) I highly suggest you check out this article from a few years back where we dive into it. Be prepared to potentially have some leakage out of your ears as your brain melts, unless you are an engineer who loves that stuff (I found that foam earplugs did a pretty good job of keeping most of my brain inside my head while writing that).
If for some reason you see a dyno graph where horsepower and torque don’t cross at all, or cross at an RPM other than 5,252, the answer is likely to be one of two things. In the first scenario, the pull probably ended before 5,252 rpm, so the two never met on the dyno graph. In the case of the second oddity, it’s likely that the horsepower and torque traces are being graphed on different scales. You’ll likely find another set of numbers on the right-side Y-axis of the graph that scale differently than they do on the left. Equalize those two scales and the traces will once again cross at 5.252 rpm.