Why do horsepower and torque cross at 5,252 rpm?

We've talked in the past about the relationship between horsepower and torque. They work together, and horsepower needs torque to make you and your car happy. There's one magic number though that doesn't get much ink spilled its way, virtual or otherwise. The number is 5,252, and it's the point in the rev range where horsepower and torque will always cross paths. Why? Let's turn to Jason Fenske of Engineering Explained for some explanation of this interesting fact.

To break it all down, Fenske turns to his wonderful whiteboard. There, we're going to learn about power, torque, and velocity. You see, power is equal to force times any velocity. Velocity is understood to be a given distance divided by the time needed to cover that distance. Finally, torque is the figure generated by a force multiplied over a given radius value.

You need a basic understanding of those three physical ideas before we figure out why horsepower and torque cross at 5,252 rpm. It all boils down to the math behind both horsepower and torque. It also boils down to a bit of history. James Watt, a Scottish engineer who developed the concept of horsepower, figured out that one metric horsepower is needed to lift 75 kilograms by one meter in one second. It's related to how much work a horse will do related to the same work done by a steam engine. Today, we use horsepower as a bragging tool to win bench races.

Back to the magic 5,252 number though, and why horsepower and torque are mystically intertwined there. You have to take a deeper dive into the equations used to determine those three areas we discussed in the beginning of all of this; power, torque, and velocity. One horsepower is equal to 33,000 foot-pounds of work per minute. Add in the equations relating to torque and velocity, and you'll find that horsepower always equals torque multiplied by rpm, divided by 5,252.

Canceling out the equal variables, you wind up with horsepower equaling torque... at 5,252 rpm. It's a lot of math, but Jason breaks it down quite easily. So click play and learn something new today.