Let’s refer to an 4 stroke internal combustion engine in this case.

In: 4

Torque and power are connected by the RPM of the engine. The formula is:

Power = constant * torque * RPM.

The value of the constant depends on the unit of power and torque you use.

The torque of an internal combustion engine has a peak and is lower at both higher and lower RPM. So where the peek power is relative to peek torque depends on how quickly the torque drops at higher RPMs

Let’s say the torque peek is at 4500 RPM and then starts to decrease to at least say 95% of max at 6000 RPM.

That is an increase in RPM by a factor of 6000/4500= 1.3 and the torque change is a factor of 0.95 which means the change in power from 4500 to 6000, RPM is 1.3 * 0.95 = 1.24. So the power increase by 24% even if the torque drops because the RPM increased even more.

The torque need to drop very quickly after it peeks to have the power peek at the same RPM. If the torque drops to 1/1.3= 0.769 = 77% of peak torque from at 6000 RPM the power is the same at 4500 and 6000 RPM. The torque need to drop off even faster to have a power peek at 4500 RPM.

Real-world engines have a relatively flat torque curve around the peek so max power will be at a higher RPM than max torque.

If I am not mistaken the peak power is at the RPM the slope of the torque curve is -1. The torque has to drop faster than the RPM increase

The number was taken from [this graph](https://x-engineer.org/wp-content/uploads/2017/07/Honda-2.0-SI-engine-torque-and-power-curves-at-full-load.jpg) fo a Honda gasoline engine. I just read out them from the grape so they are not exact. The power increase from max torque to max power is approximately 130 HP to 150 HP or an increase of 19%. The error is because the number read out from the graph are not exact

Power is torque multiplied by RPM. An engine with half of the torque but double the RPM will produce the same power.

In general, as the RPM goes above the highest torque point, the power will continue to increase for a little bit as the increased RPM makes up for the lost torque. Then, the torque drops more and the increased RPM can no longer make up for that, so power drops eventually at high enough RPM.