Power moves the work.
Torque turns the shaft.
Connect rotational speed, shaft torque and mechanical output without confusing motor output with the electrical input of the complete machine.
Power, torque and speed describe different parts of the same motion.
DOE relates motor horsepower, shaft torque and rotational speed. The SI relationship below uses watts, newton meters and radians per second directly.
Less speed means more torque for the same power.
From the equation, torque rises as RPM falls when mechanical power is held constant. Actual machine drives have torque, current, thermal and control limits; the OEM curve controls.
Power rises with speed when torque is held constant.
Doubling RPM at the same shaft torque doubles mechanical power. That relationship does not promise that a specific spindle can deliver constant torque across its range.
Peak, intermittent, 30-minute and continuous ratings answer different duty questions. Preserve the rating duration and speed point whenever power or torque is cited.
This reference explains terms and arithmetic. It does not size conductors, overcurrent protection, transformers, disconnects, grounding, arc-flash protection or a branch circuit. Use the exact machine documentation, the authority having jurisdiction and qualified electrical professionals. Servicing also requires an applicable hazardous-energy control program.