Motor Torque from Power and Speed

Power is torque times rotational speed, so torque is power divided by speed. In SI that is $T = P/2\pi N$ with P in watts, N in revolutions per second and T in newton metres: 7.5 kW at 1500 rpm is 25 rev/s, so $T = 7500/(2\pi \times 25) \approx 47.7$ N·m. Nothing else is going on — every "torque formula" in the trade is this relation wearing different units.

The North American version is $T = 5252 \times HP/RPM$ with torque in pound-feet, and 5252 is not a physical constant but a unit conversion: one horsepower is 550 ft·lbf per second, and $550 \times 60/2\pi = 5252.1$. Pick horsepower and rpm from this solver's unit menus and the two forms agree to the last digit. A 10 hp motor at 1750 rpm develops $5252 \times 10/1750 \approx 30$ lb·ft.

The 5252 also explains the one fact that surprises everyone reading a dynamometer chart: the horsepower and torque curves always cross at 5252 rpm, on every engine ever built, because that is where the multiplier equals one. Below that speed torque exceeds power numerically, above it the reverse. The practical warning for motor work is that this gives torque at rated speed only. Starting torque, breakdown torque and torque at a stall are set by the machine's speed-torque curve, not by its nameplate power, and a motor driven by a VFD below its base speed holds torque while its power falls away.