Motors are sold in kilowatts. Shafts, keys and couplings feel none of it — they feel torque. The line that crosses between the two is $P = T\omega$, read aloud P equals T omega, or turned round for what you usually want, $T = \dfrac{P}{\omega}$.

The letters: $P$ is the transmitted power in watts — so a nameplate's kilowatts get multiplied by 1000 on the way in. $T$ is the shaft torque in newton-metres. And $\omega$ — the Greek letter omega — is the angular speed, which must be in radians per second and nothing else. Nameplates print rev/min, so there is always a conversion first: $\omega = \dfrac{2\pi n}{60}$, where $n$ is the speed in rev/min. One revolution is 2π radians, one minute is 60 seconds; that is the entire derivation, and it is worth being able to rebuild rather than remember.

Dropping rpm straight in where ω belongs is the single most common error in power transmission, and it is quietly dangerous: it under-reports the torque by 60/2π, about 9.55 times, which is the difference between a shaft that lasts and a shaft that is already cracked.

The consequence to carry away is the trade-off. At constant power, torque is inversely proportional to speed. A 10 kW shaft at 3000 rev/min carries about 32 N·m; the same 10 kW at 30 rev/min carries about 3180 N·m. That is why the slow end of every gearbox is the fat end, and why low-speed machinery is so heavy for the power it moves.