A motor nameplate quotes a shaft rating in kilowatts. The conductor feeding it cares about amperes, and getting from one to the other means paying for everything that sits between the terminals and the shaft.

$I = \dfrac{P_{out}}{\sqrt{3}\, V \,\mathrm{PF}\, \eta}$ — read aloud I equals P-out over root-three V P F eta. $I$ is the full-load line current in amperes; $P_{out}$ is the nameplate SHAFT power in watts; $V$ is the line-to-line voltage in volts; PF is the power factor, $\cos\varphi$, a bare decimal; and $\eta$ is the efficiency, entered as a fraction. Both PF and $\eta$ sit below the bar, and both are less than one, so both push the current UP. Leave either out and you will under-size a conductor.

The $\sqrt{3}$ is the three-phase signature. Three conductors share the work, and the factor between line and phase quantities is $\sqrt{3} \approx 1.732$, not 3. Writing 3 there is the single most common slip in this chapter, and it reads about 42% low — comfortably enough to pass a lazy check and fail a real one.

Then the second current. At the instant of an across-the-line start the rotor is standing still, so it generates no back-EMF, and the stator looks like its own bare impedance across the line. The result is locked-rotor current: $I_{LR} = k\, I_{FL}$, where $k$ is the multiple the nameplate quotes — typically 6 to 7, sometimes 8. It lasts a second or two, it is what dims the lights across the plant, and it is why starters, breakers and generators are sized on inrush rather than on running load.