Motor calculations

full load ampsFLAmotor slipsynchronous speedmotor efficiencynameplate

Full-load current, synchronous speed, slip, efficiency and input power — reading a motor nameplate and checking what it actually draws.

Three-Phase Motor Full-Load Current

I = \frac{P_{out}}{\sqrt{3} \, V \, \text{PF} \, \eta}

Line current of a three-phase motor from its shaft output power, voltage, power factor and nameplate efficiency in percent.

Synchronous Speed from Frequency and Poles

N_{s} = \frac{2f}{p}

Speed of an AC machine's rotating field from supply frequency and pole count — the familiar 120f/p when read out in rpm.

Induction Motor Slip

s = \frac{100 \, (N_{s} - N_{r})}{N_{s}}

Percent slip of an induction motor: how far the rotor falls behind the rotating magnetic field, as a share of synchronous speed.

Motor Efficiency

\eta = \frac{100 \, P_{out}}{P_{in}}

Percentage efficiency of a motor or drive as mechanical output power divided by electrical input power, times one hundred.

Three-Phase Real Power

P = \sqrt{3} \, V_{L} I_{L} \, \text{PF}

Real power drawn by a balanced three-phase load from its line-to-line voltage, line current, and power factor.

How they fit together

An induction motor's synchronous speed comes only from the supply frequency and the pole count: 120f/p, so 1800 rpm for a four-pole motor at 60 Hz and 1500 rpm at 50 Hz. It never quite gets there — the rotor must lag the rotating field to induce current at all, and that lag is slip, typically 1 to 3% at full load, which is why the nameplate says 1750 rather than 1800. Full-load current, efficiency and input power tie the mechanical output back to what the conductors carry.

Slip is the useful diagnostic because it is proportional to load: a motor turning at 1795 rpm is at roughly a quarter of its rated torque, which is a far better read on loading than clamping the amps, since current stays stubbornly high at light load thanks to magnetising current. Nameplate FLA is the number to use for overload sizing on that specific motor; the NEC table values, which are deliberately conservative and may not match the nameplate, are the ones for conductor and feeder sizing — using the wrong one for the wrong purpose is the standard inspection failure. On VFDs, remember that reducing frequency drops synchronous speed proportionally and that a constant-torque load below about 20 Hz will overheat a self-cooled motor, because the shaft-mounted fan slows with the shaft.