Worked problem

Motor Input Power, Current and Efficiency

Find the electrical input power, apparent power and line current of a 30 kW, 400 V three-phase motor at 92% efficiency and 0.86 power factor.

Electrical & Power · Last reviewed October 17, 2026

Given

A balanced three-phase induction motor delivers 30 kW of mechanical power at the shaft. Supply 400 V line-to-line. At this load the motor efficiency is 92% and the power factor is 0.86.

Find

The electrical input power, the apparent power, the line current and the motor losses.

Solution

Efficiency is output divided by input, so input power = 30 ÷ 0.92 = 32.61 kW.
Losses = 32.61 − 30 = 2.61 kW, which leaves the motor as heat.
Apparent power S = P ÷ PF = 32.61 ÷ 0.86 = 37.92 kVA.
Line current I = P ÷ (√3 × V × PF) = 32,609 ÷ (1.732 × 400 × 0.86) = 54.7 A. The same value follows from S ÷ (√3 × V) = 37,917 ÷ 692.8.
Reactive power Q = √(37.92² − 32.61²) = 19.3 kvar.

Answer

32.6 kW input  |  37.9 kVA  |  54.7 A line current  |  2.6 kW losses

Efficiency and power factor are different things

Efficiency compares shaft power with the electrical power taken from the supply, and it is used once, to turn the mechanical rating into an electrical input. Power factor compares real power with apparent power, and it sets the current for a given real power. Neither one multiplies the other inside the current formula once the input power is known.

Reading of "30 kW"	Input power	Line current
Shaft (mechanical) output, as here	32.61 kW	54.7 A
Electrical input	30.00 kW	50.4 A

Common mistakes

Using 30 kW as the electrical input when it is the shaft rating. The current comes out about 8% too low.
Multiplying by the efficiency instead of dividing, which gives 27.6 kW input.
Leaving out √3, which makes the current 1.73 times too high (94.8 A).
Using the full-load efficiency and power factor at a part load. Both fall when a motor is lightly loaded.

Related tools and labs

Calculators, labs and simulators are part of the All-Access Pass.

Questions

Is this the motor nameplate current?

It should be close, but the nameplate gives the rated current of the actual motor at its rated load. For conductor and protection sizing the code uses its own tabulated full-load currents. See the motor branch-circuit problem in this section.

Why does the motor take more current at lower voltage?

A motor drawing a fixed mechanical load takes roughly constant power, so a lower voltage means a higher current for the same power.

Does 400 V mean line-to-line?

Yes. Three-phase voltages are quoted line-to-line unless stated otherwise. The phase voltage of a wye system is 400 ÷ √3 = 231 V.

Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.

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