Quiz: Power Factor Calculator

Try the power factor quiz to check how well you understand the power factor.

Power factor0.8cos of the phase angle, 36.87°

Current27.0633 Athree-phase AC at 400 V, as entered

Real power15 kW20.1153 hp equivalent

Apparent power18.75 kVA18.75 kVA — what the supply and cabling must carry, regardless of power factor

Reactive power11.25 kVARcirculates without doing work, yet still heats the cable

Current at unity power factor21.6506 A5.4127 A less — correcting power factor reduces current for the same useful work

Phase voltage230.9401 Vline ÷ √3

Power per phase5 kW

Same load single-phase46.875 A√3 times the current — which is the whole reason large loads are three-phase

Breaker at 125% of the load33.83 Acontinuous loads are conventionally sized this way, then rounded up to the next standard rating

Energy a day60 kWh

Cost a day18

Cost a year6,570note that most tariffs bill real energy in kWh, so a poor power factor costs a domestic customer nothing directly — industrial tariffs often penalise it

The formula

P = VI for DC; VI·pf single-phase; √3·V_L·I_L·pf three-phase

Three supplies, three different answers

The current a load draws for a given real power depends on the supply. DC is simply P/V. Single-phase AC divides by the power factor as well, because voltage and current are out of step and not all the flowing current does work. Three-phase divides additionally by √3, since the three line voltages are 120° apart. Quoting a current without saying which convention was used is how cables get undersized.

Apparent power in VA is what the cabling and the transformer must actually carry; real power in watts is what does useful work. The gap between them is reactive power, which circulates without doing anything useful and still heats the conductors. That is why transformers and generators are rated in VA rather than watts.

A motor's horsepower rating is its shaft output, not its electrical input. A 90%-efficient 5 hp motor draws about 4.1 kW, not 3.7 kW, and sizing the supply from the nameplate horsepower without dividing by efficiency undersizes it by exactly the loss.

On power factor and bills: domestic meters record real energy in kWh, so a poor power factor costs a household nothing directly. Industrial tariffs often charge for kVA or penalise low power factor, because the utility has to build for the apparent power.