Power factor explained: real, reactive and apparent power
Power factor is the ratio of real power to apparent power in an AC circuit: PF = kW Γ· kVA. It runs from 0 to 1 and tells you how much of the current a load draws actually does useful work. A heater has a power factor of almost exactly 1; an induction motor, especially one running lightly loaded, can be well below that, so it draws noticeably more current than its wattage alone suggests. The power factor calculator works out the numbers, and this guide explains what they mean.
Why AC power has a factor
In a DC circuit, power is simply volts times amps. In an AC circuit the voltage and current are both waves, reversing direction 50 or 60 times a second. For a purely resistive load, such as a kettle element, the current rises and falls exactly in step with the voltage, and volts times amps is the real power. Motors, transformers and fluorescent ballasts contain coils, which store energy in a magnetic field and hand it back every cycle; capacitors do the same with an electric field. That shifts the current wave in time relative to the voltage. For part of each cycle energy flows back towards the supply, so the current is larger than the useful power requires. When the current lags behind the voltage, as with motors, the power factor is described as lagging; when it runs ahead, as with capacitive loads, it is leading.
The power triangle
Three quantities describe an AC load:
- Real power (P, in watts or kW) does the actual work: heat, light and motion. It is what an energy meter adds up as kWh.
- Reactive power (Q, in volt-amperes reactive, VAR or kVAR) is the energy that flows back and forth every cycle without being used.
- Apparent power (S, in volt-amperes, VA or kVA) is volts times amps: the total the wiring has to carry.
The three form a right-angled triangle, so kVAΒ² = kWΒ² + kVARΒ², exactly the relationship in The Pythagorean theorem: aΒ² + bΒ² = cΒ², explained with examples. The angle Ο between real and apparent power is the phase shift between voltage and current, and for sine waves the power factor equals cos Ο. A 10 kW load at a power factor of 0.8 has an apparent power of 10 Γ· 0.8 = 12.5 kVA, reactive power of β(12.5Β² β 10Β²) = 7.5 kVAR, and a phase angle of 36.9Β°.
Why a low power factor matters
Current depends on apparent power, not real power. On a 230 V single-phase supply that 10 kW load at a power factor of 0.8 draws 10,000 Γ· (230 Γ 0.8) β 54.3 A, against 43.5 A if its power factor were 1. The extra current heats cables and transformers, adds voltage drop and uses up capacity the network could otherwise supply to someone else. That is why generators, transformers and UPS units are rated in kVA, and why utilities commonly charge commercial customers extra when their power factor falls below a limit, typically somewhere between 0.9 and 0.95. The watts to amps calculator includes power factor for single- and three-phase loads. Most households are billed only for real energy in kWh, as What is a kilowatt-hour, and how do you work out what an appliance costs? explains, so a home's power factor rarely shows up on the bill.
Displacement and distortion
Phase shift is not the only cause. Many electronic power supplies, in chargers, LED drivers and computers, draw current in short pulses near the peaks of the voltage wave rather than smoothly. Those distorted currents contain harmonics, multiples of the supply frequency, and they lower the power factor even when there is no phase shift at all. The overall power factor is therefore the product of the displacement power factor (cos Ο) and a distortion power factor. A switched-mode power supply with no correction typically manages only about 0.55 to 0.65; designs with active power factor correction shape the current into a near-sine wave and reach up to about 0.99.
Correcting power factor
Inductive loads draw lagging reactive power and capacitors draw leading reactive power, so a capacitor bank connected near the motors can supply the reactive power locally, and it no longer has to travel through the supply cables. The capacitor rating needed is kVAR = kW Γ (tan Οβ β tan Οβ), where Οβ and Οβ are the phase angles before and after correction. Raising a 50 kW load from a power factor of 0.75 to 0.95 needs about 27.7 kVAR and cuts the supply current by about 21%, because current scales with 1 Γ· PF. For a delta-connected bank on a 400 V, 50 Hz three-phase supply, that works out at roughly 183 Β΅F per phase; the calculator handles single- and three-phase supplies.
Correction is not risk-free. Over-correcting gives a leading power factor, and capacitors can resonate with harmonics from variable-speed drives, so industrial correction should be specified by an electrical engineer and installed by qualified electricians. For the real-energy side of the bill, the electricity cost calculator turns kW and hours into money.
Sources and further reading
The claims in this guide rest on these references, which were checked when the guide was last updated. Spotted an error? The contact page says how to report it.