Imagine two installations both using 100 kW. One runs at power factor 1.0; the other at 0.8. They produce the same useful electrical power, but the second needs more current from the supply.
Power factor tells us how effectively apparent power (kVA) is being used to supply active power (kW). It helps engineers size feeders, understand reactive demand and estimate power-factor correction.
What is power factor, in simple terms?
Power factor (PF) is active electrical power divided by apparent power. It ranges from zero to one for the loads in this guide. A value closer to one means less current is needed to deliver the same kW at the same voltage.
For a balanced, sinusoidal AC system, PF is also the cosine of the phase angle between voltage and current. That is where the familiar term cos φ comes from.
How P, Q and S are connected
Active (kW)
Energy actually converted to work, heat or light.
Reactive (kvar)
Power exchanged by magnetic or electric fields.
Apparent (kVA)
Total volts × RMS amps carried by the source.
For a sinusoidal system, P and Q form perpendicular sides of a power triangle; S is its hypotenuse.
Try moving the slider. With P fixed at 100 kW, improving PF reduces Q and S. This also reduces current for the same supply voltage, assuming no other change to the load.
Why the voltage–current angle matters
In a purely resistive load, voltage and current rise and fall together; the angle φ is approximately zero and displacement power factor is one.
Inductive loads such as motors and transformers typically make fundamental current lag voltage. Capacitive loads make fundamental current lead voltage. Both can have the same PF magnitude, but their reactive power signs are opposite.
Why does power factor decrease?
Motors, transformers and other magnetic equipment need magnetizing current. That extra current may increase the kVA delivered by the transformer without increasing the useful active kW by the same amount.
The power factor of an installation varies as equipment starts, stops or runs at different loading. A lightly loaded motor may have a poorer PF than the same motor near rated load.
What changes when PF is low?
For a fixed supply voltage and active power, a lower PF means a larger apparent power and current. That can increase losses and voltage drop in conductors and use up capacity in transformers and switchgear.
For single-phase AC, use line-to-neutral voltage without the √3 multiplier. Reactive-energy charging or power-factor penalties depend on the actual supplier and contract; don't assume a universal limit.
How a capacitor bank can improve PF
An inductive load typically draws positive reactive power. A correctly sized capacitor bank provides reactive power locally, reducing the reactive power the upstream supply needs to deliver.
For an inductive load corrected to another lagging target, the familiar sizing formula is:
Here P is the existing active electrical power (kW), φ₁ is the old phase angle, φ₂ is the desired angle, and Qc is the ideal compensation in kvar.
Important: if the load is already leading, more capacitors may make matters worse. A leading-to-lagging change may require inductive compensation. KiloVolt uses signed kvar internally to detect that situation.
100 kW: correct PF from 0.80 to 0.95
Assume a balanced, sinusoidal, inductive three-phase load drawing 100 kW at 400 V line-to-line. We want to improve PF from 0.80 lagging to 0.95 lagging.
Step 1 — Initial reactive power
Step 2 — Target reactive power
Step 3 — Ideal capacitor bank rating
Step 4 — Current before and after
The theoretical correction is approximately 42.13 kvar, and the upstream current falls by approximately 28.49 A for this load and these assumptions.
Does a 42.13 kvar result mean buying a 42.13 kvar capacitor bank?
No. The calculation gives a theoretical reactive-power requirement at one operating point, not a final capacitor-bank specification. Real capacitor steps are available in standard commercial sizes, and their delivered kvar depends on terminal voltage and rating.
Variable installations may need an automatic multistep bank; fixed loads may be treated differently. Before selection, check the load profile, switching, harmonic distortion, possible resonance, detuned reactors, inrush, protection, ventilation and required connection arrangements.
Displacement PF is not always true PF
For an undistorted sinusoidal waveform, PF = cos φ. But modern nonlinear loads can distort current waveforms. In that case, true power factor depends on both fundamental phase displacement and distortion.
This calculator uses the conventional sinusoidal power triangle. It does not calculate harmonics or true PF for distorted waveforms. Those belong in our future dedicated Power Quality tools.
Common mistakes to avoid
These represent active, apparent and reactive power respectively. They are not interchangeable.
Power-factor correction usually reduces upstream kVA and current, not the useful work or active power required by the load.
The √3 factor applies to balanced three-phase calculations with line-to-line voltage, not single-phase calculations.
Check the sign of reactive power before choosing capacitive or inductive compensation.
Also assess harmonics, varying loads, actual system voltage, switching and equipment ratings.
Further reading: Schneider Electric — Theoretical principles to improve power factor (external engineering reference).
Try it with your installation
Enter existing kW or kVA, current cos φ, target cos φ and supply voltage to calculate P, Q, S, line current and theoretical reactive correction.
Open Power Factor Calculator →