What Is Power Factor? Real Power, Reactive Power, and the Power Triangle

Most electrical bills charge you for apparent power, but only some of that does useful work. The gap between what you draw and what you use is power factor. Understanding it takes about five minutes, and it explains why certain motors run hot, why utilities add surcharges, and what those capacitor banks on factory floors actually do.

The three types of power

Every AC electrical system involves three related quantities:

Real power (P) is measured in watts (W) or kilowatts (kW). This is the power that does actual work: spinning a motor shaft, heating an element, lighting a bulb. Your utility bills you for kilowatt-hours, which are units of real power over time.

Reactive power (Q) is measured in volt-amperes reactive (VAR or kVAR). It doesn't do work in the traditional sense. Instead, it builds and collapses magnetic fields in inductors (motors, transformers) and charges and discharges capacitors. The energy sloshes back and forth between the source and the load rather than being consumed. You don't get billed directly for VAR, but the currents it causes still flow through your wiring and equipment.

Apparent power (S) is measured in volt-amperes (VA or kVA). It's the total power the source must supply, calculated as voltage times current without any phase correction. It's also what determines the physical size of your transformer, wiring, and breakers.

The relationship between them:

S² = P² + Q²

The power triangle

Draw a right triangle. The horizontal leg is P (real power). The vertical leg is Q (reactive power). The hypotenuse is S (apparent power). The angle between the hypotenuse and the horizontal is the phase angle, usually written as φ (phi).

This triangle isn't just a diagram for textbooks. It's genuinely useful for thinking through what happens when you add capacitors or change your load mix. Adding capacitive reactive power shrinks the vertical leg, which pulls the hypotenuse closer to the horizontal, which increases power factor.

What power factor actually is

Power factor is the ratio of real power to apparent power:

PF = P / S

It's a number between 0 and 1 (sometimes expressed as a percentage). A PF of 1.0 means all the apparent power becomes useful work. A PF of 0.7 means 70% does work and 30% circulates uselessly, causing heating and wasted capacity.

You can also express it in terms of the phase angle:

PF = cos(φ)

When current and voltage are perfectly in phase, φ = 0°, cos(0) = 1, and power factor is unity. Inductive loads cause current to lag behind voltage. Capacitive loads cause current to lead. Either way, a phase shift reduces PF.

The power factor calculator works through this directly: enter real power and apparent power (or voltage and current plus the phase angle) and it returns PF, the phase angle, and the reactive power component.

Lagging vs leading power factor

A lagging power factor means current lags voltage. This is the common case with inductive loads: motors, transformers, fluorescent ballasts. The load needs reactive power from the source.

A leading power factor means current leads voltage. This happens with capacitive loads or when you've over-corrected with capacitor banks. Leading PF causes its own problems: voltage rise, resonance issues, and potential reverse reactive flow.

Most real systems run slightly lagging, somewhere between 0.7 and 0.95.

Why it matters in practice

A low power factor forces higher currents for the same amount of real work. Higher currents mean:

Utilities size their generation and distribution infrastructure around apparent power, not just real power. A customer pulling 100 kVA at 0.7 PF delivers only 70 kW of work but causes the same infrastructure load as a 100 kVA unity-PF customer delivering 100 kW. That's why large commercial and industrial customers pay penalty surcharges when their measured PF drops below 0.85 or 0.90.

Residential customers usually aren't metered for reactive power, but that doesn't mean it's free. The heating losses in your wiring are real, and a very low PF in a home with lots of motors (well pumps, old HVAC compressors, pool pumps) will show up indirectly.

What sets the power factor of a system

Every load in your facility contributes to the overall power factor:

The system PF is a weighted combination of all these. A facility that runs motors lightly loaded most of the time will have a chronically poor PF even if the motors themselves are rated at 0.9 when fully loaded.

Measuring power factor

The simplest method is to measure real power with a wattmeter and apparent power from V × I (RMS voltage times RMS current), then compute the ratio. Modern power quality meters do this directly and often display harmonic distortion as well.

For three-phase systems, the formula picks up a factor of √3:

PF = P / (√3 × V_line × I_line)

The power factor calculator handles both single-phase and three-phase cases if you enter the right values.

A note on displacement vs total power factor

What we've described is displacement power factor, based on the fundamental frequency (50 or 60 Hz). Total power factor also accounts for harmonic distortion, which switching power supplies and variable-frequency drives inject into the supply. A device can have good displacement PF and still draw distorted current that causes problems upstream.

For most practical calculations, displacement PF is what matters. For facilities with heavy VFD or UPS loads, total harmonic distortion (THD) matters too.

If you want to skip the math and just compute the numbers, the calculator on this site takes real and apparent power (or current and voltage) and returns PF, phase angle, and reactive power in one step.