Power Factor Calculator

Power factor is calculated as the ratio of real power (P) to apparent power (S): PF = P / S. It can also be expressed as the cosine of the phase angle φ between voltage and current: PF = cos(φ). A value of 1 indicates a perfectly efficient circuit with no reactive power losses.

In an AC circuit, power factor is a dimensionless number between 0 and 1 that describes how effectively electrical power is being converted into useful work. It represents the phase difference between voltage and current caused by reactive components like inductors and capacitors. A lower power factor means more reactive power and less efficient energy transfer.

The power factor triangle is a right-angled triangle where the horizontal side represents real power (P) in watts, the vertical side represents reactive power (Q) in VAR, and the hypotenuse represents apparent power (S) in VA. The angle between P and S is the phase angle φ, and the power factor equals cos(φ). The relationship is expressed as S² = P² + Q².

Power factor is dimensionless — it has no unit. It is expressed as a pure number between 0 and 1, or sometimes as a percentage. It may also be labeled as 'leading' (capacitive load) or 'lagging' (inductive load) to indicate the nature of the reactive power in the circuit.

An ideal power factor is 1.0 (or unity), which means all supplied power is converted into useful real power with zero reactive power. In practice, most industrial systems target a power factor of 0.95 or above. Values below 0.9 are generally considered poor and may result in energy penalties from utility providers.

A power factor of 0.75 means that only 75% of the apparent power supplied to the circuit is doing useful work (real power), while the remaining 25% is reactive power cycling between the source and reactive components. This represents a relatively poor power factor, and improving it toward 1.0 would reduce energy waste and utility costs.

Power factor correction involves adding capacitors (for inductive loads) or inductors (for capacitive loads) to reduce reactive power and bring the power factor closer to 1. The required reactive compensation Q_c = P × (tan φ₁ − tan φ₂), where φ₁ is the current phase angle and φ₂ is the desired phase angle. Capacitor banks are the most common correction method in industrial settings.

Real power (P, in watts) is the actual power consumed and converted to useful work like heat or motion. Reactive power (Q, in VAR) is stored and returned by inductors and capacitors without doing useful work. Apparent power (S, in VA) is the total power delivered by the source, combining both real and reactive components via S² = P² + Q².