Power Factor and Reactive Power Calculator
Find real power, reactive power, apparent power, and power factor for an AC circuit from voltage, current, and the phase angle between them.
⚡ What is Power Factor?
Power factor is the ratio of real (usable) power to apparent (total) power delivered in an AC circuit, given by PF = cos(phi), where phi is the phase angle between voltage and current. Together, real power P, reactive power Q, and apparent power S form the classic AC power triangle, with S as the hypotenuse, P along the base, and Q along the vertical side.
Electrical engineers check power factor whenever sizing motors, transformers, and distribution equipment, or evaluating utility bills, since a low power factor means more current must flow to deliver the same useful (real) power, requiring larger conductors and equipment throughout the supply chain for no additional useful work.
A common point of confusion is treating leading and lagging power factor as the same thing. A lagging power factor (positive phase angle, current lags voltage) is typical of inductive loads like motors, a leading power factor (negative phase angle, current leads voltage) is typical of capacitive loads. Both reduce the power factor magnitude below 1, in opposite directions on the power triangle, and power factor correction capacitors specifically exploit this by adding leading reactive power to offset an inductive load's lagging reactive power.
This calculator computes the full power triangle, apparent, real, and reactive power, plus the resulting power factor, from your voltage, current, and phase angle, automatically classifying the load as leading, lagging, or unity.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Induction Motor (Lagging Power Factor)
V = 230 V, I = 10 A, φ = 30° (lagging)
Example 2 — Overcorrected Capacitor Bank (Leading Power Factor)
V = 400 V, I = 25 A, φ = -20° (leading)
Example 3 — Purely Resistive Load (Unity Power Factor)
V = 120 V, I = 15 A, φ = 0°
❓ Frequently Asked Questions
🔗 Related Calculators
What is power factor?
Power factor is the ratio of real (usable) power to apparent (total) power in an AC circuit, given by PF = cos(phi), where phi is the phase angle between voltage and current. A power factor of 1 means all delivered power does useful work, a lower power factor means more current is needed to deliver the same real power.
What is the formula for real, reactive, and apparent power?
Apparent power S = V x I, real power P = S x cos(phi), and reactive power Q = S x sin(phi), where phi is the phase angle between voltage and current. These three form the classic AC power triangle, with S as the hypotenuse.
What is reactive power and why does it matter?
Reactive power (measured in VAR) is the power that oscillates between the source and an inductive or capacitive load without doing net useful work, it still requires current-carrying capacity in the supply system. Reducing reactive power (improving power factor) frees up capacity for real power delivery.
What is the difference between leading and lagging power factor?
A lagging power factor (positive phase angle) means current lags voltage, typical of inductive loads like motors and transformers. A leading power factor (negative phase angle) means current leads voltage, typical of capacitive loads. Both reduce power factor magnitude below 1, but in opposite directions on the power triangle.
Why do utilities penalize low power factor?
A low power factor means more current must flow to deliver the same real power, requiring larger conductors, transformers, and generation capacity throughout the distribution system for the same useful energy delivered. Utilities often charge industrial and commercial customers a penalty for power factor below a threshold, commonly around 0.9, to recover this extra infrastructure cost.
How is power factor corrected?
Power factor correction typically adds capacitor banks in parallel with an inductive load to supply its reactive power locally, reducing the reactive power the utility supply must deliver, and pushing power factor closer to 1 without changing the real power delivered to the load.
What is apparent power measured in?
Apparent power S is measured in volt-amperes (VA) or kilovolt-amperes (kVA), rather than watts, specifically to distinguish it from real power, since it represents the total current-and-voltage product, not the actual useful work being done.
Can power factor be greater than 1?
No, power factor is always between 0 and 1 (or -1 and 1 if sign is tracked for leading/lagging), since it equals cos(phi) and cosine's magnitude never exceeds 1. A calculated value outside this range indicates an input error.
What does a phase angle of exactly 90 degrees mean?
A phase angle of 90 degrees means the load is purely reactive (either purely inductive or purely capacitive), with power factor equal to 0. All the apparent power is reactive, none of it is real (useful) power, this is a physically extreme case rarely seen for a real load.
What units does this calculator use?
Voltage is entered in volts, current in amperes, and phase angle in degrees. Results are shown in volt-amperes (VA) for apparent power, watts (W) for real power, and volt-amperes-reactive (VAR) for reactive power.