Power factor is the ratio of real power (P, doing useful work) to apparent power (S, total power drawn from the source). A low PF means the electrical system is inefficient, requiring higher current for the same real power. This causes increased line losses and utility demand charges.
⚠Utilities charge penalties for PF below 0.90-0.95. Power factor correction capacitors reduce reactive power, lower current, and eliminate penalties. Always use automatic PF correction for varying loads.
Understanding Power Factor
Power factor arises from the phase difference between voltage and current in AC circuits. Inductive loads (motors, transformers) cause current to lag voltage (lagging PF). Capacitive loads cause current to lead (leading PF). The power factor correction creates a balanced system where the utility sees unity PF, minimizing wasted current.
Real Power P
P = V×I×cos φ (watts). The power that does actual work: heating, lighting, motion. Measured by wattmeter. Billed by utility.
Reactive Power Q
Q = V×I×sin φ (VAR). Stored and returned by inductors/capacitors. Does no work but causes line current. Corrected with capacitors.
Apparent Power S
S = V×I (VA). Total power drawn from source. S = √(P²+Q²). Transformer and generator ratings are in VA or kVA.
Power Triangle
Right triangle: P (adjacent), Q (opposite), S (hypotenuse). φ = arctan(Q/P). PF = cos φ = P/S. S² = P²+Q².
Teaching Example: Motor: P=100W, Q=50VAR (inductive).
S = √(100²+50²) = √12500 = 111.8 VA. PF = 100/111.8 = 0.894.
φ = arccos(0.894) = 26.6° (lagging). Current = S/V = 111.8/120 = 0.932A.
If PF corrected to 0.95: S = 100/0.95 = 105.3 VA. Current = 105.3/120 = 0.877A (6% reduction).
Applications
Industrial MotorsPower DistributionUPS SystemsSolar InvertersHVAC Systems
Frequently Asked Questions
What is power factor?▼
PF = P/S = cos φ. Ratio of real to apparent power. PF=1 is ideal. Low PF causes higher current and utility penalties.
How to improve PF?▼
Add capacitors in parallel with inductive loads. Capacitors supply leading reactive power to cancel lagging Q from motors. Target PF > 0.95.
Lagging vs leading PF?▼
Lagging: current lags voltage (inductive, motors). Leading: current leads voltage (capacitive, overcorrected). Inductive is more common industrially.
Does PF affect my electricity bill?▼
Yes. Utilities charge PF penalties below 0.90-0.95. Poor PF increases line current, requiring larger conductors and causing more losses. PF correction often pays for itself in < 2 years.
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