Power Factor Formula
Calculate power factor PF = Real Power / Apparent Power.
Returns efficiency ratio, reactive power in VAR, and capacitor sizing for power factor correction.
Need to calculate, not just reference? Use the interactive version.
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The Formula
PF = P / S = cos(φ)
Power factor measures how much of the electrical power is actually doing useful work. A power factor of 1.0 (unity) means all power is used efficiently. Lower values mean wasted energy.
Variables
| Symbol | Meaning |
|---|---|
| PF | Power factor (unitless, 0 to 1) |
| P | Real (active) power — actual work done (Watts) |
| S | Apparent power — total power supplied (Volt-Amps, VA) |
| φ | Phase angle between voltage and current |
Example 1
A motor draws 5,000 VA of apparent power but uses only 4,000 W of real power
PF = 4,000 / 5,000
PF = 0.80 (80% of the power is doing useful work)
Example 2
A circuit has a phase angle of 25°. What is the power factor?
PF = cos(25°)
PF = 0.906 (fairly efficient)
When to Use It
Use the power factor formula when:
- Evaluating the efficiency of electrical equipment
- Sizing generators and transformers for industrial loads
- Calculating power factor correction capacitor requirements
- Reducing electricity costs (utilities penalize low power factor)
Key Notes
- Most industrial motors and fluorescent lighting have lagging power factors (0.7–0.95) because inductive loads draw reactive magnetizing current that does no useful work but still heats conductors
- Utilities penalize commercial customers for power factors below ~0.90 because low PF forces them to generate and transmit more apparent power for the same useful output
- Power factor is corrected by adding capacitor banks in parallel with inductive loads — capacitors supply reactive power locally, canceling inductive reactive demand and raising PF toward unity
Key Notes
- Power factor = cosφ = P/S: φ is the phase angle between voltage and current. Real power P (watts) performs useful work. Apparent power S = V_rms × I_rms (volt-amperes). PF = 1 means all current does work; PF < 1 means some current is wasted on reactive energy exchange.
- Power triangle: S² = P² + Q²: Real power P, reactive power Q (VAR), and apparent power S form a right triangle. Inductive loads (motors) create lagging current (positive Q); capacitive loads create leading current (negative Q). The power factor angle φ = arctan(Q/P).
- Why low power factor is costly: The utility must generate and transmit more apparent power (higher current) to deliver the same real power. Cables, transformers, and switchgear must be sized for peak current, not average useful power — a direct cost with no benefit to the customer.
- Power factor correction: Adding capacitor banks in parallel with inductive loads (motors, fluorescent lights) cancels reactive power — Q_cap + Q_inductor ≈ 0 — raising PF toward 1.0. Industrial facilities often install automatic capacitor banks to avoid utility penalties for PF below 0.9.
- Applications: Power factor analysis is used in industrial plant efficiency auditing, motor drive design, UPS and generator sizing, grid stability management, and the design of switching power supplies (which include active PFC circuits to maintain PF close to 1.0).