Power Factor Calculator
Calculate power factor from real power (W) and apparent power (VA) or reactive power (VAR). Understand the relationship between real, reactive, and apparent power in AC circuits. See also our Ohm's Law Calculator and kVA to kW Calculator.
How to Calculate Power Factor
Power factor (PF) is the ratio of real power (watts) to apparent power (volt-amperes) in an AC circuit. It represents how effectively electrical power is being converted into useful work. A power factor of 1.0 (unity) means all power is doing useful work. A lower power factor means more current is required to deliver the same real power, resulting in larger conductors, higher losses, and utility penalties.
Power factor is caused by the phase difference between voltage and current waveforms. In purely resistive loads, voltage and current are in phase (PF = 1). Inductive loads (motors, transformers) cause current to lag voltage, while capacitive loads cause current to lead voltage. Most industrial loads are inductive, resulting in lagging power factor.
Power Factor Formulas
Power Factor:
PF = P / S = cos(θ)
Power Triangle:
S² = P² + Q²
S = √(P² + Q²)
Where:
P = Real Power (Watts) — does useful work
Q = Reactive Power (VAR) — oscillates, no work
S = Apparent Power (VA) — total power delivered
θ = Phase angle between V and I
Relationships:
P = S × cos(θ) = V × I × PF
Q = S × sin(θ) = V × I × sin(θ)
S = V × I (apparent power)
Example Calculation
A motor draws 1000W of real power and 1200VA of apparent power:
Power Factor = P/S = 1000W / 1200VA = 0.833 (lagging)
Phase Angle = arccos(0.833) = 33.56°
Reactive Power = √(1200² - 1000²) = √(440000) = 663.3 VAR
Current at 240V: I = S/V = 1200/240 = 5.0A
If PF were 1.0: I = P/V = 1000/240 = 4.17A (17% less current!)
To correct to PF = 0.95:
Q_new = P × tan(arccos(0.95)) = 1000 × 0.329 = 328.7 VAR
Capacitor needed = 663.3 - 328.7 = 334.6 VAR
Power Factor Reference Table
| Load Type | Typical PF | Phase Angle |
|---|---|---|
| Resistive heater | 1.00 | 0° |
| Incandescent bulb | 1.00 | 0° |
| LED lighting | 0.90-0.99 | 6-26° |
| Fluorescent (ballast) | 0.50-0.70 | 45-60° |
| Computer/electronics | 0.60-0.75 | 41-53° |
| Induction motor (full) | 0.80-0.90 | 26-37° |
| Induction motor (no load) | 0.15-0.30 | 73-81° |
| Welding machine | 0.50-0.70 | 45-60° |
| Air conditioner | 0.75-0.85 | 32-41° |
| Synchronous motor | 0.90-1.00 | 0-26° |
| Capacitor bank | 0 (leading) | -90° |
| Industrial plant (avg) | 0.70-0.85 | 32-45° |
Frequently Asked Questions
What is a good power factor?
A power factor above 0.95 is considered good. Most utilities require industrial customers to maintain PF above 0.90 to avoid penalties. Unity (1.0) is ideal but rarely achievable in practice. Residential customers typically have PF between 0.85-0.95 and are not penalized because their loads are relatively small.
Why does low power factor cost money?
Low power factor means more current flows for the same real power. This requires larger transformers, thicker cables, and causes greater I²R losses in the distribution system. Utilities charge penalties (typically $0.50-$2.00 per kVAR) because they must supply the extra current even though it does no useful work. Correcting PF from 0.70 to 0.95 can reduce electricity bills by 10-30%.
How do I correct power factor?
The most common method is adding capacitor banks in parallel with inductive loads. Capacitors supply reactive power locally, reducing the reactive current drawn from the utility. Other methods include synchronous condensers, active power factor correction (PFC) circuits in electronic equipment, and properly sizing motors (oversized motors have poor PF at partial load).
What is the difference between leading and lagging power factor?
Lagging PF means current lags voltage (inductive loads — motors, transformers, solenoids). Leading PF means current leads voltage (capacitive loads — capacitor banks, long cable runs, some electronic power supplies). Most loads are inductive (lagging), which is why capacitors (leading) are used for correction.
Does power factor affect my home electricity bill?
Residential customers are typically billed only for real power (kWh) and are not charged power factor penalties. However, poor power factor still increases current in your home wiring, causing slightly higher I²R losses and potentially tripping breakers sooner. Power factor correction devices marketed to homeowners provide negligible savings.
Can power factor be greater than 1?
No. Power factor ranges from 0 to 1 (or 0% to 100%). A PF of 1 means voltage and current are perfectly in phase. If your calculation gives PF > 1, check your measurements — apparent power (VA) must always be greater than or equal to real power (W). Measurement errors or non-sinusoidal waveforms can cause apparent discrepancies.
Power Factor Correction
Power factor correction (PFC) is the process of improving power factor by adding reactive components (usually capacitors) to offset the reactive power demand of inductive loads. The goal is to reduce the apparent power (and thus current) drawn from the supply while maintaining the same real power delivery. Proper PFC reduces utility penalties, decreases I²R losses, frees up transformer and cable capacity, and improves voltage regulation. Overcorrection (leading PF) should be avoided as it can cause voltage rise and resonance issues.
Practical Applications
- Industrial plants: Capacitor banks correct PF to avoid utility penalties and reduce demand charges
- Motor circuits: Individual capacitors at each motor provide optimal correction
- UPS systems: Input PFC circuits reduce current draw and improve efficiency
- Generator sizing: Low PF loads require larger generators (sized by kVA, not kW)
- Transformer loading: PF correction frees transformer capacity for additional real power loads
- LED drivers: Active PFC circuits in LED drivers maintain PF > 0.9 per energy codes