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PF = kW ÷ kVA = cos(θ)
kVA = √(kW² + kVAR²)
kVAR = kW × tan(θ)
Where:
The relationship between kW, kVA, and kVAR forms a right triangle. kVA is the hypotenuse, kW is the adjacent side, and kVAR is the opposite side. Power factor is the cosine of the angle between kW and kVA.
| Power Factor | Phase Angle | kVAR per kW | Status |
|---|---|---|---|
| 1.00 | 0.0° | 0.000 | Excellent |
| 0.95 | 18.2° | 0.329 | Excellent |
| 0.90 | 25.8° | 0.484 | Acceptable |
| 0.85 | 31.8° | 0.620 | Acceptable |
| 0.80 | 36.9° | 0.750 | Poor |
| 0.75 | 41.4° | 0.882 | Poor |
| 0.70 | 45.6° | 1.020 | Poor |
| 0.65 | 49.5° | 1.169 | Poor |
| 0.60 | 53.1° | 1.333 | Poor |
| 0.55 | 56.6° | 1.518 | Poor |
| 0.50 | 60.0° | 1.732 | Poor |
Power factor is a dimensionless number between 0 and 1 that describes how effectively electrical power is being converted into useful work output. It is defined as the ratio of real power (measured in watts or kilowatts) to apparent power (measured in volt-amperes or kilovolt-amperes). A power factor of 1.0 (unity) means all the power supplied by the source is being consumed as useful work, while a lower power factor indicates that a portion of the current flowing through the circuit is reactive -- it oscillates between the source and the load without performing any work. In AC circuits, this reactive component arises from inductive loads such as motors and transformers, which cause the current waveform to lag behind the voltage waveform, or from capacitive loads that cause current to lead voltage. Understanding and managing power factor is essential for efficient electrical system design, lower utility bills, and compliance with utility power factor requirements.
Use a wattmeter or read the kW value from your utility meter or power analyzer. Real power is the actual energy consumed by the load to perform useful work such as turning a motor shaft or generating heat.
Multiply the measured RMS voltage by the RMS current to get apparent power in VA, then divide by 1,000 for kVA. Alternatively, read the kVA directly from a power analyzer. This represents the total power drawn from the supply.
Power Factor = kW / kVA. The result will be a number between 0 and 1. For example, if a motor draws 45 kW of real power and 50 kVA of apparent power, the power factor is 45 / 50 = 0.90.
If the power factor is below your target (typically 0.95), calculate the required reactive compensation: kVAR needed = kW × (tan(arccos(PF_old)) - tan(arccos(PF_new))). This gives the capacitor bank size needed for correction.
Many commercial and industrial utility tariffs include power factor penalties when PF falls below 0.90 or 0.95. Improving power factor from 0.70 to 0.95 can reduce demand charges by up to 30%, translating to thousands of dollars in annual savings for facilities with large motor loads.
Low power factor means conductors and transformers carry more current than necessary for the actual work being done. Correcting power factor frees up capacity in transformers, cables, and switchgear, potentially deferring expensive infrastructure upgrades and allowing additional loads to be connected.
Reactive current flowing through cables and transformers causes I²R losses and voltage drop. Improving power factor reduces the total current drawn, which decreases copper losses, reduces voltage drop along feeders, and improves voltage regulation at the point of use.
| Load Type | Typical Power Factor | Type | Notes |
|---|---|---|---|
| Incandescent Lighting | 1.00 | Resistive | Unity PF -- purely resistive load |
| Electric Heaters | 0.95 - 1.00 | Resistive | Near-unity with minor reactive components |
| LED Lighting (with driver) | 0.85 - 0.95 | Capacitive | Depends on driver quality |
| Fluorescent Lighting | 0.50 - 0.95 | Inductive | Higher with electronic ballast |
| Induction Motor (full load) | 0.80 - 0.90 | Inductive | Improves as load increases |
| Induction Motor (half load) | 0.55 - 0.75 | Inductive | PF drops significantly at partial load |
| Induction Motor (no load) | 0.10 - 0.30 | Inductive | Very poor -- mostly magnetizing current |
| Welding Machine (arc) | 0.50 - 0.70 | Inductive | Highly variable with arc conditions |
| Variable Frequency Drive | 0.95 - 0.98 | Varies | Active front end improves PF |
| Computer / Server | 0.60 - 0.99 | Capacitive | PFC-equipped PSUs achieve 0.95+ |
| Air Compressor | 0.75 - 0.85 | Inductive | Large motor-driven load |
| Transformer (no load) | 0.10 - 0.20 | Inductive | Core magnetization dominates |
Lagging power factor occurs when current lags behind voltage, caused by inductive loads like motors and transformers. Leading power factor occurs when current leads voltage, caused by capacitive loads or overcorrection with capacitor banks. Most industrial loads are inductive and produce a lagging power factor.
Capacitor bank costs typically range from $25 to $50 per kVAR for fixed installations and $50 to $100 per kVAR for automatic switched banks. A typical 100 kVAR automatic bank might cost $5,000 to $10,000 installed. Payback periods of 1 to 3 years are common for industrial facilities with power factor penalties.
Yes, VFDs with active front-end rectifiers maintain near-unity power factor regardless of motor loading. Standard VFDs with diode rectifiers typically have a displacement power factor of 0.95-0.98 but may introduce harmonic distortion that lowers the true (total) power factor.
The power triangle is a right triangle showing the relationship between real power (kW), reactive power (kVAR), and apparent power (kVA). The horizontal side is kW, the vertical side is kVAR, and the hypotenuse is kVA. The angle between kW and kVA is the phase angle, and its cosine equals the power factor.
Most residential utility meters only measure real power (kWh), so residential customers are not charged for poor power factor. However, it can still cause issues in the home such as voltage drop on long runs, higher current in wiring, and interference with sensitive electronics. Large residential HVAC systems may benefit from a capacitor on the compressor motor.
Convert between apparent power (kVA) and real power (kW) using power factor. Essential for sizing generators, transformers, and UPS systems.
Calculate electrical power from voltage and current. Supports single-phase and three-phase calculations with power factor correction.
Calculate inductive and capacitive reactance at any frequency. Useful for designing power factor correction capacitor banks.