Power Factor Calculator

Analyze AC circuits, calculate P, Q, S relationships, and size capacitors for power factor correction. Ideal for students and professional engineers.

Watts (W) or Kilowatts (kW)
VAR or kVAR
VA or kVA

Results

Power Factor
0.000
Poor
Phase Angle
0.0°
leading
Real Power
0.0 W
Reactive Power
0.0 VAR
Apparent Power
0.0 VA

Formulas Used:

PF = P / S = cos(θ)
S = √(P² + Q²)
Q = P × tan(θ)
θ = arccos(PF)

Power Factor Guidelines:

  • • Excellent: PF ≥ 0.95
  • • Good: PF = 0.85 - 0.94
  • • Fair: PF = 0.75 - 0.84
  • • Poor: PF < 0.75
  • • Lagging: Inductive loads (motors, transformers)
  • • Leading: Capacitive loads (capacitor banks)

Understanding Power Factor in AC Circuits

Power factor is a crucial concept in AC electrical systems that measures how effectively electrical power is being converted into useful work. A poor power factor means you're drawing more current than necessary, resulting in higher utility bills, increased losses, and reduced system capacity. Power factor correction can save 10-30% on electricity costs.

What is Power Factor?

Power factor (PF) is the ratio of real power (P) to apparent power (S), expressed as:

PF=\ racPS=cos⁡(ϕ)PF = \ rac{P}{S} = \cos(\phi)
  • Real Power (P): Measured in watts (W) - actual power consumed doing work
  • Reactive Power (Q): Measured in volt-amperes reactive (VAR) - power oscillating between source and load
  • Apparent Power (S): Measured in volt-amperes (VA) - total power drawn from supply
  • Phase Angle (φ): Angle between voltage and current waveforms

Power Triangle Relationships

The relationship between P, Q, and S forms a right triangle:

  • S2=P2+Q2S^2 = P^2 + Q^2
    (Pythagorean theorem)
  • Q=P imes an(ϕ)Q = P \ imes \ an(\phi)
  • PF=\ racPS=cos⁡(ϕ)PF = \ rac{P}{S} = \cos(\phi)

Leading vs Lagging Power Factor

  • Lagging (Inductive): Current lags voltage - typical in motors, transformers, inductive loads
  • Leading (Capacitive): Current leads voltage - typical in capacitive loads, over-corrected systems
  • Unity (PF = 1.0): Ideal condition where current and voltage are in phase

How to Use This Calculator

  1. Enter any two values (P, Q, S, or PF)
  2. The calculator automatically computes all other parameters
  3. View the power triangle visualization
  4. Determine if power factor is leading or lagging
  5. Calculate required capacitor size for correction

Calculating Required Capacitor Size

To improve power factor from PF₁ to PF₂:

Qcapacitor=P imes( an(ϕ1)− an(ϕ2))Q_{capacitor} = P \ imes (\ an(\phi_1) - \ an(\phi_2))

Where φ₁ and φ₂ are the angles corresponding to the current and desired power factors.

Example Calculations

Example 1: Industrial Motor Load
Real Power: 100 kW, Power Factor: 0.75 (lagging)

S=\ racPPF=\ rac1000.75=133.3  extkVAS = \ rac{P}{PF} = \ rac{100}{0.75} = 133.3\ \ ext{kVA}
Q=S2−P2=133.32−1002=88.2  extkVARQ = \sqrt{S^2 - P^2} = \sqrt{133.3^2 - 100^2} = 88.2\ \ ext{kVAR}
ϕ=arccos⁡(0.75)=41.4∘\phi = \arccos(0.75) = 41.4^\circ

Example 2: Power Factor Correction
Current PF: 0.70, Target PF: 0.95, Load: 50 kW

ϕ1=arccos⁡(0.70)=45.57∘, an(ϕ1)=1.02\phi_1 = \arccos(0.70) = 45.57^\circ, \ an(\phi_1) = 1.02
ϕ2=arccos⁡(0.95)=18.19∘, an(ϕ2)=0.33\phi_2 = \arccos(0.95) = 18.19^\circ, \ an(\phi_2) = 0.33
Qrequired=50 imes(1.02−0.33)=34.5  extkVARQ_{required} = 50 \ imes (1.02 - 0.33) = 34.5\ \ ext{kVAR}

Benefits of Power Factor Correction

  • Reduced Electricity Bills: Eliminate utility power factor penalties (typically 10-30% savings)
  • Increased System Capacity: Free up capacity for additional loads without upgrading infrastructure
  • Reduced I²R Losses: Lower current flow reduces heating losses in cables and equipment
  • Improved Voltage Regulation: Better voltage stability across the system
  • Extended Equipment Life: Reduced stress on motors, transformers, and cables

Common Causes of Low Power Factor

  • Induction motors operating at partial load
  • Transformers operating below rated capacity
  • Arc welding equipment
  • Induction furnaces
  • Discharge lighting (fluorescent, HID)

Frequently Asked Questions

Q: What is a good power factor?
A: Most utilities require PF ≥ 0.90 to avoid penalties. Industrial facilities should target 0.95-0.98. A PF of 1.0 (unity) is ideal but not always necessary.

Q: Can power factor be greater than 1.0?
A: No, power factor ranges from 0 to 1.0. However, it can be leading (capacitive) or lagging (inductive), both with values between 0 and 1.

Q: How do capacitors improve power factor?
A: Capacitors supply reactive power locally, reducing the reactive power drawn from the utility. This brings current and voltage closer to being in phase.

Q: Should I correct power factor to 1.0?
A: Not necessarily. Over-correction can cause leading power factor issues and resonance problems. Target 0.95-0.98 for optimal results without over-correction risks.