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Power Factor Calculator

Calculate power factor, phase angle, reactive power, and design power factor correction systems
Basic Calculator
PF Correction
Power Triangle
Applications

Power Factor Calculator

Power Factor Equations:
PF = cos(φ)   (Power Factor = cosine of phase angle) PF = P / S   (Power Factor = Real Power / Apparent Power) φ = arccos(PF)   (Phase angle = inverse cosine of Power Factor)
PF 0.8
PF 0.85
PF 0.9
PF 0.95
PF 1.0
30°
45°
Select calculation method and enter values to calculate power factor
0.00
0.0 0.2 0.4 0.6 0.8 1.0
Auto-calculate as you type

Power Factor Correction Calculator

Power Factor Correction:
Qc = P × (tan(φ₁) - tan(φ₂))   (Capacitive Reactive Power needed) C = Qc / (2π × f × V²)   (Capacitance required)
Enter load details to calculate power factor correction requirements

Power Triangle Visualization

Power Triangle Relationships:
S² = P² + Q²   (Pythagorean theorem) P = S × cos(φ)   (Real Power) Q = S × sin(φ)   (Reactive Power)
Enter any two values to see the power triangle visualization

Power Factor Applications

Industrial Power Systems

Power factor is crucial in industrial applications:

  • Utility Penalties: Many utilities charge penalties for poor power factor (typically below 0.9)
  • Equipment Efficiency: Better power factor reduces losses in transformers and cables
  • Capacity Utilization: Improved power factor allows more real power from the same apparent power

Example: A factory with 1000kW load at 0.7 PF requires 1429kVA. Improving to 0.95 PF reduces requirement to 1053kVA.

Motor Applications

Electric motors are major contributors to poor power factor:

  • Induction Motors: Typically operate at 0.8-0.9 PF at full load
  • Lightly Loaded Motors: Power factor drops significantly at partial loads
  • Motor Capacitors: Used for power factor correction in motor circuits

Correction Methods: Capacitor banks, synchronous condensers, or power electronic devices.

Residential Systems

Power factor in residential applications:

  • LED Drivers: Some LED lights have poor power factor
  • Electronic Devices: Switch-mode power supplies can create reactive power
  • HVAC Systems: Air conditioners and heat pumps affect residential power factor

Standards: Many countries require residential equipment to maintain PF > 0.9.

Economic Benefits

Financial advantages of power factor correction:

  • Reduced Utility Bills: Avoid power factor penalty charges
  • Equipment Savings: Smaller transformers, cables, and switchgear
  • Energy Efficiency: Reduced I²R losses in distribution system
  • Voltage Regulation: Better voltage stability and regulation

Payback Period: Typical payback for PF correction is 1-3 years.

Understanding Power Factor

Power Factor (PF) is a measure of how effectively electrical power is being used. It represents the ratio of real power (doing useful work) to apparent power (total power drawn from the source).

Example 1: Motor Power Factor

A 50HP motor draws 100A at 480V with a power factor of 0.85. Calculate the real and reactive power.

Solution:

Apparent Power: S = √3 × V × I = 1.732 × 480 × 100 = 83.1 kVA

Real Power: P = S × PF = 83.1 × 0.85 = 70.6 kW

Reactive Power: Q = S × sin(φ) = 83.1 × 0.527 = 43.8 kVAR

Example 2: Power Factor Correction

A 500kW load operates at 0.7 PF. Calculate the capacitor size needed to improve PF to 0.95.

Solution:

φ₁ = arccos(0.7) = 45.57°, φ₂ = arccos(0.95) = 18.19°

Qc = 500 × (tan(45.57°) - tan(18.19°)) = 500 × (1.02 - 0.33) = 345 kVAR

Example 3: Cost Savings

A factory pays $0.10/kVAR penalty for PF below 0.9. Current load: 1000kW at 0.75 PF.

Before Correction: S = 1000/0.75 = 1333 kVA, Q = 882 kVAR

Monthly Penalty: 882 × $0.10 × 730 hours = $64,386

After Correction to 0.95 PF: Q = 329 kVAR, No penalty