Power Factor Correction Calculator Formula

Understand the math behind the power factor correction calculator. Each variable explained with a worked example.

Use the Power Factor Correction Calculator

Formulas Used

Required Capacitor Bank

capacitor_kvar = kvar_reduction

Current Reactive Power

current_kvar = real_power_kw * tan(theta_current)

New Reactive Power

new_kvar = real_power_kw * tan(theta_target)

Apparent Power Reduction

kva_reduction = real_power_kw / current_pf - real_power_kw / target_pf

Variables

VariableDescriptionDefault
real_power_kwReal Power(kW)100
current_pfCurrent Power Factor0.75
target_pfTarget Power Factor0.95
theta_currentDerived value= acos(current_pf)calculated
theta_targetDerived value= acos(target_pf)calculated
kvar_reductionDerived value= real_power_kw * (tan(theta_current) - tan(theta_target))calculated

How It Works

Power Factor Correction

Low power factor means the utility must deliver more current (and apparent power) than the load actually uses. Capacitor banks supply reactive power locally.

Formula

kVAR needed = kW x (tan(arccos(PF_current)) - tan(arccos(PF_target)))

Benefits

  • Reduced utility power factor penalties
  • Lower line current (smaller cables, less loss)
  • Freed transformer and distribution capacity

    • Most utilities penalize power factors below 0.90. Correcting to 0.95 is a common economic target.

    Worked Example

    100 kW load at PF 0.75, correcting to PF 0.95.

    real_power_kw = 100current_pf = 0.75target_pf = 0.95
    1. 01Current angle: arccos(0.75) = 41.41 degrees, tan = 0.8819
    2. 02Target angle: arccos(0.95) = 18.19 degrees, tan = 0.3287
    3. 03kVAR needed: 100 x (0.8819 - 0.3287) = 55.3 kVAR
    4. 04kVA reduction: 100/0.75 - 100/0.95 = 133.3 - 105.3 = 28.1 kVA

    Ready to run the numbers?

    Open Power Factor Correction Calculator