AC power
Power factor correction: required kvar
- where
- required correction (var)
- active power (W)
- initial phase angle (cos φ₁ = initial power factor)
- target phase angle (cos φ₂ = target power factor)
Explain this equation
Works out how much capacitive reactive power is needed to raise a lagging power factor to a target value. Use it for a first estimate when sizing a capacitor bank.
P is the active power in watts, which stays the same before and after correction. φ₁ is the phase angle at the existing power factor (cos φ₁ = initial PF) and φ₂ the angle at the target. tan φ is the ratio of reactive to active power. Q_c is the correction needed, in var.
Reactive power is P × tan φ, so working out the reactive power before and after and subtracting gives what the capacitors must supply. The calculator gets tan φ from the power factor as √(1 − PF²) / PF.
10 kW at 0.8 corrected to unity needs 7.5 kvar, since tan φ₁ = 0.75. Stopping at 0.95 needs only about 4.2 kvar; the last stretch to unity costs the most.
Watch out: the answer is in var, so divide by 1000 for kvar. Don't simply subtract the power factors. Harmonics, varying loads and resonance need specialist assessment.
Correction offsets part of an inductive load's reactive demand, reducing upstream current for the same active power. Calculate the original and desired reactive powers and subtract.
Use acos to recover each angle before using tan, or calculate tan φ = √(1/PF² − 1). This is a sizing principle, not a complete capacitor-bank design.
Enter your values to see the result.
Common mistake
Do not subtract the power factors themselves and multiply by kW.
Limits
Sinusoidal lagging PF improved towards unity at constant kW. Harmonics, resonance, variable load, switching, discharge and overcompensation require specialist/manufacturer assessment. Results are in var (divide by 1000 for kvar).
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.