Power Factor Correction Calculator
Raising a 100 kW load from 0.7 to 0.95 power factor needs 69.152 kVAR of capacitors, cutting the line current by about 26 %.
69.1519956041544 kVAR
Full answer, then cut to fewer decimals (not rounded):
- 69.1519956041544 kVAR
- 69.151995604154 kVAR
- 69.15199560415 kVAR
- 69.1519956041 kVAR
- 69.151995604 kVAR
- 69.15199560 kVAR
- 69.1519956 kVAR
- 69.151995 kVAR
- 69.15199 kVAR
- 69.1519 kVAR
- 69.151 kVAR
- 69.15 kVAR
- 69.1 kVAR
- Capacitance per phase
- 426.0272676 µF
- Reactive power before
- 102.0204061 kVAR
- Reactive power after
- 32.86841052 kVAR
- Apparent power before
- 142.8571429 kVA
- Apparent power after
- 105.2631579 kVA
- Line current reduced by
- 26.31578947 %
Step-by-step solution
- tan φ₁ = tan(arccos 0.7) = 1.020204061; tan φ₂ = tan(arccos 0.95) = 0.3286841052
- Q_C = P (tan φ₁ − tan φ₂) = 100 × (1.020204061 − 0.3286841052) = 69.1519956 kVAR
- Delta: C per phase = Q_C ÷ (3 × 2πf V_L²) = 426.0272676 µF
Power Factor Correction Formula
Q_C = P (tan φ₁ − tan φ₂)
C = Q_C / (2πf V²) single-phase; delta bank C per phase = Q_C / (3·2πf V_L²)
Worked Example
A 100 kW, 415 V, 50 Hz three-phase load from 0.7 to 0.95 power factor with delta capacitors:
- tan φ₁ = tan(arccos 0.7) = 1.020204061; tan φ₂ = tan(arccos 0.95) = 0.3286841052
- Q_C = P (tan φ₁ − tan φ₂) = 100 × (1.020204061 − 0.3286841052) = 69.1519956 kVAR
- Delta: C per phase = Q_C ÷ (3 × 2πf V_L²) = 426.0272676 µF
Reactive power before: 102.0204061 kVAR · Reactive power after: 32.86841052 kVAR · Apparent power before: 142.8571429 kVA · Apparent power after: 105.2631579 kVA · Line current reduced by: 26.31578947 %
GATE tip
Work with tan φ, not angles: tan(arccos 0.8) = 0.75 and tan(arccos 0.6) = 1.333 are worth memorising, and many GATE questions use 0.8 and 0.6.
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S = VI (√3 V_L I_L), P = S cos φ, Q = S sin φ
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Example: A 10 kΩ resistor charging a 100 µF capacitor from 10 V, after 1 s: Time constant τ = 1 s.
Frequently asked questions
Why not correct to unity?
The last few hundredths need a lot of extra kVAR, and over-correction at light load can make the power factor leading and raise voltages. 0.95–0.98 is the usual target.
Star or delta capacitors?
Delta capacitors see the full line voltage, so they need one third of the capacitance of a star bank for the same kVAR.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Power Factor Correction Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/power-factor-correction-calculator/
IEEE
Scientific Converters, "Power Factor Correction Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/power-factor-correction-calculator/