Calculate correction capacitor size (kVAR), kW, kVA, kVAR, phase angle & current reduction — single-phase & three-phase AC systems.
⚡ Key Insight: Power Factor (PF) = Real Power (kW) ÷ Apparent Power (kVA) = cos(θ). A PF of 1.0 means all apparent power is doing useful work. Most utilities penalise PF below 0.90–0.95 lagging. Capacitor banks offset lagging reactive kVAR from inductive loads (motors, transformers).
📌 Field Example: A factory has a 100 kW load running at PF 0.80 lagging on a 415 V 3-phase supply. The utility demands PF ≥ 0.95.
Required capacitor bank ≈ 42 kVAR | kVA drops from 125 → 105.3 kVA | Line current falls from 174 A → 146 A (~16% reduction).
Use the PF Correction Capacitor tab (open by default) to calculate your own values.
Presets:
Real Power (kW)
Reactive Power (kVAR)
Load Type
Presets:
System Type
Voltage (V)
Current (A)
A
Power Factor (0–1)
PF Type
Frequency (Hz)
Presets:
System Type
Real Load (kW)
Supply Voltage
Existing PF (lagging)
Target PF
Frequency (Hz)
Universal Solver: Enter any two known values (kW / kVA / kVAR / PF) and the rest are calculated automatically.
Real Power kW (optional)
Apparent Power kVA (optional)
Reactive Power kVAR (optional)
Power Factor (optional)
PF Type
📐 Power Triangle Formulas
Real Power (P)
P = S × cos(θ) P = S × PF P = √(S²−Q²) Unit: kW
Apparent Power (S)
S = V × I (1-ph) S = √3×V_L×I (3-ph) S = √(P²+Q²) Unit: kVA
Reactive Power (Q)
Q = S × sin(θ) Q = P × tan(θ) Q = √(S²−P²) Unit: kVAR
Lagging vs Leading PFInductive loads (motors, transformers) draw lagging reactive current — current lags voltage. Capacitive loads produce leading current. Most industrial PF is lagging. Capacitor banks are installed to offset lagging kVAR and bring PF closer to unity.
Why Correct Power Factor?High kVAR increases apparent power (kVA), raising line current for the same useful kW. This increases I²R losses, reduces transformer and cable capacity, and triggers utility surcharges. Correction to 0.95+ minimises penalties and frees system capacity.
Capacitor Sizing CautionOver-correction (PF going leading past unity) can cause voltage rise, resonance with harmonics, and overvoltage trips. Always target 0.95–0.99 lagging, not unity. Use detuned reactors (e.g. 7% at 50 Hz) in harmonic-rich environments to prevent resonance.
Displacement PF vs True PFThis calculator computes displacement PF (fundamental frequency). True (total) PF also accounts for harmonic distortion: True PF = DPF / √(1+THD²). For VFDs, UPS and SMPS loads, true PF is often significantly lower than displacement PF.
Power Factor Correction Calculator for 3-Phase Motors
Three-phase induction motors are the single largest source of lagging reactive power in industrial facilities. At full load, a typical motor runs at PF 0.85–0.90; at half load, this can fall to 0.65–0.75. The kVAR correction required is: Q_c = kW × (tan θ₁ − tan θ₂). For a 3-phase system, the total three-phase capacitor bank supplies this Q_c. Delta-connected banks use the full line voltage (415 V); star-connected banks use the phase voltage (415 ÷ √3 = 240 V). Always verify with the motor nameplate and measured PF before sizing the final bank.
What is Power Factor?
Power factor (PF) is a number between 0 and 1 describing how efficiently electrical power is used. It equals the cosine of the phase angle θ between voltage and current: PF = cos(θ) = kW ÷ kVA. A PF of 1.0 (unity) means all supply power is converted to useful work; lower values mean wasted reactive energy circulates in the circuit.
The Power Triangle
Real Power (kW), Reactive Power (kVAR), and Apparent Power (kVA) form a right triangle: kVA² = kW² + kVAR². kW is the horizontal leg (useful work), kVAR the vertical leg (reactive exchange with inductors/capacitors), and kVA the hypotenuse (total supply draw). The angle θ gives PF = cos θ.
Capacitor Sizing Formula
Required correction: Q_c = P × (tan θ₁ − tan θ₂). Capacitance (single-phase): C = Q_c × 10⁶ ÷ (2π × f × V²) µF. For three-phase delta connection, divide by 3 and use line voltage; for star, use phase voltage (V_L ÷ √3).
Most utilities require a minimum PF of 0.90–0.95 lagging to avoid surcharges. The ideal industrial target is 0.95–0.99 lagging. Unity or leading PF can cause voltage regulation issues and capacitor switching transients.
Targeting unity PF is risky in practice. Any slight overcorrection pushes PF leading, which can cause voltage rise at the point of supply, overvoltage trips on capacitor contactors, and resonance with supply harmonics. The practical target is 0.95–0.99 lagging to stay safely on the inductive side.
The magnetising (reactive) current of an induction motor is approximately constant regardless of load, while active current drops at light load. At 50% load, reactive current dominates, pushing PF down to 0.65–0.75 versus 0.85–0.90 at full load.
Fixed capacitor banks are suitable for steady, constant loads — they stay connected permanently. Automatic Power Factor Correction (APFC) panels switch capacitor steps in/out based on the load's reactive demand, using a PF controller relay. APFC is recommended when load varies by more than 20–30%, preventing over-correction at light loads.
kVA (kilovolt-amperes) is the apparent power demand seen by the supply transformer and conductors. Many utilities — especially in India and the UK — levy a kVA demand charge or a kVARh (reactive energy) tariff, and may impose a PF penalty or surcharge when PF falls below 0.90–0.95. Billing structures vary: some use kWh + kVAR penalty, others use pure kVA maximum demand. Check your tariff schedule.
No. In pure DC circuits there is no phase angle between voltage and current, so PF = 1 always. Power factor is purely an AC concept arising from reactive elements (inductors, capacitors) that store and release energy each half-cycle.