Power Factor Correction Capacitor

C = Qc / (ω × V²)

Quick answer

This calculator solves C = Qc / (2πf × V²) for Capacitance. With Reactive Power 0.5, Line Frequency 1 kHz, Line Voltage RMS 12 V, the result is 0.5526 µF.

Calculator

Capacitance (µF)
—

Formula

C = Qc / (2πf × V²)

Description

Power factor correction (PFC) capacitors supply leading reactive power to compensate for the lagging reactive power drawn by inductive loads like motors, transformers, and fluorescent lighting. The required capacitance depends on the reactive power to be compensated (in VAR), the line frequency, and the voltage. By improving the power factor close to unity, PFC capacitors reduce current drawn from the utility, lower I²R losses in wiring, and avoid utility power factor penalties. In industrial settings, PFC capacitor banks are often switched in stages to match varying loads.

Variables

  • C — Required capacitance (F)
  • Qc — Reactive power to compensate (VAR)
  • f — Line frequency (Hz)
  • V — RMS line voltage (V)

Practical Notes

Qc = P × (tan(φ₁) − tan(φ₂)), where φ₁ is the initial power factor angle and φ₂ is the target. PFC capacitors must be rated for continuous AC operation and are typically self-healing metallized polypropylene film. Do not confuse with active PFC in switch-mode power supplies, which is a different technique using boost converter topology.

Symbols and units

Symbol Meaning Default unit Accepted units
C Capacitance µF pF, nF, µF, mF, F
Qc Reactive Power — —
f Line Frequency Hz Hz, kHz, MHz, GHz
V Line Voltage RMS V pV, nV, µV, mV, V, kV

Step by step

  1. 1. What you know: Reactive Power 0.5, Line Frequency 1 kHz, Line Voltage RMS 12 V
  2. 2. The relation: C = Qc / (2πf × V²)
  3. 3. Substitute: Qc = 0.5, f = 1 kHz, V = 12 V
  4. 4. Result: Capacitance = 0.5526 µF

Nearest standard component values

Series Nearest value Error
E12 0.56 µF 1.3%
E24 0.56 µF 1.3%

Worked examples

Minimum range

Given: Reactive Power 0.025, Line Frequency 5 Hz, Line Voltage RMS 0.33 V

Result: Capacitance = 7.307 mF

Low range

Given: Reactive Power 0.25, Line Frequency 50 Hz, Line Voltage RMS 3.3 V

Result: Capacitance = 73.07 µF

Typical

Given: Reactive Power 0.5, Line Frequency 1 kHz, Line Voltage RMS 12 V

Result: Capacitance = 0.5526 µF

High range

Given: Reactive Power 0.8, Line Frequency 20 kHz, Line Voltage RMS 0.23 kV

Result: Capacitance = 120.3 pF

Maximum range

Given: Reactive Power 8, Line Frequency 0.2 MHz, Line Voltage RMS 2.3 kV

Result: Capacitance = 1.203 pF

How Capacitance changes with Reactive Power

Reactive Power (input) Capacitance (result)
0.05 55.26 nF
0.125 138.2 nF
0.25 0.2763 µF
0.375 0.4145 µF
0.5 0.5526 µF
0.75 0.8289 µF
1 1.105 µF
2 2.21 µF
3.5 3.868 µF
5 5.526 µF

The same result in other units

Unit Value
pF 552600
nF 552.6
µF 0.5526
mF 0.0005526

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Frequently asked questions

How do you calculate Power Factor Correction Capacitor?

Use C = Qc / (2πf × V²). With Reactive Power 0.5, Line Frequency 1 kHz, Line Voltage RMS 12 V, Capacitance works out to 0.5526 µF.

What is the formula for Power Factor Correction Capacitor?

The formula is C = Qc / (2πf × V²). Power factor correction (PFC) capacitors supply leading reactive power to compensate for the lagging reactive power drawn by inductive loads like motors, transformers, and fluorescent lighting.

What units does Power Factor Correction Capacitor use?

Capacitance is shown in pF, nF, µF, mF. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All AC Circuits formulas →
Resonant Frequency Impedance (RLC Series) Quality Factor (Bandwidth) Quality Factor (RLC) Power Factor Apparent Power Reactive Power RLC Circuit Bandwidth

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