How do I calculate the capacitor size for power factor correction?

To find the capacitor size for power factor correction, you need the real power (W), the existing power factor, and the target power factor. First, calculate the reactive power currently consumed: Q_initial = P x tan(arccos(PF_initial)). Then find the target reactive power: Q_final = P x tan(arccos(PF_target)). The reactive power the capacitor must supply is Q_c = Q_initial - Q_final (in VAr). Finally, the required capacitance is C = Q_c / (2 x pi x f x V^2), where f is the supply frequency in Hz and V is the supply voltage in volts. The result in farads is usually converted to microfarads (1 F = 1,000,000 µF).

What capacitor size do I need for a 50 Hz RC filter?

For an RC low-pass filter at a given cutoff frequency, the capacitor size is C = 1 / (2 x pi x f_c x R), where f_c is the desired cutoff frequency in Hz and R is the resistance in ohms. For example, to set a cutoff at 1,000 Hz with a 10,000 ohm resistor: C = 1 / (2 x pi x 1000 x 10000) = 15.9 nF. The cutoff frequency is the point at which the output signal is attenuated to 70.7% of its input level (the -3 dB point).

What is the difference between µF, nF, and pF for capacitors?

Capacitance is measured in farads (F). Because a farad is a very large unit, capacitors are commonly rated in microfarads (µF, 1/1,000,000 of a farad), nanofarads (nF, 1/1,000,000,000 of a farad), and picofarads (pF, 1/1,000,000,000,000 of a farad). Power factor correction capacitors are typically in the range of 1 to 100 µF. Signal-filtering capacitors are often in the nF to pF range. The conversions are: 1 µF = 1,000 nF = 1,000,000 pF.

Capacitor Size Calculator

Enter your load power, power factor and voltage to size a power factor correction capacitor, or enter resistance and cutoff frequency to size an RC low-pass filter, in microfarads, nanofarads or farads.

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Standard formula IEC 60831 and standard RC filter theory. Applicable at 50 Hz (NZ/AU) and 60 Hz (US).

Power Factor Correction

RC Filter Sizing

1. Load Details

Real load power (W)

Existing power factor

Target power factor

2. Supply

Supply voltage (V RMS, line-to-neutral)

Supply frequency

Connection

1. Filter Parameters

Resistance (R)

Ω

Cutoff frequency (f_c)

2. Notes

The RC filter formula gives the capacitance needed so the circuit attenuates signals above the cutoff frequency. At f_c, the output is 70.7% of the input (the -3 dB point). Enter the resistance in ohms (Ω) and the desired cutoff frequency in Hz.

Required Capacitor Size

Capacitance (µF)
-
Microfarads

Capacitance (nF)

Nanofarads

Capacitance (F)

Farads

Reactive Power

VAr supplied

Calculation Breakdown

Real power-

Initial reactive power-

Target reactive power-

Reactive power (Qc)-

Supply voltage-

Supply frequency-

Required capacitance-

Common Capacitor Values

Nearest E12 value below-

Nearest E12 value above-

Voltage rating-

Typical capacitor type-

Temperature coefficient-

Result: Adjust inputs above to calculate the required capacitor size.

How to Calculate Capacitor Size

The required capacitance depends on what the capacitor is doing. The two most common sizing problems are power factor correction in AC power systems and setting the cutoff frequency of an RC filter circuit.

Power Factor Correction Formula

Power factor (PF) is the ratio of real power (watts) to apparent power (volt-amps). Inductive loads such as motors, transformers, and fluorescent lighting ballasts draw reactive current that does no useful work but still flows through cables and equipment, causing losses. A capacitor bank supplies leading reactive current that cancels the lagging reactive current of the inductive load, raising the power factor and reducing the total current drawn from the supply.

Q_initial = P × tan(arccos(PF_initial))
Q_target = P × tan(arccos(PF_target))
Q_c = Q_initial − Q_target [VAr needed from capacitor]
C = Q_c / (2 × π × f × V²) [farads]

Where P is real power in watts, PF is power factor (0 to 1), f is supply frequency in Hz, and V is the RMS voltage in volts. The result in farads is converted to microfarads by multiplying by 1,000,000.

RC Filter Formula

An RC low-pass filter passes low-frequency signals and attenuates high-frequency signals above the cutoff frequency. The cutoff frequency is the point at which the signal is attenuated to 1/sqrt(2) of its original amplitude (approximately 70.7%, or -3 dB).

C = 1 / (2 × π × f_c × R)

Where f_c is the cutoff frequency in Hz and R is the resistance in ohms. The result in farads is converted to nanofarads or microfarads as appropriate.

Worked Example: Power Factor Correction

A 1,000 W single-phase motor operates at a power factor of 0.80 on a 230 V, 50 Hz supply. The target is to raise the power factor to 0.95.

Initial reactive power: Q_initial = 1000 × tan(arccos(0.80)) = 1000 × 0.7500 = 750.0 VAr
Target reactive power: Q_target = 1000 × tan(arccos(0.95)) = 1000 × 0.3287 = 328.7 VAr
Reactive power needed from capacitor: Q_c = 750.0 − 328.7 = 421.3 VAr
Capacitance: C = 421.3 / (2 × π × 50 × 230²) = 421.3 / 16,619,025 = 0.00002535 F = 25.35 µF

A standard 25 µF motor-run capacitor (available from electrical wholesalers) would be selected. Use a capacitor rated for at least 400 V AC (approximately 1.73 times the supply voltage for safety margin).

Capacitor Types by Application

Application	Typical Range	Capacitor Type	Voltage Rating
Power factor correction (single-phase)	1 to 100 µF	AC film (polypropylene)	250 V AC or 400 V AC
Motor-start	50 to 500 µF	Electrolytic (intermittent duty)	125 V AC or 250 V AC
Motor-run	1 to 70 µF	AC film (continuous duty)	250 V AC or 440 V AC
Audio crossover filter	1 to 100 µF	Electrolytic or film	50 V to 100 V DC
Signal filtering (RC circuit)	1 nF to 1 µF	Ceramic or film	16 V to 100 V DC
RF / high-frequency filter	1 pF to 100 pF	Ceramic (NP0/C0G)	50 V to 200 V DC

Voltage Rating

Always select a capacitor whose voltage rating exceeds the peak voltage in the circuit. For AC supplies, the peak voltage is the RMS voltage multiplied by sqrt(2). For a 230 V RMS supply, the peak is approximately 325 V. A 400 V AC-rated capacitor is commonly used for single-phase mains applications to provide adequate safety margin. Never use a DC-rated capacitor directly on an AC supply unless it is specifically approved for that use.

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Method: Power factor correction formula derived from IEC 60831 / IEEE 1036. RC filter cutoff formula from standard passive filter theory (Sedra and Smith, Microelectronic Circuits). E12 standard capacitor values from IEC 60063.

This calculator is for educational and estimation purposes. For industrial power factor correction installations, consult a licensed electrical engineer. Capacitor selection must account for harmonics, transient voltages, and ambient temperature. Always comply with AS/NZS 3000 wiring rules and work with a licensed electrician for mains-connected applications.