Select reactive power magnitude, capacitance, or RMS voltage, then enter frequency and the two requested values. The ideal single-capacitor sinusoidal AC formula is |Q| = 2πfCV² in F, V, and VAR.

Find the reactive power of one ideal capacitor with sinusoidal AC voltage. Use the RMS voltage across that capacitor.

Default: 60 Hz. Set the actual sinusoidal AC frequency; it must be greater than zero.

Nonnegative capacitance. Changing units converts the entered value.

Use RMS, not peak or three-phase line voltage. Changing units converts the value.

Capacitor Reactive Power Formula

The calculator uses the capacitive reactive power relationship for a sinusoidal AC circuit. Voltage is RMS voltage, capacitance is converted to farads, frequency is in hertz, and reactive power is returned as a positive magnitude.

|Q| = 2π f C V²

Rearranged to solve for capacitance:

C = (|Q|) / (2π f V²)

Rearranged to solve for RMS voltage:

V = √((|Q|) / (2π f C))
  • |Q| = capacitive reactive power magnitude, in VAR
  • f = AC frequency, in hertz (Hz)
  • C = capacitance, in farads (F)
  • V = RMS voltage across the capacitor, in volts (V)
  • Ï€ = pi, approximately 3.14159

Choose the value to solve for. Reactive power magnitude uses capacitance and RMS voltage; capacitance uses reactive power and RMS voltage; RMS voltage uses reactive power and capacitance. Frequency is required in every mode. Voltage is across one capacitor, not automatically the line voltage of a three-phase bank.

The result is shown as a magnitude because an ideal capacitor has negative reactive power by sign convention, but sizing calculations often use the positive VAR, kVAR, or MVAR value.

Common Unit Conversions for Capacitor Reactive Power

Quantity Unit Base unit conversion
Capacitance 1 mF 0.001 F
Capacitance 1 µF 0.000001 F
Voltage 1 kV 1,000 V
Voltage 1 mV 0.001 V
Reactive power 1 kVAR 1,000 VAR
Reactive power 1 MVAR 1,000,000 VAR

Typical Frequency Values

Application Typical frequency
North American utility power 60 Hz
Many European and international utility systems 50 Hz
Aircraft power systems 400 Hz

Example Calculations

Example 1: Find reactive power from capacitance and voltage

Suppose a capacitor has a capacitance of 100 µF, the voltage across it is 240 V RMS, and the frequency is 60 Hz.

|Q| = 2π(60)(0.0001)(240²)
|Q| ≈ 2171.47 VAR

The reactive power magnitude is about 2171.47 VAR, or 2.171 kVAR.

Example 2: Find capacitance from reactive power and voltage

Suppose you need 5 kVAR at 480 V RMS and 60 Hz.

C = (5000) / (2π(60)(480²))
C ≈ 0.00005756 F

The required capacitance is about 0.00005756 F, or 57.56 µF.

FAQs

Why does the calculator use RMS voltage?

Reactive power calculations in AC power systems normally use RMS voltage. RMS voltage gives the equivalent heating or power-related value for an AC waveform. Do not enter peak voltage unless you first convert it to RMS voltage.

Is capacitor reactive power positive or negative?

By standard sign convention, a capacitor supplies reactive power, so its reactive power is often written as negative Q. This calculator uses the magnitude, |Q|, so you enter and receive positive VAR, kVAR, or MVAR values.

What happens if frequency changes?

Capacitive reactive power is directly proportional to frequency. If capacitance and voltage stay the same, increasing frequency increases |Q|. For example, the same capacitor produces more reactive power at 60 Hz than at 50 Hz.