Calculate capacitor reactive power, capacitance, or RMS voltage from frequency and any two known values using |Q| = 2πfCV² in F, V, and VAR.
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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| = 2\pi f C V^2
Rearranged to solve for capacitance:
C = \frac{|Q|}{2\pi f V^2}Rearranged to solve for RMS voltage:
V = \sqrt{\frac{|Q|}{2\pi 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)
- π = pi, approximately 3.14159
If you enter capacitance and RMS voltage, the calculator finds reactive power magnitude. If you enter reactive power and voltage, it finds the capacitance needed. If you enter reactive power and capacitance, it finds the RMS voltage across the capacitor.
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| = 2\pi(60)(0.0001)(240^2)
|Q| \approx 2171.47\text{ 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 = \frac{5000}{2\pi(60)(480^2)}C \approx 0.00005756\text{ 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.
