Qc = Qr / (2 * π * f * U₂)
Qr = Qc * 2 * π * f * U₂
Qr = Reactive power (VAr)
Qc = Capacity (F)
U = Voltage (V)
f = Frequency (Hz)
π = 3.1415926535
A tool for converting between reactive power (VAR) and capacitance (μF) of a capacitor, supporting single-phase and three-phase systems.
This calculator helps users compute the reactive power (VAR) provided by a capacitor based on its voltage, frequency, and capacitance, or vice versa. Useful for power factor correction and capacitor sizing in electrical systems.
Q (VAR) = 2π × f × C (μF) × V² × 10⁻⁶
Q (VAR) = 3 × 2π × f × C (μF) × V² × 10⁻⁶
| Parameter | Description |
|---|---|
| Power (Reactive Power) | Reactive power supplied by the capacitor, unit: VAR. Input to calculate capacitance (μF). |
| Voltage | - Single-phase: Phase-Neutral voltage - Two-phase or three-phase: Phase-Phase voltage Unit: Volts (V) |
| Frequency | Number of cycles per second, unit: Hz. Common values: 50 Hz or 60 Hz. |
Voltage V = 230 V
Frequency f = 50 Hz
Capacitance C = 40 μF
Q = 2π × 50 × 40 × (230)² × 10⁻⁶ ≈ 6.78 kVAR
If Q = 6.78 kVAR, then C ≈ 40 μF
1. Power factor correction in electrical systems
2. Capacitor sizing and capacity calculation
3. Industrial electrical system commissioning
4. Academic learning and exams
The reactive power (VAR) of a capacitor is proportional to the square of voltage, frequency, and capacitance, expressed as Q = 2π × f × C × V². This means the same capacitor provides completely different reactive power at different voltages or frequencies. For example, a 40 μF capacitor delivers only about 661 VAR at 230V/50Hz, but about 2763 VAR at 480V/60Hz. Therefore, voltage and frequency are indispensable parameters in the conversion.
In a single-phase system, the reactive power of a capacitor is Q = 2π × f × C × V²; in a three-phase system, the total reactive power is Q = 3 × 2π × f × C × V², which is 3 times the single-phase value (where C is the capacitance per phase). Note that the value of V in a three-phase system depends on the connection type: for delta connection, V is the line-to-line voltage; for wye (star) connection, each phase capacitor sees the phase voltage (V_phase = V_line / √3), so the actual formula differs. Please confirm the system type and connection method when using this calculator.
Active power (W) is the power actually consumed and converted into heat or mechanical energy in a circuit; reactive power (VAR) is the power periodically stored and released by capacitors and inductors in AC circuits, producing no net energy consumption. A capacitor stores electric field energy during the positive half-cycle and releases it during the negative half-cycle, which is why VAR rather than W is used to describe its power characteristics. In power systems, properly sized reactive power compensation capacitors can improve the power factor and reduce line losses by 5%–15%.
It is commonly used for power factor correction in electrical systems (calculating required capacitance from target kVAR), industrial capacitor sizing and capacity calculation, reactive power compensation configuration during electrical system commissioning, capacitor parameter evaluation for dynamic loads such as PV inverters and variable frequency drives, and academic learning and exams in electrical engineering and physics.
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