About the Capacitive Reactance Calculator
This capacitive reactance calculator finds Xc, the opposition a capacitor offers to alternating current, from its capacitance and the signal frequency. It can also work backwards: give it a target reactance and either the frequency or the capacitance, and it solves for the other — handy when choosing a coupling, bypass or filter capacitor.
Enter capacitance in pF, nF, µF, mF or F and frequency in Hz, kHz or MHz. Add an RMS voltage and the calculator also shows the current that flows through the capacitor, along with the angular frequency and susceptance. A sweep chart shows how Xc falls as frequency rises around your operating point.
Students use it for AC circuit homework, audio builders for crossover and coupling capacitors, and power engineers for power-factor correction and capacitive dropper supplies. The capacitor is treated as ideal — no ESR, leakage or self-resonance — which is accurate well below the part's self-resonant frequency.
How to use the capacitive reactance calculator
- 1Choose what to solve for: reactance, capacitance or frequency.
- 2Enter the known capacitance and pick its unit.
- 3Enter the known frequency and pick its unit, or the target reactance.
- 4Optionally enter the RMS voltage to get the current.
- 5Read the answer and check the sweep chart for how Xc changes with frequency.
Formula and method
A capacitor passes alternating current by charging and discharging every cycle. The faster the voltage changes, the more current flows for a given voltage, so its opposition — the capacitive reactance — is inversely proportional to both frequency and capacitance: Xc = 1/(2πfC), measured in ohms. Rearranging the same equation gives the capacitance for a required reactance, or the frequency at which a capacitor reaches it.
Reactance behaves like resistance in Ohm's law for magnitudes (I = V/Xc), but the current leads the voltage by 90°, so an ideal capacitor stores and returns energy without dissipating it. In complex notation its impedance is −jXc. The angular frequency ω = 2πf and susceptance B = 1/Xc are shown for convenience.
- Xc
- Capacitive reactance (Ω)
- f
- Frequency (Hz)
- C
- Capacitance (F)
- ω
- Angular frequency 2πf (rad/s)
- V, I
- RMS voltage across and current through the capacitor
Worked examples
1 µF at 1 kHz
Xc = 1 ÷ (2π × 1,000 × 0.000001) = 159.15 Ω. With 10 V RMS across it, 10 ÷ 159.15 = 62.8 mA flows, leading the voltage by 90°.
100 nF across 230 V mains at 50 Hz
Xc = 1 ÷ (2π × 50 × 100 × 10⁻⁹) = 31,831 Ω (about 31.8 kΩ). On 230 V that passes 230 ÷ 31,831 = 7.23 mA — the principle behind capacitive dropper power supplies.
Capacitor for 50 Ω reactance at 10 kHz
C = 1 ÷ (2π × 10,000 × 50) = 3.183 × 10⁻⁷ F, or 0.318 µF (a standard 330 nF part is close). At 10 V it carries 10 ÷ 50 = 200 mA.
Frequency where 10 µF reaches 10 Ω
f = 1 ÷ (2π × 10 × 10⁻⁶ × 10) = 1,591.5 Hz. Above about 1.6 kHz this capacitor presents less than 10 Ω, which is why it works as an audio-frequency bypass.
Frequently asked questions
What is the formula for capacitive reactance?+
Xc = 1 ÷ (2πfC), where f is the frequency in hertz and C the capacitance in farads. The result is in ohms. For example, 10 µF at 60 Hz has a reactance of about 265 Ω.
Why does capacitive reactance decrease with frequency?+
At higher frequencies the capacitor charges and discharges more times per second, so more current flows for the same voltage. Less opposition to current means lower reactance; Xc halves every time the frequency doubles.
What is the reactance of a capacitor at DC?+
At 0 Hz the formula gives infinite reactance: once charged, an ideal capacitor blocks direct current completely. That is why capacitors are used to block DC while passing AC signals between amplifier stages.
Is capacitive reactance the same as impedance?+
For an ideal capacitor its impedance is purely reactive, Z = −jXc, so the magnitude equals Xc. A real capacitor also has equivalent series resistance (ESR) and inductance, which matter at high frequencies.
What is the difference between capacitive and inductive reactance?+
Inductive reactance XL = 2πfL rises with frequency and makes current lag voltage, while capacitive reactance falls with frequency and makes current lead. At resonance the two are equal and cancel.