Capacitive Reactance Calculator
Capacitive reactance (XC) quantifies how much a capacitor opposes AC current at a given frequency. The formula XC = 1 / (2 * pi * f * C) shows that reactance decreases as frequency or capacitance increases. This is the opposite behavior from inductors. Capacitors block DC and low-frequency signals while passing high-frequency signals, making them indispensable in coupling, decoupling, and filter circuits. Enter the frequency in hertz and the capacitance in farads. Common conversions: 1 microfarad (uF) = 0.000001 F, 1 nanofarad (nF) = 0.000000001 F, 1 kHz = 1,000 Hz.
Capacitive reactance formula
XC = 1 / (2 * pi * f * C)
Where f is frequency in hertz (Hz) and C is capacitance in farads (F). The result XC is in ohms. Example: 10 uF at 1,000 Hz gives XC = 1 / (2 * pi * 1,000 * 0.00001) = 15.92 ohms.
Capacitive reactance in practical circuits
- AC coupling capacitors in audio circuits must have XC much less than the load impedance at the lowest signal frequency to avoid bass rolloff.
- Power factor correction capacitors counteract inductive reactance in industrial motors, reducing reactive power and improving efficiency.
- Bypass capacitors (decoupling) have very low XC at switching frequencies, providing a low-impedance path for supply noise.
- The cutoff frequency of an RC low-pass filter is where XC = R, giving f_c = 1 / (2 * pi * R * C).
Frequently asked questions
What is capacitive reactance?
Capacitive reactance (XC) is the opposition a capacitor offers to alternating current. It decreases as frequency increases, meaning capacitors pass high-frequency signals more easily than low-frequency ones. XC is measured in ohms.
What is the capacitive reactance formula?
XC = 1 / (2 * pi * f * C), where f is frequency in hertz and C is capacitance in farads. For example, a 10 uF capacitor at 60 Hz has XC = 1 / (2 * pi * 60 * 0.00001) = 265.26 ohms.
Why does XC decrease as frequency increases?
At higher frequencies, the capacitor charges and discharges more rapidly, allowing more current to flow. At very high frequencies, XC approaches zero and the capacitor acts as a short circuit. At DC (f = 0), XC is infinite and no current flows.
How is capacitive reactance used in filter design?
A high-pass filter uses a capacitor in series with the load. At low frequencies, XC is high and blocks the signal; at high frequencies, XC is low and passes the signal. The cutoff frequency is f_c = 1 / (2 * pi * R * C).
What is the phase relationship in a capacitive circuit?
In a purely capacitive AC circuit, current leads voltage by 90 degrees. In a series RC circuit, the phase angle is theta = arctan(-XC / R), which is negative (current leads).
Official sources
- NIST: NIST SP 811, Guide for SI Units.
- OpenStax University Physics: Simple AC Circuits, Vol. 2 Ch. 15.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.