Capacitive Reactance - Xc = 1/(2πfC) Formula

A capacitive reactance calculator solves Xc = 1 / (2π f C) for any capacitor in an AC circuit, taking the capacitance in farads and the signal frequency in hertz and returning the magnitude of the capacitor's AC opposition in ohms, so an engineer, technician, or student can size a coupling, bypass, or filter capacitor without re-deriving the equation each time.

• • AC circuit homework: Find the Xc that a textbook problem gives for a capacitor and a chosen frequency so the rest of the series or parallel circuit can be solved in the time domain.
• • Audio and coupling capacitor sizing: Estimate how much reactance a coupling capacitor presents at a 20 Hz to 20 kHz audio signal so the corner frequency of the high-pass filter it forms with the input impedance is known.
• • Mains filter and X/Y capacitor selection: Check the Xc of an X2 or Y2 safety capacitor at 50 Hz or 60 Hz line frequency when evaluating conducted EMI and leakage-current budgets.
• • RF and antenna matching: Convert a chosen capacitance into a reactance at an RF or microwave frequency so a matching network, an antenna tuner, or a stub filter can be designed in the same units.

The calculator assumes an ideal capacitor with a purely reactive AC impedance, so the printed Xc is the magnitude of the impedance; real-world capacitors add a small equivalent series resistance (ESR) and a leakage term, which are ignored in the textbook formula but should be checked on a datasheet for power applications.

If the capacitance is not yet known, the Capacitance Calculator takes the parallel-plate geometry and dielectric material of the capacitor and returns the C in farads that this calculator then converts into reactance.

The capacitive reactance calculator applies the AC-circuit equation Xc = 1 / (2π f C) to the capacitance and frequency that the user enters, with automatic conversion of the chosen unit prefixes into the SI base units the formula expects.

• C: Capacitance of the capacitor in farads (F). Calculator accepts F, mF, µF, nF, or pF prefixes.
• f: Frequency of the AC signal applied to the capacitor in hertz (Hz). Calculator accepts Hz, kHz, MHz, or GHz prefixes.
• π: The mathematical constant pi ≈ 3.14159265358979. Used to convert between angular frequency ω (rad/s) and cyclic frequency f (Hz).
• Xc: Capacitive reactance in ohms (Ω). Auto-prefixed to mΩ, Ω, kΩ, or MΩ so the printed value stays readable across audio, mains, and RF.

The formula is the magnitude of the complex impedance of an ideal capacitor Z = 1 / (j ω C) = -j / (ω C), which is why Xc falls as 1 / f and 1 / C and why a capacitor looks like an open circuit at DC and a short circuit at very high frequencies.

According to OpenStax University Physics Volume 2, the capacitive reactance of an ideal capacitor at frequency f is Xc = 1 / (2π f C), where C is the capacitance in farads.

Once Xc is known, the next step is the AC current through the capacitor at a given voltage, and the Ohm's Law & Basic Circuit Calculator handles V = I · R for any voltage, current, or resistance on the same circuit.

Four ideas make the result panel easier to read: the role of frequency, the inverse scaling with capacitance, the open-circuit behavior at DC, and the 90° phase lead of capacitor current.

The angular frequency ω = 2π f in rad/s is the form some sources use, with Xc = 1 / (ω C); the calculator displays ω alongside Xc so the same value can be reused in a Bode plot or a phasor diagram.

The same C that sets Xc also sets the RC time constant τ = R C, and the Capacitor Charge Time Calculator pairs this C with a resistance and a voltage threshold to estimate the finite charge or discharge time on the same circuit.

Type a capacitance, type a frequency, and read Xc in the ohm prefix the calculator picks for you.

1. 1 Enter the capacitance: Type the capacitor value and pick F, mF, µF, nF, or pF as the unit prefix. The calculator converts the value to farads before the formula runs.
2. 2 Enter the frequency: Type the signal frequency and pick Hz, kHz, MHz, or GHz as the unit prefix. The calculator converts the value to hertz before the formula runs.
3. 3 Read Xc: Read the Xc result in the auto-selected ohm prefix (Ω, kΩ, or MΩ). The supporting rows show the capacitance in F, the frequency in Hz, the angular frequency ω, and the wavelength.
4. 4 Rescale for the next band: Change one unit prefix at a time to move between audio, mains, and RF ranges without recomputing the formula by hand.
5. 5 Compare several capacitors: Switch the capacitance prefix or value to see how the reactance moves at the same frequency, which is the routine check for a bypass or decoupling network.

To find the reactance of a 100 nF decoupling capacitor at a 1 MHz switching frequency, pick 100 nF and 1 MHz. The calculator returns Xc ≈ 1.591 Ω, the right order of magnitude for a decoupling capacitor at the input of a high-frequency rail.

If the goal is to size the stored charge Q = C · V and the stored energy E = (1/2) C V² at a chosen voltage, the Capacitor Charge Calculator takes the same C this calculator already uses and returns the joules, electron-volts, and watt-hours of stored work.

This calculator replaces a unit-conversion-plus-log step with a single result panel that updates as you change capacitance, frequency, or unit prefix.

• • No re-derivation of Xc = 1 / (2π f C): Stops you from retyping the AC-circuit formula every time the frequency or capacitance changes - the form takes the inputs and the result panel takes the arithmetic.
• • Capacitance prefix library: Covers F, mF, µF, nF, and pF so values from datasheets and lab readings drop in without manual conversion to farads.
• • Frequency prefix library: Covers Hz, kHz, MHz, and GHz so the same form handles audio, mains, RF, and microwave bands in one place.
• • Auto-selected ohm prefix: Picks mΩ, Ω, kΩ, or MΩ for the printed Xc so the value stays in a readable range from pF capacitors at GHz to mF capacitors at 1 Hz.
• • Traceable result panel: Reports capacitance in farads, frequency in hertz, angular frequency in rad/s, and wavelength in meters alongside Xc, so the inputs and the formula result can both be reviewed without leaving the page.

The unit-prefix libraries keep the form usable straight from a datasheet, and the Capacitance Conversion Calculator translates any single-prefix value into the rest of the F, mF, µF, nF, pF ladder so the C value feeding Xc = 1 / (2π f C) matches the rest of the design.

Two inputs drive every number in the result panel: the capacitance the user picks and the frequency of the AC signal applied to the capacitor.

• • The textbook Xc = 1 / (2π f C) assumes an ideal capacitor with no parasitic resistance or inductance, so the printed reactance is the magnitude of the AC impedance only; at high frequencies the capacitor's self-resonant frequency and ESR will dominate and the real impedance deviates from the formula.
• • The formula assumes a single-tone sinusoidal signal. A square wave or a multi-tone waveform contains harmonics at higher frequencies, and the capacitor's reactance is different at every harmonic, so the calculator should be re-run at the dominant harmonic frequency for non-sinusoidal inputs.

The calculator rejects zero or negative values for capacitance and frequency because both make the formula undefined. When Xc is below 1 Ω, the auto-prefix moves to mΩ so the small reactance of large filter capacitors at high frequency stays readable.

According to NIST CODATA, the speed of light in vacuum is exactly 299,792,458 m/s, which the calculator uses to convert the chosen frequency into the wavelength readout.

According to HyperPhysics (Georgia State University), the capacitive reactance of a capacitor equals 1 / (2π f C) and decreases as the signal frequency rises, so the capacitor acts more like a short circuit at high frequencies and more like an open circuit at low frequencies.

When Xc is paired with a series resistor to make an RC filter, the Electrical Resistance Calculator sizes R for the corner frequency f = 1 / (2π R C) to land where the filter needs it.