Capacitive Reactance Calculator
Calculates capacitive reactance (Xc) for a capacitor in an AC circuit at a given frequency. Used by engineers and students analyzing filters, coupling networks, tuned circuits, and impedance matching.
Last updated: May 2026
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About this calculator
Capacitive reactance (Xc) describes how strongly a capacitor opposes the flow of alternating current at a given frequency. The formula is Xc = 1 / (2π × f × C), where f is the frequency in hertz (Hz) and C is the capacitance in farads (F). Because capacitance is commonly given in microfarads (μF), the calculator converts it first: C(F) = C(μF) / 1,000,000, giving Xc = 1 / (2 × π × f × (C_μF / 1,000,000)). Variables: frequency (Hz), capacitance (μF). Reactance is measured in ohms (Ω), just like resistance, but unlike resistance it varies with frequency — Xc is inversely proportional to frequency, so at very high frequencies a capacitor approaches a short circuit, and at DC (f = 0) it acts as an open circuit. Reference values at 60 Hz: 1 μF → 2,653 Ω; 100 μF → 26.53 Ω; 10,000 μF → 0.265 Ω. Edge cases: the formula assumes an ideal capacitor with no equivalent series resistance (ESR) or equivalent series inductance (ESL). Real capacitors have ESR (which produces heat at high ripple currents) and ESL (which dominates above a self-resonant frequency, typically 1–100 MHz depending on package). Electrolytic capacitors are polarized and must not see reverse voltage; ceramic capacitors have voltage and temperature coefficients that change capacitance (Y5V, X7R, NPO classes differ significantly). The formula gives only the magnitude of impedance for a pure capacitor; full AC analysis uses complex impedance Z_C = 1 / (jωC) = −j × Xc to capture the 90° phase lead of current over voltage.
How to use
Example 1: 100 μF capacitor at 60 Hz (US mains frequency). Step 1: convert capacitance — C = 100 / 1,000,000 = 0.0001 F. Step 2: Xc = 1 / (2π × 60 × 0.0001) = 1 / (0.0377) ≈ 26.53 Ω. Verify: at 50 Hz (EU mains), Xc would be 1 / (2π × 50 × 0.0001) ≈ 31.83 Ω — proportionally larger as frequency drops, confirming inverse relationship. Example 2: 0.01 μF (10 nF) capacitor at 1 kHz (audio frequency). Step 1: C = 0.01 / 1,000,000 = 1e-8 F. Step 2: Xc = 1 / (2π × 1000 × 1e-8) = 1 / (6.28e-5) ≈ 15,915 Ω ≈ 15.92 kΩ. Verify: at 100 kHz (RF), the same capacitor would have Xc = 1 / (2π × 100000 × 1e-8) ≈ 159.2 Ω — 100× smaller as frequency rises 100×, consistent with 1/f relationship.
Frequently asked questions
What is capacitive reactance and how does it affect an AC circuit?
Capacitive reactance (Xc) is the opposition a capacitor offers to alternating current, measured in ohms. Unlike resistance, it is not constant — it depends on both the capacitance value and the signal frequency. A high Xc means the capacitor blocks most of the AC signal; a low Xc allows it to pass freely. This frequency-dependent behavior makes capacitors essential in high-pass filters (blocking DC and low frequencies, passing high), AC coupling between amplifier stages, bypass capacitors that shunt high-frequency noise to ground, and tuned LC resonant circuits in radio and audio applications. Unlike a resistor, a capacitor does not dissipate energy as heat (in the ideal case) — it stores energy in its electric field and returns it to the circuit each cycle.
How does frequency affect capacitive reactance?
Capacitive reactance is inversely proportional to frequency: as frequency goes up, Xc goes down. At very low frequencies (approaching DC), Xc becomes extremely large, effectively blocking current — a capacitor is an open circuit to DC in steady state. At high frequencies, Xc approaches zero, allowing current to flow almost unimpeded. This is why capacitors are used as high-pass filter elements (they pass high-frequency signals and attenuate low-frequency ones) and as DC-blocking coupling capacitors between amplifier stages. The relationship Xc = 1 / (2πfC) means each decade of frequency reduces Xc by a factor of 10. At very high frequencies (above the capacitor's self-resonant frequency), parasitic inductance ESL dominates and Xc effectively rises again — a real capacitor stops behaving like a capacitor.
How do I use capacitive reactance in an impedance or filter design calculation?
In AC circuits, capacitive reactance is treated like resistance in Ohm's Law: V = Xc × I, but with a 90° phase shift. Current leads voltage by 90° in a pure capacitor. To design a simple RC high-pass filter, choose a resistor and capacitor such that the cutoff frequency fc = 1 / (2π × R × C) falls where you want the filter to transition; at fc, Xc = R and the signal is attenuated by 3 dB. Knowing Xc also lets you compute total impedance in series or parallel RC and RLC circuits: for a series RC circuit, Z = √(R² + Xc²) and phase angle φ = −arctan(Xc/R). For matching networks and tuned circuits, the resonant frequency where Xc = XL gives a sharp impedance minimum (series) or maximum (parallel) used in radios, oscillators, and power-factor correction.
What are common mistakes when computing capacitive reactance?
Forgetting to convert capacitance from μF to F (divide by 1,000,000) gives Xc that is 1,000,000× too small. Using base-10 frequency where Hz is expected without verifying units. Confusing Xc with impedance Z when other components are present — a pure capacitor gives Xc, but with resistance R in series the total impedance Z = √(R² + Xc²) is larger. Treating Xc as a real number when phase information matters — for transient or detailed AC analysis use complex Z_C = −jXc. Forgetting the 90° phase lead of current in a pure capacitor when computing power: average power in a pure capacitor is zero. Ignoring the capacitor's ESR and ESL, which dominate at very high or very low frequencies. Picking the wrong capacitor type (electrolytic vs ceramic vs film) for the application — electrolytic capacitors have huge ESR at high frequencies and shouldn't be used as RF bypasses.
When should I NOT rely on the basic Xc formula?
Above a capacitor's self-resonant frequency (SRF), parasitic inductance (ESL) takes over and the component behaves like an inductor — the formula gives the wrong magnitude entirely. For high-current applications, use the manufacturer's impedance-vs-frequency curve to account for ESR, which dominates at the SRF. Electrolytic capacitors have ESR that ranges from 0.01 Ω (low-ESR types) to several ohms at low frequencies — ignoring it underestimates losses in switching power supplies. Ceramic Class 2 dielectrics (X7R, Y5V) lose 10–80% of their rated capacitance under DC bias and over temperature; the nominal value in the formula isn't what you actually get. Polarized capacitors (electrolytic, tantalum) fail if reverse-biased — the formula assumes the capacitor is operating in spec. For non-sinusoidal waveforms (square waves, PWM), Xc only describes the fundamental harmonic; Fourier analysis is needed for accurate response. For very high-voltage capacitors (kV range), corona losses and partial discharge complicate the simple model.