Capacitive Reactance Calculator – Xc Formula
Calculate capacitive reactance (Xc) and angular frequency for any capacitor in an AC circuit using Xc = 1/(2πfC).
Enter the AC frequency and capacitance value with its unit to instantly find the capacitive reactance, angular frequency, and signal period.
Capacitive Reactance Calculator – Xc Formula
Calculate capacitive reactance (Xc) and angular frequency for any capacitor in an AC circuit using Xc = 1/(2πfC).
About the Capacitive Reactance Calculator
Capacitive reactance (Xc) is the opposition that a capacitor presents to alternating current (AC) in an electrical circuit. Unlike resistance, which dissipates energy as heat, capacitive reactance stores and releases energy in an electric field. It is measured in ohms (Ω) but is frequency-dependent — as frequency increases, capacitive reactance decreases, and as frequency decreases, Xc increases. At DC (zero frequency), the reactance is theoretically infinite, which is why capacitors block direct current.
The fundamental formula is Xc = 1 / (2π × f × C), where f is the frequency in hertz (Hz), C is the capacitance in farads (F), and 2π ≈ 6.2832 is the angular factor relating ordinary frequency to angular frequency. Angular frequency ω = 2πf (measured in radians per second) is used in complex impedance calculations: the capacitor's impedance is Z = 1 / (jωC) = –j·Xc, where j is the imaginary unit.
Capacitive reactance plays a central role in AC circuit analysis. In a purely capacitive circuit, the current leads the voltage by exactly 90°. In real circuits, capacitors are combined with resistors (RC circuits) and inductors (RLC circuits), creating frequency-dependent behaviour used in filters, oscillators, and tuned amplifiers. The RC time constant τ = RC describes how quickly a capacitor charges or discharges, while the 3 dB cutoff frequency of an RC low-pass filter is f₃dB = 1 / (2π × R × C).
Capacitor unit prefixes in common use include millifarad (mF, 10⁻³ F), microfarad (μF, 10⁻⁶ F), nanofarad (nF, 10⁻⁹ F), and picofarad (pF, 10⁻¹² F). This calculator handles all of these automatically — select the appropriate unit from the dropdown and the conversion is performed internally.
Practical applications of capacitive reactance calculations include: designing crossover networks in loudspeakers (where capacitors block low frequencies to tweeters), computing impedance matching in RF circuits, calculating the reactance of decoupling capacitors in power supply bypassing, and verifying filter cutoff frequencies in audio and signal processing circuits. When selecting a capacitor for a specific reactance at a known frequency, simply rearrange the formula: C = 1 / (2π × f × Xc).
Resonance is another key concept. In a series LC circuit, the inductive reactance XL = 2πfL equals the capacitive reactance Xc at the resonant frequency f₀ = 1 / (2π × √(LC)), where the total reactance is zero and only resistance limits the current. This principle is exploited in radio tuning, bandpass filters, and impedance-matching networks across the full spectrum from audio (20 Hz–20 kHz) through RF (kHz–GHz) to microwave applications.
Worked Examples
Three common AC circuit scenarios demonstrating how capacitive reactance changes with frequency and capacitance.
| Inputs | Xc Result | Notes |
|---|---|---|
| f = 60 Hz, C = 100 μF | Xc ≈ 26.53 Ω, ω ≈ 376.99 rad/s | Mains-frequency capacitor — typical for motor-run and power factor correction applications. |
| f = 1000 Hz, C = 10 μF | Xc ≈ 15.92 Ω, ω ≈ 6283.19 rad/s | Audio-frequency bypass capacitor — lower reactance at 1 kHz than at 60 Hz for the same capacitance. |
| f = 100 kHz, C = 100 nF | Xc ≈ 15.92 Ω, ω ≈ 628,318.5 rad/s | RF decoupling capacitor — 100 nF at 100 kHz gives the same reactance as 10 μF at 1 kHz. |
How to Use the Capacitive Reactance Calculator
- Enter the AC signal frequency in hertz (Hz). For mains power use 50 Hz (Europe) or 60 Hz (North America); for audio circuits use the frequency of interest; for RF circuits enter the carrier frequency.
- Enter the capacitance value as a number. Choose the correct unit from the dropdown: F (farads), mF (millifarads), μF (microfarads), nF (nanofarads), or pF (picofarads).
- Click Calculate. The tool displays the capacitive reactance Xc in ohms, the angular frequency ω in rad/s, and the signal period T in seconds.
- Use the Xc value in impedance divider calculations, filter design, or to compare the reactance against a series resistance to determine the –3 dB cutoff frequency.
- Click Reset to clear all fields and start a new calculation.
Frequently Asked Questions
What is capacitive reactance?
Capacitive reactance (Xc) is the frequency-dependent opposition a capacitor offers to alternating current, expressed in ohms. Unlike resistance, it does not dissipate power — it stores energy in an electric field and returns it each cycle. The formula Xc = 1/(2πfC) shows that reactance decreases as frequency or capacitance increases.
Why does capacitive reactance decrease with increasing frequency?
At higher frequencies, the capacitor's plates charge and discharge more rapidly, allowing more current to flow per unit time. Mathematically, since Xc = 1/(2πfC), doubling the frequency halves the reactance. At very high frequencies a capacitor approaches a short circuit, while at DC (f = 0 Hz) the reactance is infinite and no steady-state current flows.
What is the difference between reactance and impedance?
Reactance (X) is the imaginary part of impedance (Z). For a pure capacitor Z = –jXc = 1/(jωC), so the impedance magnitude equals the reactance magnitude at any frequency. When a capacitor is combined with a resistor, the total impedance is Z = √(R² + Xc²) and the phase angle is θ = –arctan(Xc/R). Impedance is the general term for the total opposition in a complex circuit.
How do I find the capacitance needed for a specific reactance?
Rearrange the formula: C = 1 / (2π × f × Xc). For example, to achieve Xc = 50 Ω at 1 kHz: C = 1 / (2π × 1000 × 50) ≈ 3.18 μF. Similarly, to find the frequency at which a known capacitor reaches a target reactance: f = 1 / (2π × C × Xc).
What is angular frequency and how is it related to ordinary frequency?
Angular frequency ω (omega) is measured in radians per second and equals 2π × f. It arises naturally in sinusoidal signal analysis because one complete cycle corresponds to 2π radians. Using ω simplifies many formulas in circuit analysis — for example, the capacitor's impedance is simply Z = 1/(jωC) rather than 1/(j·2π·f·C).
Does capacitive reactance apply to DC circuits?
In a steady-state DC circuit (f = 0) the capacitive reactance is theoretically infinite, meaning a fully charged capacitor blocks DC current entirely. However, during the transient charging or discharging phase (an RC circuit), current does flow. Once the capacitor reaches steady state, current drops to zero. This is why capacitors are used as DC-blocking elements in amplifier coupling stages.