Capacitor Reactance Calculator

Formula used

Capacitive reactance is the opposition a capacitor provides to AC current. It depends on frequency and capacitance.

• ω = 2πf
• X_C = 1 / (ωC) = 1 / (2πfC)
• For a series RC circuit: |Z| = √(R² + X_C²)
• Phase angle (series RC): φ = −tan⁻¹(X_C/R)

Reactance is in ohms, capacitance in farads, frequency in hertz.

How to use this calculator

1. Select whether you will enter frequency f or angular frequency ω.
2. Enter the capacitor value and choose its unit.
3. Optionally enable advanced options for series resistance and RMS voltage.
4. Press Calculate to see results above the form.
5. Use CSV or PDF buttons to export your computed values.

Example data table

Values shown assume ideal capacitors and steady sinusoidal signals.

Capacitor Reactance and Practical AC Design

Capacitive reactance is a frequency-dependent opposition to alternating current. Because X_C = 1/(2πfC), doubling frequency halves reactance, and doubling capacitance does the same. This calculator converts common units and reports reactance, impedance magnitude, and phase.

1) Why reactance matters in real circuits

Reactance controls how much AC current can flow through a capacitor. In coupling networks, a lower X_C at the signal frequency reduces attenuation. In timing and filtering, the same relationship sets cutoffs, ripple, and transient behavior when paired with resistance.

2) Mains frequency examples with numeric context

At 50 Hz, a 1 µF capacitor has X_C ≈ 3183 Ω. A 10 µF capacitor drops that to about 318 Ω. At 60 Hz, 1 µF becomes ≈ 2653 Ω. These values help estimate leakage current in capacitive droppers and line filters.

3) Audio-band coupling and impedance targets

Audio coupling often targets reactance well below the load impedance. For example, at 100 Hz, 10 µF gives X_C ≈ 159 Ω, which is comfortable for a 10 kΩ input but too high for an 8 Ω speaker. Selecting C from the desired minimum frequency keeps bass response predictable.

4) High-frequency behavior and parasitics

At 1 MHz, 100 pF yields X_C ≈ 1592 Ω. In RF and fast digital edges, capacitor ESR, ESL, and resonance can dominate, so measured impedance may deviate from the ideal model. Use the calculator for first-pass sizing, then validate with component curves.

5) Using angular frequency for control work

Many controls and signal-processing equations use ω directly. Entering angular frequency avoids repeated conversions, and the calculator reports the equivalent f and period. This is useful when comparing capacitor impedance inside transfer functions and Laplace-domain models.

6) Series RC impedance and phase interpretation

With optional resistance enabled, the calculator returns |Z| = √(R² + X_C²) and phase φ = −tan⁻¹(X_C/R). When X_C ≫ R, the phase approaches −90°, indicating current leads voltage strongly, typical of capacitive dominance.

7) Tolerance, temperature, and safety notes

Capacitance tolerance commonly ranges from ±5% to ±20%, and temperature coefficients can shift C further. Because X_C scales inversely with C, a −20% change increases reactance by 25%. In mains applications, always use safety-rated capacitors and appropriate discharge paths.

8) Quick workflow for design decisions

Start with a target reactance at your key frequency, then solve for C by rearranging the formula. Confirm reactance at adjacent frequencies to check bandwidth or ripple. Add series resistance to estimate current, voltage division, and reactive power, then export CSV or PDF for documentation.

FAQs

1) What is capacitor reactance?

Capacitor reactance is the effective AC opposition of a capacitor, measured in ohms. It decreases as frequency increases and decreases as capacitance increases, following X_C=1/(2πfC).

2) Why does the phase angle show a negative value?

In capacitive behavior, current leads voltage. Using the common sign convention for impedance, capacitive reactance contributes a negative imaginary term, so the series RC phase angle is negative.

3) Can I use angular frequency instead of frequency?

Yes. Choose the angular-frequency option and enter ω in rad/s (or scaled units). The calculator converts to f and computes the same reactance and related values.

4) What does the impedance magnitude represent?

It is the overall opposition to AC in a series RC path: |Z|=√(R²+X_C²). It is useful for estimating RMS current when an RMS voltage is applied.

5) Why might my measured value differ from the ideal result?

Real capacitors include ESR, ESL, tolerance, and dielectric losses. At high frequencies, resonance and layout parasitics can dominate. Use ideal reactance for sizing, then check component impedance curves and prototypes.

6) How do I pick a capacitor for coupling audio signals?

Choose C so X_C at the lowest desired frequency is well below the load/input impedance. This reduces bass attenuation and keeps the cutoff frequency low for flatter response.

7) Is it safe to use capacitors on mains voltage?

Only use properly rated safety capacitors (for example, X or Y classes where required), add discharge resistors when appropriate, and follow applicable standards. The calculator helps estimate reactance, not safety compliance.