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Impedance of a Capacitor

A capacitor opposes changes in voltage, so in AC circuits it blocks low frequencies more than high ones. Its impedance is 1 divided by j times omega times C. The j means the voltage lags the current by 90 degrees. As frequency goes up, the impedance goes down, so a capacitor acts like a high-pass filter, passing high frequencies while blocking DC and low frequencies.

Written by the Vorzep Team

AC Circuits Impedance

Capacitor Impedance Calculator

Ideal & practical capacitive reactance, complex impedance, and frequency-response analysis

AC Circuits
ZC = 1 / (jωC) = −jXC
XC = 1 / (2πfC)  ·  ω = 2πf
Mode
Solve For
Operating frequency f (0 = DC, ideal-impedance mode only)
Capacitance C
AC Voltage / Current (optional)
Vrms
Leave blank to skip current / reactive power results
Quick Presets
Loads values, then calculates
Capacitor Frequency Behavior
Low f  High |ZC| High f  Low |ZC|
A capacitor's impedance falls as frequency rises, because XC = 1 / (2πfC) is inversely proportional to f. Enter values and calculate to place the marker at your operating point.
Capacitor Reactance Reference Table
XC = 1 / (2πfC), generated dynamically for representative capacitance and frequency pairs.
Formula Reference
Angular Frequency
ω = 2πf
Capacitive Reactance
XC = 1 / (2πfC)
Capacitor Impedance
ZC = 1 / (jωC) = −jXC
Magnitude
|ZC| = XC
Phase
θ = −90°
Solve for Capacitance
C = 1 / (2πfXC)
Solve for Frequency
f = 1 / (2πCXC)
Practical Model (Advanced)
Z = ESR + j(2πfL − 1/2πfC)
ZCCapacitor impedance (complex, Ω)
XCCapacitive reactance (Ω)
jImaginary unit
ωAngular frequency (rad/s)
fFrequency (Hz)
CCapacitance (F)
ESREquivalent series resistance (Ω)
ESLEquivalent series inductance (H)
What This Capacitor Impedance Calculator Offers
Ideal capacitor impedance, reactance, angular frequency
Complex impedance in rectangular and polar form
Magnitude and phase angle
Reverse solving for capacitance or frequency
Automatic engineering-unit conversion & scaling
Frequency sweep analysis with table and chart
Capacitor reactance reference table
Optional RMS voltage/current & reactive power
Optional ESR/ESL practical capacitor modeling
Self-resonant frequency estimation
Dynamic step-by-step calculation breakdown
Result-specific engineering interpretation
How to Use the Capacitor Impedance Calculator
  1. Select what you want to calculate under Solve For: impedance/reactance, capacitance, or frequency.
  2. Enter the frequency (or, in Solve-for-Capacitance mode, the frequency is one of your knowns).
  3. Select the correct frequency unit (Hz, kHz, MHz, GHz).
  4. Enter the capacitance, or the required reactance, depending on the selected mode.
  5. Select the matching unit for that field.
  6. Optionally enter an RMS voltage to see current and reactive power.
  7. Enable Advanced Mode if you want ESR/ESL practical-model analysis.
  8. Click Calculate.
  9. Review the primary impedance result at the top of the dashboard.
  10. Check the magnitude and phase angle cards.
  11. Expand Calculation Steps to see the full derivation using your own numbers.
  12. Use the sweep chart and table to see how impedance changes with frequency.
Engineering Applications

Capacitive reactance and impedance calculations are used throughout AC circuit design, including:

Real capacitor selection also depends on voltage rating, tolerance, ESR, ESL, ripple-current rating, temperature, dielectric type, aging, and the manufacturer's specifications — not reactance alone.
Capacitor Types & Practical Behavior
TypeTypical RangeESRHigh-Freq UsePolarity
Qualitative comparison only — actual specifications vary significantly by construction and manufacturer; consult the datasheet for real designs.
Important Engineering Concepts
Capacitor at DC — as f → 0, XC → ∞. After charging under steady-state DC, an ideal capacitor behaves like an open circuit. Real capacitors still carry a small leakage current, so they are never truly infinite-resistance at DC.
Increasing frequency — XC decreases because XC = 1/(2πfC) is inversely proportional to f.
Effect of capacitance — larger C produces lower reactance at the same frequency.
Phase relationship — ideal capacitor impedance phase is −90°; capacitor current leads capacitor voltage by 90° in the sinusoidal steady state.
Real capacitors — ESR, ESL, dielectric losses, leakage, tolerance, temperature, and frequency all shift actual behavior away from the ideal formula, especially near and above self-resonance.
Self-resonant frequency (SRF) — f_SRF = 1/(2π√(L·C)) is the frequency at which a real capacitor's parasitic ESL and its capacitance resonate. Below f_SRF the part behaves primarily capacitively; near f_SRF impedance drops to a minimum set largely by ESR; above f_SRF the parasitic inductance dominates and the part can behave inductively instead of capacitively.
References & Engineering Notes
  • Alexander & Sadiku, Fundamentals of Electric Circuits — AC steady-state and phasor/impedance treatment.
  • Hayt, Kemmerly & Durbin, Engineering Circuit Analysis — sinusoidal steady-state analysis.
  • Sedra & Smith, Microelectronic Circuits — frequency response fundamentals, where relevant.
  • Manufacturer capacitor application notes and datasheets — for practical ESR, ESL, and self-resonance data on a specific part.
For real capacitor selection, always confirm ESR, ESL, and self-resonant frequency against the specific manufacturer's datasheet — values here are user-entered estimates, not verified component specs.

Engineering Disclaimer: This tool is intended for education, preliminary design, circuit analysis, and engineering estimation. Real capacitors are non-ideal. For production electronics, high-voltage systems, power electronics, RF circuits, safety-critical designs, motor applications, and power-factor-correction systems, engineers must verify manufacturer datasheets, capacitance tolerance, voltage rating, ripple-current rating, ESR, ESL, operating frequency range, dielectric characteristics, temperature rating, lifetime, and applicable safety requirements before use.

Vorzep · Capacitor Impedance Analysis Tool

Variables

Symbol Quantity Unit
ZC Capacitive impedance Ω
j Imaginary unit (√−1) —
ω Angular frequency (2πf) rad/s
C Capacitance F

What it means

The impedance of a capacitor is Z_C = 1/(jωC) = −j/(ωC). It is purely imaginary, with a negative sign indicating that the voltage lags the current by 90°. The magnitude |Z_C| = 1/(ωC) decreases with increasing frequency. At DC (ω=0), the impedance is infinite (open circuit), and at high frequencies, it approaches zero (short circuit). This behaviour is used in coupling capacitors, decoupling capacitors, and filters. Capacitors pass AC while blocking DC. They are used in signal processing, power supplies, and timing circuits. Example: A capacitor C=100µF at f=50Hz (ω≈314) has |Z_C| = 1/(314*100e-6) = 1/0.0314 = 31.8Ω. At 1kHz (ω=6283), |Z_C| = 1/(6283*100e-6) = 1/0.6283 = 1.59Ω.

Worked example

Impedance of a Capacitor – Practical Example

Real‑World
Scenario: A 100 µF capacitor is used at 50 Hz. Calculate its impedance.
ParameterValue
C100 µF = 100×10⁻⁶ F
f50 Hz
FormulaZC = -j / (ω·C), ω = 2πf
1ω = 2π×50 = 314.16 rad/s
2ZC = -j / (314.16 × 100e-6) = -j / 0.031416 = -j·31.83 Ω
Final Design ZC = -j·31.83 Ω ✓ Capacitive reactance
Why: Capacitive impedance decreases with frequency – it is reactive with -90° phase.

Common mistakes

  • j in denominator: 1/(jωC) = −j/(ωC) – the negative sign indicates phase shift.
  • Phase: Current leads voltage by 90° (capacitor).
  • Magnitude: |Z_C| = 1/(ωC) – decreases with frequency.
  • Units: Ohms.
  • DC: At DC (ω=0), impedance is infinite (open circuit).

Applications

The impedance of a capacitor is Z_C = −j/(ωC), which decreases with increasing frequency. Capacitors oppose changes in voltage, so they pass high‑frequency signals and block DC. Engineers use this formula to design high‑pass and band‑pass filters, to couple AC signals between stages, and to bypass noise to ground. In power supplies, capacitors smooth the output voltage. By understanding the frequency dependence, professionals can select appropriate capacitors for filtering, coupling, and timing applications. This impedance is fundamental to AC circuit analysis and is used in many practical circuits.

  • Filter design (high‑pass, band‑pass, notch)
  • AC coupling between amplifier stages
  • Decoupling and bypass capacitors for noise reduction
  • Power supply smoothing and ripple reduction
  • Educational understanding of capacitive reactance

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  • Published July 10, 2026
  • Last updated September 25, 2026