Capacitor Impedance Calculator

Capacitor Impedance Calculator results give the capacitor's reactance at any frequency, then the real impedance with ESR and lead inductance, plus current, heat and self-resonance.

Capacitor Impedance Calculator With ESR and ESL

A capacitor's opposition to AC current depends on frequency. It blocks low frequencies and passes high ones, which is why the same part can be a power-factor capacitor on a 60 Hz line or a decoupling capacitor at megahertz.

Electricians use the result to size run and power-factor capacitors and check the current they draw. Electronics designers and students use it for filters, coupling and decoupling, where the real part stops behaving like an ideal capacitor above a certain frequency.

The Capacitor Impedance Calculator solves the ideal reactance first, then adds the part's series resistance (ESR) and lead inductance (ESL). That gives the real impedance, phase, current, reactive power, heating and the frequency where the capacitor turns inductive.

Solving for Reactance, Capacitance or Frequency

In the Capacitor Impedance Calculator, Solve For picks the unknown. Reactance mode takes capacitance and frequency, Capacitance mode takes frequency and the reactance you want, and Frequency mode finds where a given capacitor reaches a set reactance.

Each value has its own unit menu, from pF to F, Hz to GHz and mΩ to MΩ, so values can be entered as they appear on a part or schematic. The AC voltage in volts rms sets the current results.

The Real Capacitor and Resistor accordion takes the series resistance in ohms and the lead inductance in nanohenries. Set both to zero to see the ideal capacitor alone, or enter a series resistor there to model an RC circuit.

Capacitive Reactance Formula

An ideal capacitor's reactance falls as frequency or capacitance rises. It is measured in ohms, like resistance, but it stores and returns energy instead of turning it into heat.

$$X_C=\frac{1}{2\pi fC}$$

A 200 µF capacitor at 60 Hz has a reactance of 13.26 Ω, and the same part on a 50 Hz supply rises to 15.92 Ω. Doubling either the frequency or the capacitance halves the reactance.

The common mistake is dropping the 2π. Without it, the 200 µF example gives 83.3 Ω, more than six times too high, and unit slips between µF and nF throw the answer off by 1,000 in the same way.

Impedance of a Real Capacitor

A real capacitor behaves like an ideal one in series with a small resistance and a small inductance. Its impedance is that resistance plus the difference between the inductive and capacitive reactance.

$$Z=R+j\left(\omega L-\frac{1}{\omega C}\right)$$

The magnitude |Z| is the square root of R² plus that reactance squared. At low frequency the capacitive term dominates, and the current leads the voltage by close to 90°.

As frequency rises, the two reactances cancel at the self-resonant frequency. Murata's capacitor impedance article shows the resulting V-shaped |Z| curve, with |Z| equal to ESR at the bottom and the parasitic inductance in control above it.

$$f_{SRF}=\frac{1}{2\pi \sqrt{LC}}$$

With the Capacitor Impedance Calculator's default 0.1 Ω ESR and 10 nH of lead inductance, the 200 µF capacitor self-resonates at 112.5 kHz. At 1 MHz the same part measures 0.118 Ω with a phase of +31.8°, so it acts as a small inductor, not a capacitor.

ESR is not a fixed number. Capacitor maker AIC tech shows ESR changing with both frequency and temperature, so take the datasheet ESR at your working frequency and temperature rather than a single headline figure.

Current, Reactive Power and ESR Heating

Current through the capacitor is the voltage divided by |Z|. On a 120 V, 60 Hz line, the 200 µF example draws 9.05 A and trades 1.086 kVAR of reactive power back and forth each cycle.

The dissipation factor is ESR divided by the reactance, 0.754% here, and the ESR turns I²R into heat. That is 8.19 W of heat inside this part, so check the ripple current rating on the datasheet before running a capacitor this hard.

The phase angle starts at -90° for an ideal capacitor and moves toward zero as resistance grows. When ESR or a series resistor reaches 10% of the reactance, the Capacitor Impedance Calculator warns that the part no longer acts like a pure capacitor.

Impedance Graph and Working Steps

The Capacitor Impedance Calculator plots |Z| against frequency on log scales, from a hundredth of your frequency to a hundred times it. The dashed line is the ideal reactance, and the solid line is the real impedance with ESR and ESL, which flattens at ESR and then rises past self-resonance.

A dot marks your working point, and a dashed marker shows self-resonance when it falls inside the range. The step table under the graph writes out each stage, from ω through Xc, the net reactance, |Z| and the complex impedance to the current.

The fourth card adds the RC time constant through the series resistance and the quarter-cycle lead of current over voltage, 4.17 ms at 60 Hz. For charge and discharge timing in more detail, the RC Time Constant Calculator covers the full curve.

Capacitor Impedance Questions

What is the capacitive reactance of a 200 µF capacitor at 60 Hz?

A 200 µF capacitor at 60 Hz has a capacitive reactance of 13.26 Ω, from 1 divided by 2π × 60 × 0.0002. That is the default example in the Capacitor Impedance Calculator.

On a 120 V supply it draws 9.05 A. With a typical 0.1 Ω ESR added, the real impedance is still 13.26 Ω, because the resistance is tiny next to the reactance at that frequency.

How do you find a capacitor's resistance?

A capacitor has two kinds of opposition. Reactance comes from the formula above and stores energy, while the equivalent series resistance (ESR) is a real loss that turns current into heat.

ESR is listed on the datasheet at a stated test frequency, or measured with an ESR meter or LCR meter. At the self-resonant frequency, a sweep of |Z| bottoms out at the ESR, which is how impedance analyzers read it.

What is the impedance formula for a capacitor and resistor?

In series, the impedance is the square root of R² plus Xc². A 1 kΩ resistor in series with 1 µF at 1 kHz, where Xc is 159.2 Ω, gives 1,012.6 Ω with the current leading by 9.0°.

In parallel, the impedance is R × Xc divided by the square root of R² plus Xc², which gives 157.2 Ω at -81.0° for the same parts. The Capacitor Impedance Calculator models the series case, through the series resistance field.

What is the capacitance of a 103 capacitor?

A 103 marking means 10 followed by three zeros in picofarads, or 10,000 pF, which is 10 nF, as Kitronik's capacitor code guide explains. A 104 is 100 nF by the same rule.

A 10 nF capacitor has a reactance of about 15.9 kΩ at 1 kHz and 15.9 Ω at 1 MHz. Pick nF in the capacitance unit menu and enter 10 to see its full impedance curve and self-resonance.