Reactance and Resonance Calculator

How it works

A capacitor’s opposition to AC (its reactance) falls with frequency: X_C = 1 ÷ (2π f C). An inductor’s rises: X_L = 2π f L. Both are in ohms, but the current is 90° out of step with the voltage and no power is dissipated (unlike a resistor). A series L and C have equal and opposite reactances at the resonant frequency f₀ = 1 ÷ (2π √(L C)), where the circuit is easiest to drive. The characteristic impedance √(L ÷ C) sets how big the circulating currents are. See Capacitors and Inductors.

Worked example

A 100 nF capacitor at 1 kHz has X_C = 1 ÷ (2π × 1000 × 100 × 10⁻⁹) = 1 592 Ω; across 5 V rms it passes 3.14 mA. A 10 mH inductor at 10 kHz has X_L = 2π × 10 000 × 0.01 = 628 Ω. A 10 µH inductor with a 100 nF capacitor resonates at 1 ÷ (2π √(10⁻⁵ × 10⁻⁷)) = 159.2 kHz, with Z₀ = √(10 µH ÷ 100 nF) = 10 Ω.

Things to know

These are ideal parts. Real capacitors have series inductance (ESL) and real inductors have capacitance, so above their self-resonant frequency a capacitor behaves as an inductor and the reverse.

Reactance is not resistance: it stores and returns energy rather than dissipating it, so there is no I² × R heat from it (the resistance of the winding and the capacitor’s ESR still heat).

For a series R and C or R and L, the total impedance is √(R² + X²), with a phase angle of arctan(X ÷ R).

Common questions

Why does a capacitor block DC?

At 0 Hz its reactance is infinite: once charged, no current flows.

What happens at resonance?

A series LC has the smallest impedance (only the resistance remains); a parallel LC has the largest. It is the basis of tuned filters and oscillators.

How do I find the filter cutoff from this?

A low-pass RC cuts off where X_C equals R: see the RC Time Constant and Filter Calculator.

Sources

• Horowitz, P. and Hill, W., The Art of Electronics, 3rd ed., Cambridge University Press: chapter 1, capacitors, inductors and impedance.

Last reviewed: October 22, 2026