RLC Impedance & Reactance
Reactance at a frequency and the impedance of R, L and C in series or parallel — magnitude and phase, resonance, Q, bandwidth, current and power at a voltage.
X_L and X_C, the complex impedance as R + jX with magnitude, phase angle and whether the circuit looks inductive or capacitive, the resonant frequency with Q and bandwidth, and the rms current, real and reactive power at your voltage.
Example: 100 Ω, 10 mH and 10 µF in series at 1 kHz: X_L 62.8 Ω, X_C 15.9 Ω, Z = 100 + j46.9 Ω = 110.5 Ω ∠ 25.1° (inductive); resonance at 503.3 Hz with Q 0.32. In parallel the same parts give 20.8 Ω ∠ −78°.
Reactances first,
then the complex sum.
How reactance and impedance are computed for each connection, what resonance means, and what ideal parts leave out.
Reactance and impedance
At a frequency f, an inductor opposes current with X_L = 2πfL and a capacitor with X_C = 1 ÷ (2πfC); resistance opposes it without phase shift. In series the impedance is Z = R + j(X_L − X_C): the magnitude is √(R² + X²) and the phase atan(X ÷ R), positive (current lags) when the inductor dominates, negative (current leads) when the capacitor does. In parallel the admittances add instead — Y = 1/R + j(ωC − 1/ωL) — and Z = 1/Y; a parallel L and C with no R at exact resonance has infinite impedance, which the page reports as ∞. Blank elements are simply left out, so RC, RL and LC circuits use the same page.
Resonance
When X_L = X_C the reactances cancel: f₀ = 1 ÷ (2π√LC). A series circuit is then purely resistive at its minimum impedance R; a parallel circuit at its maximum. The quality factor Q = ω₀L ÷ R (series) or R ÷ ω₀L (parallel) sets the sharpness, and the −3 dB bandwidth is f₀ ÷ Q. With a supply voltage the page also gives the rms current V ÷ |Z|, real power V·I·cos φ and reactive power V·I·sin φ.
Ideal parts
Real inductors have winding resistance and self-capacitance, capacitors have ESR and lead inductance, and both drift with temperature; at radio frequencies these dominate. The figures here are for the ideal elements you enter — measure or take the data-sheet parasitics for anything precise. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- X_L = 2πfL, X_C = 1/(2πfC); series Z = R + j(X_L − X_C); parallel Y = 1/R + j(ωC − 1/ωL); f₀ = 1/(2π√LC); Q = ω₀L/R (series) or R/ω₀L (parallel); ideal elements, no ESR
Last reviewed 22 September 2026. How results are checked: How we verify.