What is the resonant frequency of an RLC circuit?

The resonant frequency is f₀ = 1 / (2π√(LC)). At this frequency the inductive reactance XL equals the capacitive reactance XC, so they cancel. In a series circuit this gives minimum impedance; in a parallel circuit it gives maximum impedance.

What does the Q-factor measure?

The quality factor Q indicates how selective (narrow-bandwidth) the resonance is. A higher Q means the circuit responds sharply around f₀ and dissipates little energy per cycle. For a series RLC circuit Q = (1/R)√(L/C); for a parallel circuit Q = R√(C/L).

How is bandwidth related to Q?

Bandwidth BW = f₀ / Q. A high-Q circuit has a narrow bandwidth (selective), while a low-Q circuit passes a wider range of frequencies. The 3 dB frequencies are f₁ = f₀ − BW/2 and f₂ = f₀ + BW/2.

Why is impedance complex?

Impedance Z = R + j(XL − XC) for a series circuit. The real part R causes energy dissipation; the imaginary part (reactance) stores energy. The magnitude |Z| = √(R² + (XL−XC)²) gives the ratio of voltage to current amplitude, and the phase angle φ = arctan((XL−XC)/R) gives the phase shift.

What units should I use?

R in ohms (Ω), L in henries (H) or millihenries (mH), C in farads (F), microfarads (μF), or picofarads (pF). The calculator accepts unit multipliers so you can enter values as they appear on component labels.

RLC Circuit Calculator

Enter resistance, inductance, and capacitance to compute resonant frequency, impedance, Q-factor, and bandwidth for series or parallel RLC circuits.

Circuit Parameters

Circuit topology

Resistance R

Inductance L

Capacitance C

Analysis frequency (optional)

Computes impedance & phase at this frequency. Defaults to f₀.

Enter R, L, C values and click Calculate

Summary

An RLC circuit contains a resistor (R), inductor (L), and capacitor (C) connected in series or parallel. At the resonant frequency, the inductive and capacitive reactances cancel, producing minimum impedance (series) or maximum impedance (parallel). This calculator derives the resonant frequency, total impedance at any frequency, quality factor Q, and 3 dB bandwidth.

How it works

Select the circuit topology: series or parallel.
Enter the resistance R (ohms), inductance L (henries or millihenries), and capacitance C (farads, microfarads, or picofarads).
Optionally enter an AC frequency to compute impedance and phase angle at that frequency.
The calculator outputs resonant frequency f₀, angular frequency ω₀, Q-factor, bandwidth, and impedance components.
Read the phasor summary to understand whether the circuit is inductive or capacitive at the given frequency.

Use cases

Design bandpass and notch filters for audio or RF circuits.
Tune an LC tank circuit to a target resonant frequency.
Analyze the selectivity and damping of an oscillator.
Calculate impedance matching for antenna or transmission line work.
Verify textbook RLC problems and homework assignments.
Prototype radio receiver front-end filters.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu