What is a resonant frequency?

The resonant frequency f_r = 1/(2π√(LC)) is where inductive reactance XL equals capacitive reactance XC. At resonance, a series RLC circuit has minimum impedance (Z=R) and a parallel RLC has maximum impedance.

What is the Q factor in an RLC circuit?

Q = (1/R)√(L/C) for series RLC. It measures selectivity — how sharply the circuit responds to its resonant frequency. Higher Q means narrower bandwidth. Q = f_r / BW.

What is damping ratio ζ?

ζ = R/(2√(L/C)). If ζ 1 is overdamped (slow exponential decay).

How is bandwidth related to Q?

Bandwidth BW = f_r / Q. A high-Q resonator (like a crystal oscillator with Q ≈ 100,000) has extremely narrow bandwidth. A wide-band filter may have Q < 1.

RLC Circuit Calculator

Calculate impedance Z, resonant frequency, Q factor, bandwidth, phase angle, and damping ratio for series and parallel RLC circuits.

Resistance R (Ω)

Inductance L (mH)

Capacitance C (μF)

μF

Frequency f (Hz)

Impedance Z (Ω)

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Resonant Frequency f_r (Hz) —

Phase Angle θ (°) —

Extended More scenarios, charts & detailed breakdown ▾

R (Ω)

L (mH)

C (μF)

Frequency (Hz)

Impedance Z (Ω)

—

XL (Ω) —

XC (Ω) —

Phase Angle (°) —

Professional Full parameters & maximum detail ▾

R (Ω)

L (mH)

C (μF)

Resonant Frequency (Hz)

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Damping Ratio ζ —

Damping Regime —

Q Factor —

Bandwidth (Hz) —

Phase at f_r (°) —

How to Use This Calculator

Enter R (Ω), L (mH), C (μF), and frequency (Hz).
Simple tier shows Z, f_r, and phase angle.
Use Extended tabs for Series, Parallel, or Resonance-only analysis.
Professional mode adds damping regime, Q factor, and bandwidth.

Formula

Series Z = √(R² + (XL − XC)²)
XL = 2πfL | XC = 1/(2πfC)
Resonance: f_r = 1/(2π√(LC))
Q = (1/R)√(L/C) | ζ = R/(2√(L/C))

Example

R=10Ω, L=50mH, C=10μF: f_r = 1/(2π√(0.05×10⁻⁵)) ≈ 225 Hz. Q = (1/10)√(50×10⁻³/10⁻⁵) = 22.4.

Frequently Asked Questions

The resonant frequency f_r = 1/(2π√(LC)) is where inductive reactance XL equals capacitive reactance XC. At resonance, a series RLC circuit has minimum impedance (Z=R) and a parallel RLC has maximum impedance.
Q = (1/R)√(L/C) for series RLC. It measures selectivity — how sharply the circuit responds to its resonant frequency. Higher Q means narrower bandwidth. Q = f_r / BW.
ζ = R/(2√(L/C)). If ζ < 1 the circuit is underdamped and oscillates; ζ = 1 is critically damped (fastest settling without overshoot); ζ > 1 is overdamped (slow exponential decay).
Bandwidth BW = f_r / Q. A high-Q resonator (like a crystal oscillator with Q ≈ 100,000) has extremely narrow bandwidth. A wide-band filter may have Q < 1.

Related Calculators

Sources & References (5) ▾

HyperPhysics – RLC Series Circuit — Georgia State University
OpenStax University Physics Vol. 2 Ch. 15 – Alternating-Current Circuits — OpenStax
Sedra & Smith – Microelectronic Circuits, 8th Ed. — Oxford University Press
NIST Guide to SI Units – Electrical Quantities — NIST
Khan Academy – AC Circuits — Khan Academy