Resonant angular frequency
ω₀ = 1/√(LC)
Ideal series resonance occurs where X_L and X_C cancel.
RLC Resonant Frequency Calculator
Calculate ideal series-RLC resonance, quality factor, bandwidth, and approximate half-power frequencies.
Access: Free to use, no installation, and No account required.
Inputs
This uses the ideal series-RLC relationships. Component ESR, inductor winding loss, parasitics, frequency-dependent losses, and source/load impedance can materially change real resonance.
Results
Resonance formulas
Ideal resonance occurs at ω0 = 1/√(LC) and f0 = ω0/(2π). For the series model, Q = ω0L/R and bandwidth is approximated by BW = f0/Q.
Use the workbench for context
The AC Circuits Workbench adds impedance, phase, filters, power-factor behavior, transformers, and related AC analysis.
Engineering reference
RLC Resonant Frequency Calculator: background and worked detail
Use the RLC Resonant Frequency Calculator to estimate ideal series-RLC resonance, angular frequency, quality factor, bandwidth, and approximate half-power frequencies from resistance, inductance, and capacitance.
Resonance in LC and RLC networks
At ideal series resonance, inductive and capacitive reactances have equal magnitude and opposite sign, leaving the series resistance as the net impedance. The LC product determines the resonance frequency, while resistance controls damping and Q.
Real resonators include inductor winding resistance, capacitor ESR, parasitics, self-resonance, source/load impedance, frequency-dependent losses, and component tolerances.
Equations used by this calculator
Resonant frequency
f₀ = 1/(2π√(LC))
Angular frequency converted to hertz.
Series quality factor
Q = ω₀L/R
For the idealized series RLC model, lower series resistance produces higher Q.
Reference cases
LC scaling
Case: Multiply L by 4 while holding C fixed.
Expected: Resonant frequency should halve.
Resistance change
Case: Double R while holding L and C fixed.
Expected: Resonant frequency should stay the same while series Q approximately halves.
10 Ω, 10 mH, 1 µF series RLC
Use R = 10 Ω, L = 10 mH, and C = 1 µF.
- ω₀ = 10,000 rad/s.
- f₀ ≈ 1.592 kHz.
- Q = 10 and the approximate bandwidth is about 159 Hz.
Result: The calculation provides a compact ideal reference before parasitic and loaded-Q effects are added.
Assumptions and model boundaries
Assumptions
- A lumped series RLC circuit.
- L and C are frequency-independent ideal components.
- Q and bandwidth use the series-resonator approximation implemented by the workbench engine.
Limitations
- Does not model component self-resonance, ESR/ESL, source/load loading, skin effect, radiation, or distributed transmission-line behavior.
- Half-power estimates become less representative when the simple series-RLC model is not dominant.
RLC Resonant Frequency Calculator FAQ
Does resistance change the ideal resonant frequency?
In this calculator's ideal series-RLC resonance expression, f₀ depends on L and C. Resistance primarily changes Q and bandwidth.
What does a higher Q mean?
Higher Q corresponds to a narrower, more weakly damped resonance in the ideal series model.
Can I use this for RF resonators?
Only as a first-order lumped estimate. At RF, parasitics and distributed effects often require a higher-fidelity model or measurement.
Where this calculation comes from
Shared with the AC Circuits Workbench, which adds Q factor, bandwidth, and impedance sweeps.
Open the source workbench →Read calculation and source methodology →