RLC Resonant Frequency Calculator

The ideal resonant angular frequency for an LC network is: ω₀ = 1 / √(L·C). The resonant frequency in hertz is: f₀ = ω₀ / (2π).

If resistance is provided, this calculator also estimates damping and a damped frequency ω_d = √(ω₀² − α²) for underdamped cases. For a series RLC model, α = R / (2L). For a parallel RLC model, α = 1 / (2RC).

Quality factor and bandwidth are estimated as: Series: Q = ω₀L/R, BW = R/(2πL). Parallel: Q = R√(C/L), BW = 1/(2πRC).

1. Choose series or parallel RLC to match your circuit.
2. Enter inductance L and select its unit.
3. Enter capacitance C and select its unit.
4. Optionally enter resistance R to estimate losses.
5. Click Calculate Resonance to view results above.
6. Use Download CSV or Download PDF for reporting.

Resonance as an energy exchange

Resonance occurs when the inductor and capacitor swap stored energy, creating a strong response at one frequency. Inductive and capacitive reactance cancel, leaving resistance to limit amplitude. Tuned filters, receivers, and oscillators rely on this cancellation.

Ideal resonant frequency equation

The ideal LC resonance is set by f₀ = 1 / (2π√(LC)). Use L in henries and C in farads. L = 10 mH and C = 0.1 µF gives about 5,033 Hz, matching the example table.

Component ranges and frequency bands

Practical designs span wide ranges: power converters may use 10–200 µH with 10–470 nF, often landing in 10–200 kHz. RF tanks might use 50–200 nH with 2–20 pF, producing tens to hundreds of MHz. Ceramic capacitors can vary with bias and temperature. Treat results as nominal targets before final tuning.

Series RLC behavior in real circuits

A series RLC has minimum impedance near resonance, so current peaks when Q is high. With resistance R, Q = ω₀L/R. If L = 1 mH, C = 10 nF, and R = 2 Ω, Q is about 50 and the resonance becomes narrow. Higher R increases damping and can suppress oscillation.

Parallel RLC behavior and impedance peak

A parallel RLC tank shows maximum impedance near resonance, useful for band‑stop sections and oscillators. With R across L and C, Q = R√(C/L) indicates how strongly the tank rejects off‑frequency signals. Higher R and lower losses raise the impedance peak.

Quality factor and selectivity

Q measures selectivity: higher Q means less damping, larger peaks, and longer ringing after a disturbance. In audio filters, Q values of 0.7–10 are common, while RF resonators can exceed 100. Use Q to judge whether ESR, copper loss, or loading is acceptable.

Bandwidth and half‑power points

Bandwidth links to Q through BW ≈ f₀/Q. A 50 kHz resonance with Q = 25 has a bandwidth near 2 kHz, so detuning matters. Designers often reference the −3 dB (half‑power) points around resonance.

Design checks, tolerances, and measurement

Real parts include tolerance and parasitics: many inductors are ±10% and capacitors are ±5% to ±20%, so f₀ can shift. ESR and winding resistance reduce Q, especially at higher frequency, and layout adds stray capacitance. Check inductor self‑resonant frequency for RF work. Validate with an LCR meter or network analyzer and trim L or C if needed.

1) What is the resonant frequency of an RLC circuit?

It is the frequency where inductive and capacitive reactance cancel. The circuit response peaks (or impedance dips/rises) and the behavior is dominated by losses represented by resistance.

2) Does resistance change the ideal resonant frequency?

Resistance does not change the ideal LC formula, but it changes damping and may reduce the oscillation frequency in underdamped cases. High losses can eliminate oscillations entirely.

3) Why does the calculator ask for series or parallel type?

Series and parallel models use different loss relationships. Q, bandwidth, and damping depend on how resistance appears in the circuit, even though the ideal f₀ still comes from L and C.

4) What is a good Q value?

It depends on purpose. Broad filters may use Q below 1 to a few, while narrowband filters and resonators often use Q from 10 to 100+. Higher Q usually means lower loss and tighter tuning.

5) How do I convert units correctly?

Enter the numeric value and choose the unit dropdown. The calculator converts internally to henries and farads before applying formulas, reducing mistakes when using mH, µH, nF, or pF.

6) What does bandwidth mean here?

Bandwidth is an estimate of how wide the resonance is. For many designs, BW ≈ f₀/Q. Smaller bandwidth means stronger selectivity but greater sensitivity to component drift.

7) Why are my measured results different from the calculation?

Parasitic capacitance, inductor self‑capacitance, ESR, and component tolerances shift resonance and reduce Q. Layout and measurement setup also matter. Use the calculator as a baseline, then tune with real measurements.