RLC Resonant Frequency Calculator

Resonant frequency, Q-factor, bandwidth and impedance curve of a series RLC / LC tank.

What it does

At resonance the inductor’s and capacitor’s reactances cancel. In a series RLC circuit the impedance drops to just R and the current peaks. Q-factor and bandwidth tell you how sharp that peak is.

Where it's used

Tuned circuits, band-pass and notch filters, radio tuning and wireless-charging coils.

How to use it

Enter L and C — prefixes help: 100u, 1n.
Enter the total series resistance.
Read f₀, Q and bandwidth, and look at the impedance curve.

The formula explained

f₀: 1 / (2π√(LC)) — resonant frequency
Q: (1/R)·√(L/C) — sharpness of the peak
BW: f₀ / Q — width between the −3 dB points
|Z|: impedance magnitude at any frequency

Worked example

A 100 µH coil with a 1 nF capacitor and 5 Ω of loss.

Inputs:

Inductance L: 100u H
Capacitance C: 1n F
Series resistance R: 5 Ω

The calculator gives:

Resonant frequency f₀: 503.3 kHz
Angular frequency ω₀: 3.162 Mrad/s
Period: 1.987 µs

Tips and common mistakes

Lower resistance gives a higher Q and a narrower peak.
Include the coil’s DC resistance and the capacitor’s ESR in R.
At resonance the voltage across L or C can be Q times the input — check component ratings.

Questions people ask

What is the formula for the resonant frequency?

f₀ = 1 / (2π √(L × C)). 100 µH with 1 nF resonates at about 503 kHz. Making L or C four times bigger halves the frequency.

How are Q and bandwidth found?

For a series circuit Q = (1 / R) × √(L / C) and the bandwidth is f₀ / Q. With 5 Ω of loss the example has Q ≈ 63 and a bandwidth of about 8 kHz.

Where are series resonant circuits used?

In radio tuning and filters, in resonant wireless chargers, and in tests that need a high voltage from a small input — at resonance the voltage across L or C is Q times the input.

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Enter your values to get the result with the formula, substituted values and an explanation of each step.

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