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RLC Resonance Calculator (fr)

Quick answer

This calculator computes resonant frequency fr = 1/(2 pi root(LC)) with Q factor and bandwidth.

  • Enter L, C, and R to see fr, the impedance peak or dip, and the -3 dB band edges.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How Does the RLC Resonance Calculator Work?

fr = 1 ÷ (2π√(LC))

At resonance inductive and capacitive reactance cancel: XL = XC leaves only R, so a series RLC dips to minimum impedance and a parallel tank peaks to maximum - the basis of every tuned filter. The calculator returns fr, Q = XL/R (series), and bandwidth BW = fr/Q. Example: L = 100 uH, C = 253 pF resonate at 1 MHz; with R = 5 ohm, Q = 125.7 and the -3 dB bandwidth is 8 kHz - a narrow, selective filter. Parallel tanks invert the behavior: impedance peaks at resonance instead of dipping, which is how the same LC pair selects one station in a radio while rejecting everything around it.

  1. 1

    Enter inductance

    L in uH, mH, or H.

  2. 2

    Enter capacitance

    C in pF, nF, or uF.

  3. 3

    Enter resistance

    R sets Q and bandwidth.

Use Cases

Tuning crystal-less radio front-ends and IF transformers

Designing induction heaters matched to work coils

Setting bandpass and notch filters in crossovers

Common Mistakes

  • Ignoring the voltage magnification at series resonance and arcing the capacitor

  • Using ideal L and C values while strays shift narrow high-Q tanks

  • Forgetting load resistance damps Q far below the calculated value

FAQs

What happens at resonance in a series RLC circuit?

Impedance drops to R alone: current peaks at I = V/R and voltages across L and C can each exceed the supply Q times - a 9 V source with Q 50 puts 450 V across the capacitor, a real insulation risk.

How do I widen a resonant filter's bandwidth?

Lower Q: add series resistance (or use parallel damping). BW = fr/Q, so a 1 MHz tank at Q 20 passes 50 kHz while Q 100 passes 10 kHz. Radio front-ends need high Q; audio crossovers need low.

Why does my measured resonance differ from calculation?

Stray capacitance of coils (5-20 pF), component tolerance, and load resistance all shift fr. A 10 percent capacitor tolerance moves resonance about 5 percent - measure and trim with a trimmer.

How do I design a simple bandpass filter?

Set fr to the center frequency and Q to the wanted width: BW = fr/Q. For a 7 MHz center and 200 kHz width, Q = 35; L and C then follow from fr = 1/(2 pi root(LC)) with any convenient split.

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