LC Resonant Frequency Calculator
Enter L and C with units and instantly get an LC tank's natural resonant frequency f₀ = 1 / (2π · √(L · C)), plus its period T and angular frequency ω. Useful for tuning radio receivers, designing AM/FM front ends, oscillators, filters and EMI suppression networks.
Please enter a valid number
Resonant frequency f₀
159.155 kHz
f₀ = 1 / (2π · √(L · C))
Period T
6.283 µs
T = 1 / f₀
Angular frequency ω
1.000 Mrad/s
ω = 2π · f₀ = 1 / √(L · C)
Summary
Result assumes an ideal lossless LC tank; real-world Q and component tolerances shift the measured frequency slightly. The same expression covers series and parallel LC resonance to first order.
Formula
f₀ = 1 / (2π · √(L · C)) T = 1 / f₀ ω = 2π · f₀ = 1 / √(L · C)
- · Plug L in henries (H) and C in farads (F). The tool accepts H / mH / µH / nH and F / mF / µF / nF / pF and converts internally to SI before calculating.
- · f₀ ∝ 1 / √(LC), so multiplying either L or C by 4 halves the resonant frequency. That is why radio receivers tune with a variable capacitor and high-power transmitters often sweep with a roller inductor.
- · An ideal series LC has minimum impedance (near 0 Ω) at resonance — used as a band-pass element. An ideal parallel LC tank has maximum impedance at resonance — used to select a band or block EMI on a power line. Both topologies share the same f₀.
- · Real components have ESR and finite quality factor Q, lowering the measured frequency by roughly 1 / √(1 − 1/(4Q²)). Discrete inductors are typically Q ≈ 30–100; ceramic capacitors hundreds to thousands.
- · At high frequencies a capacitor's ESL and an inductor's EPC introduce a self-resonant frequency (SRF) of the part itself. Above the SRF the part flips reactance type, so an LC calculation is only accurate well below either part's SRF.
- · References: Sedra & Smith "Microelectronic Circuits" §17.5; Horowitz & Hill "The Art of Electronics" 3rd ed. §1.7.16; ARRL Handbook (LC tank).
Frequently asked
Is the resonant frequency of a series LC the same as a parallel LC?
Identical: f₀ = 1 / (2π · √(L · C)) for both. The two topologies differ in impedance behaviour. A series LC has minimum impedance (zero in the ideal case) at resonance, so it short-circuits the f₀ signal. A parallel LC ("tank") has maximum impedance (infinite in the ideal case) at resonance, so it open-circuits the f₀ signal. Pick by what you want — pass f₀ or block everything else. Real-world resistance makes both impedances finite and shifts the resonant peak slightly downward.
My measured LC resonant frequency is lower than the formula. Did I do something wrong?
Usually nothing wrong — common reasons: (1) part tolerance: ordinary inductors are ±10 % and electrolytic caps ±20 %, easily explaining 5–10 % drift; (2) stray capacitance from PCB traces, probes and the chassis adds several pF that matter at RF; (3) finite Q lowers the resonant peak by about 1/(8Q²); (4) the inductor's effective L drops at higher frequencies as core losses kick in; (5) the scope probe's input capacitance (typically 10–20 pF) loads the tank. Verify the actual L and C with an LCR meter or vector network analyser, then re-compute.
How do I split a target frequency between L and C?
Many L/C combinations give the same f₀, but three things constrain the choice: (1) impedance level — at resonance |X_L| = |X_C| = √(L/C); high impedance (large L, small C) suits high-impedance loads, low impedance (small L, large C) matches low-Z antennas or carries higher currents; (2) part availability — at RF prefer big caps + small inductors, at audio reverse it; (3) Q — high Q typically comes from C0G/NP0 ceramic caps paired with air-core or powdered-iron inductors. Rules of thumb: FM range (~100 MHz) use 100 nH + 25 pF; AM range (~1 MHz) 250 µH + 100 pF; audio filter (~1 kHz) 1 H + 25 µF.
What are the everyday uses of LC resonant circuits?
Nearly every radio relies on LC resonance: an AM/FM tuning knob rotates a variable cap so the LC tank lands on your chosen station; 2.4 GHz Wi-Fi and Bluetooth antenna-matching networks use LC to hit 50 Ω; oscillators (e.g. crystal + parallel LC) generate stable clocks; EMI filters use LC to block noise bands; Qi wireless charging transfers power at a 100–200 kHz LC resonance; metal detectors sense an LC tank's frequency drifting as metal approaches; the RF coils inside an MRI scanner are essentially very-high-Q LC tanks.
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