🔌 LC Resonance Calculator

An inductor and capacitor in parallel (or series) form an LC tank circuit — the resonator at the heart of every radio, oscillator and filter. The circuit stores energy alternately in the magnetic field of the inductor and the electric field of the capacitor, swapping back and forth at a natural frequency given by f₀ = 1/(2π√(LC)). At that frequency the reactances cancel and the impedance peaks (parallel) or dips to a minimum (series).

The magic of the LC tank is that it rings: tap it with one pulse and it oscillates on its own while the stored energy slowly decays. Tune the capacitor (or the inductor) and the resonant frequency moves — which is exactly how an old radio dial selects a station out of the hundreds arriving at the antenna.

The calculator converts inductance (nH, µH, mH, H) and capacitance (pF, nF, µF, mF, F) to base units, then applies f₀ = 1/(2π√(LC)). It also derives the characteristic impedance Z₀ = √(L/C), which for filters tells you the impedance level the resonator presents, and the quality factor Q = Z₀/R when a series loss resistance is supplied.

The derived period (1/f₀) is handy when timing oscillator behaviour in a simulation, and the Q factor tells you how sharp the resonance is — a high-Q tank selects a narrow band, which is what you want in a tuner. For the reactive behaviour on either side of resonance, see the reactance calculator.

1. Enter the inductance and choose its unit (nH, µH, mH, H).
2. Enter the capacitance and choose its unit (pF, nF, µF, mF, F).
3. Optionally enter a series loss resistance to get the Q factor.
4. Click Calculate to see the resonant frequency in Hz, kHz and MHz.
5. Use the characteristic impedance output when designing filter matching.

Why does the resonant frequency depend on the product LC?

The stored energy swaps between the magnetic field of L and the electric field of C, and the exchange rate depends on both together. Doubling either L or C lowers the frequency by √2; the formula f = 1/(2π√(LC)) captures this symmetric dependence.

What is the difference between series and parallel resonance?

In a series tank the impedance is minimum at resonance (the reactances cancel, leaving R), so it passes its own frequency. In a parallel tank the impedance is maximum at resonance, so it blocks its own frequency. Both resonate at the same f₀ when L and C are ideal.

How do I pick L and C for a target frequency?

Choose a reasonable C first — for RF circuits tens of pF, for audio microfarads — then solve L = 1/((2πf)²C). The calculator works both directions if you rearrange: try values and iterate until the readout matches your target.

What sets the bandwidth of a tuned circuit?

The loaded Q: bandwidth = f₀/Q. Higher Q means a narrower, sharper resonance. Q is lowered by inductor resistance, capacitor losses, and especially by the load you couple to the tank — a heavily loaded tank can lose most of its selectivity.

Why do real circuits tune slightly lower than calculated?

Stray capacitance (wiring, the inductor's own inter-turn capacitance, PCB traces) adds to C, and parasitic inductance adds to L. Both lower f₀. Designers leave room for trimmer capacitors precisely because of this.

Can a tank circuit oscillate by itself?

Only with an amplifier. A pure LC tank is a resonator — tap it and it rings down. In an oscillator, a transistor or op-amp adds just enough energy each cycle to replace the losses, and the tank sets the frequency.

Watch the units — nH × pF gives a very different result from mH × µF; the calculator handles them, but always double-check your decimal point when typing. Real inductors have series resistance, which limits Q; a typical small inductor has Q between 20 and 100, enough for a usable oscillator but not for a precision filter. Parasitic capacitance in the inductor and stray capacitance of the wiring always lower the real resonant frequency below the calculated value — measure and trim. In a parallel tank the impedance peaks at resonance, so it blocks its own frequency and passes everything else; a series tank does the opposite. If you are designing a filter, remember the tank only fixes the centre frequency; the bandwidth is set by Q, and Q depends on the loading you attach to the circuit.