Last updated: 2026-06-15

LC resonant frequency

An inductor and a capacitor connected together form a resonant circuit, often called a tank circuit. Energy oscillates between the inductor's magnetic field and the capacitor's electric field at a single natural frequency, the resonant frequency:

Here $L$ is the inductance in henries and $C$ the capacitance in farads. This calculator solves for the frequency, the inductance or the capacitance.

What happens at resonance

At the resonant frequency the inductive reactance $X_L = 2\pi f L$ and the capacitive reactance $X_C = 1/(2\pi f C)$ are equal and cancel. A series LC circuit then has minimum impedance and passes the resonant frequency most easily; a parallel LC circuit has maximum impedance and rejects it. Either way the circuit responds most strongly at one frequency, which is what makes LC circuits useful for tuning and filtering.

Formula

Because the frequency depends on the square root of the product $L\,C$, quadrupling either component halves the frequency.

Worked example

A radio tuning stage uses a $100\ \mu\text{H}$ coil and a $100\ \text{pF}$ capacitor:

That falls in the AM broadcast band. Replacing the fixed capacitor with a variable one sweeps the resonant frequency across the band, which is exactly how an analogue radio is tuned.

Where LC resonance is used

Tuned LC circuits set the operating frequency of radio receivers and transmitters, oscillators, and band-pass or band-stop filters. The same idea appears in wireless charging, metal detectors and the clock circuits of older electronics. Whenever a circuit needs to pick out or generate one frequency, an LC pair is a natural choice.

Limitations

The formula describes an ideal, lossless LC circuit. Real inductors and capacitors have resistance, which damps the oscillation and slightly lowers the peak frequency. The sharpness of the resonance is captured by the quality factor $Q$; a higher $Q$ means a narrower, taller response. For a precise design, the parasitic resistance and the $Q$ of the components must be taken into account.