Resonant Frequency Calculator (LC)

An LC circuit, also called a resonant, tank, or tuned circuit, consists of an inductor (L) and a capacitor (C) connected together in series or parallel. It is an idealized circuit with zero resistance. Energy oscillates between the inductor's magnetic field and the capacitor's electric field at a specific natural frequency called the resonant frequency.

Resonant frequency is the natural frequency at which an LC circuit oscillates with the greatest amplitude. At this frequency, the inductive reactance (XL) and capacitive reactance (XC) are equal in magnitude and cancel each other out, resulting in minimum impedance in a series circuit or maximum impedance in a parallel circuit.

The resonant frequency formula is f = 1 / (2π × √(L × C)), where L is inductance in henries and C is capacitance in farads. The angular frequency is ω = 1 / √(L × C) in radians per second. Simply plug in your inductance and capacitance values to find the resonant frequency.

Using the formula f = 1 / (2π × √(L × C)): L = 0.001 H and C = 220 × 10⁻¹² F. So √(L × C) = √(2.2 × 10⁻¹³) ≈ 4.69 × 10⁻⁷. The resonant frequency f ≈ 1 / (2π × 4.69 × 10⁻⁷) ≈ 339.4 kHz.

Radios use LC circuits as tunable band-pass filters. By adjusting the capacitance (using a variable capacitor), the resonant frequency of the circuit changes to match a specific radio station's broadcast frequency. Only the signal at the resonant frequency passes through with significant amplitude, allowing the radio to isolate one station from all others.

In a series LC circuit, resonance results in minimum impedance (ideally zero), allowing maximum current to flow. In a parallel LC circuit (tank circuit), resonance results in maximum impedance, minimizing current from the source. Both configurations resonate at the same frequency f = 1 / (2π × √(L × C)).

LC resonant circuits are widely used in radio transmitters and receivers, oscillator circuits, notch filters, band-pass filters, impedance matching networks, induction heating systems, and wireless power transfer. Any application requiring signal selection or frequency generation can benefit from an LC resonant circuit.

The standard SI units are henries (H) for inductance and farads (F) for capacitance. In practice, inductors are often in the millihenry (mH) or microhenry (µH) range, while capacitors are commonly in the microfarad (µF), nanofarad (nF), or picofarad (pF) range. This calculator accepts all common unit prefixes and converts automatically.