LC Resonant Frequency Calculator NZ
This calculator finds the resonant frequency of an LC circuit, the frequency at which a circuit made of an inductor and a capacitor naturally oscillates. When an inductor and capacitor are connected together, energy sloshes back and forth between the magnetic field of the inductor and the electric field of the capacitor, oscillating at one special frequency, the resonant frequency. This resonance is the foundation of an enormous range of electronics: it is how radios and televisions tune to one station and reject the rest, how oscillators generate clean signals, how wireless and RF circuits select frequencies, and how metal detectors and induction systems work. The resonant frequency depends only on the inductance and the capacitance, in a simple and elegant relationship. This tool computes it. You enter the inductance in henries and the capacitance in farads, using scientific notation for the typically small values, and the calculator returns the resonant frequency, along with the angular frequency, the value in kilohertz for convenience, and the period of oscillation. The results update as you type, so you can size an inductor and capacitor to resonate at a target frequency. Use it for radio and RF design, for building oscillators and tuned filters, or for electronics study. The formula is the resonant frequency equals one over two pi times the square root of the inductance times the capacitance. A key insight it reveals is the inverse square-root relationship: to double the resonant frequency you must reduce the product of inductance and capacitance to a quarter, which is why tuning a radio across its band requires a sizeable change in one component, usually a variable capacitor. At resonance the circuit responds most strongly to that frequency, which is exactly what makes tuning possible.
Resonant frequency = 1 / (2 pi x square root of (L x C)). Use scientific notation for small values (e.g. 1e-3 H, 1e-6 F). Rounded for display.
How it works
At resonance the inductive and capacitive reactances are equal and cancel, leaving the circuit free to oscillate. The resonant frequency is one over two pi times the square root of the inductance times the capacitance. The angular frequency is two pi times that, and the period of oscillation is its reciprocal.
Worked example
An LC circuit with a 1 millihenry inductor and a 1 microfarad capacitor resonates at one over two pi times the square root of 0.001 times 0.000001. That square root is about 0.0000316, so the resonant frequency is about 5,032.92 hertz, or roughly 5.03 kilohertz, with a period of about 0.0001987 seconds.
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