LC Resonance Frequency Calculator
Compute the resonance frequency f = 1/(2π√(LC)) of an LC circuit. Useful for radio, filters and oscillators. Everything in your browser.
f = 1 / (2π√(LC))
LC resonant frequency: formula and tuning
An LC oscillator — an inductor (L) connected to a capacitor (C) — resonates at f = 1 / (2π · √(L · C)), with L in henries (H), C in farads (F) and f in hertz (Hz). At resonance the capacitive reactance equals the inductive reactance (XC = XL): in a series LC the current peaks, in a parallel LC the current drops to a minimum. The quality factor Q describes how sharp the resonance is — higher Q means a narrower passband. Heinrich Hertz used a resonant LC circuit in 1887 to confirm Maxwell's electromagnetic waves, opening the door to radio. Example: L = 1 mH, C = 100 nF → f = 1 / (2π · √(10-3 · 10-7)) ≈ 15.9 kHz (audio range). For tuning AM radio at 1 MHz, the LC product must be around 25 µH·nF.
Applications: radio, filters and beyond
LC resonance powers AM/FM radio tuning, RF filters (band-pass, band-stop), clock generation in oscillators, and antenna design (quarter-wave antennas have length λ/4 = c / (4f)). It also appears in MRI (proton precession frequency in a magnetic field) and in acoustic instruments by analogy — strings and tubes resonate at frequencies determined by length and tension, much like LC circuits do with L and C.
FAQ
What is the difference between series and parallel LC? In series, impedance is minimum at resonance (maximum current). In parallel, impedance is maximum (minimum current) — a parallel LC is called a tank circuit.
Why is resistance not in the formula? The ideal LC formula assumes no losses. Real circuits have resistance that lowers Q and slightly shifts the peak, but resonance frequency is dominated by L and C.
How do I tune to a specific frequency? Pick L, then solve C = 1 / ((2πf)² · L). For variable tuning, use a trimmer capacitor or a varicap diode.
What units should I use? SI: henries and farads give hertz. For practical values, 1 µH = 10-6 H, 1 nF = 10-9 F. With L in µH and C in nF, frequency in MHz: fMHz ≈ 159.2 / √(LµH · CnF).
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.