LC Resonant Frequency Calculator

William Thomson (later Lord Kelvin) derived the formula f = 1 / (2π√LC) in 1853 while analyzing the oscillations of charge in a Leyden jar discharged through a coil — one of the earliest studied examples of a physical oscillator. Thomson's formula predicted the ringing discharge Joseph Henry had observed two decades earlier and is still often called "Thomson's formula" in European texts.

The practical impact came half a century later. When Heinrich Hertz generated and detected radio waves in 1888, both transmitter and receiver relied on resonant LC tanks. Guglielmo Marconi's early spark-gap radios (1895 onward) were shotgun-wide in bandwidth until resonant tuning was added around 1900 — allowing multiple stations to share the airwaves by transmitting and receiving on different LC resonant frequencies. Every radio receiver since has been a cascade of tuned resonant networks, and the same formula governs crystal oscillators, wireless charging pads, quartz watch timing elements, and MRI gradient coils.

Q-factor as a quantitative figure of merit was introduced by K. S. Johnson at Bell Labs in 1914 — he chose the letter Q arbitrarily (no, it does not stand for "quality"). High Q means a narrow, selective resonance; low Q means a broad, well-damped one. Air-core coils and vacuum capacitors push Q to the thousands; crystals and surface-acoustic-wave resonators reach tens of thousands; superconducting cavities in particle accelerators hit 10¹⁰.

Enter inductance L and capacitance C with engineering suffixes (nH, µH, mH, pF, nF, µF). The calculator returns the resonant frequency via Thomson's formula, the characteristic impedance Z₀ = √(L/C), and — if you supply a series resistance R — the quality factor Q and −3 dB bandwidth BW = f₀/Q.

Real resonators deviate from the ideal: wire DC resistance in the inductor, ESR in the capacitor, core loss, and radiation from open coils all add damping. Q below 10 is common for PCB inductors; Q of 100+ requires air-core or carefully chosen RF parts; Q above 1000 needs crystals or acoustic resonators. Everything runs client-side; no values leave your browser.