LC Resonant Frequency Calculator
Calculate the resonant frequency of an LC circuit from inductance and capacitance values, or find L or C needed for a target frequency.
What Is an LC Circuit? An LC circuit (also called a tank circuit or resonant circuit) consists of an inductor (L) and a capacitor (C) connected together. When given an initial charge, energy oscillates back and forth between the magnetic field of the inductor and the electric field of the capacitor — just like a mechanical pendulum swings energy between kinetic and potential forms.
The Resonance Formula At the resonant frequency f, the inductive reactance (XL = 2πfL) exactly equals the capacitive reactance (XC = 1/2πfC). Setting these equal and solving for f gives the fundamental formula: f = 1 / (2π√(LC)). The angular frequency ω = 2πf = 1/√(LC) radians per second.
Why Resonance Matters At resonance, the LC circuit presents either maximum impedance (parallel LC — used in band-pass filters) or minimum impedance (series LC — used in band-stop filters). This selectivity is what makes radio tuning possible. By varying the capacitance of a variable capacitor, the resonant frequency shifts to match a different radio station’s carrier frequency.
Radio Frequency Ranges AM radio broadcasts from 535 kHz to 1,705 kHz. FM radio uses 87.5 MHz to 108 MHz. These different bands require very different L and C values. An AM radio tuner might use 250 μH inductance with a variable capacitor ranging from 10–400 pF. An FM tuner requires much smaller components — a few nanohenries of inductance and picofarads of capacitance.
Crystal Oscillators For applications requiring extremely precise frequency stability — clocks, GPS receivers, microprocessors — quartz crystal oscillators replace the LC tank circuit. A quartz crystal acts like a very high-Q LC circuit with exceptional stability. The crystal in a typical computer runs at tens to hundreds of MHz and drifts only a few parts per million per year.
Wavelength Connection Every frequency corresponds to a wavelength: λ = c/f, where c is the speed of light (299,792,458 m/s). At 100 MHz (FM radio), the wavelength is about 3 meters. At 2.4 GHz (Wi-Fi), the wavelength is about 12.5 cm — which is why Wi-Fi antennas are measured in centimeters.