LC Resonant Frequency Calculator
The resonant frequency of an LC circuit is the frequency at which the inductive reactance (XL = 2*pi*f*L) exactly equals the capacitive reactance (XC = 1/(2*pi*f*C)). At this frequency, the two reactive elements cancel and the circuit exhibits special properties: minimum impedance in series configuration, maximum impedance in parallel configuration. LC resonant circuits are the foundation of radio tuners, oscillators, bandpass filters, and impedance matching networks. Enter inductance in henries and capacitance in farads (use consistent units, e.g., 1 uH = 0.000001 H, 100 pF = 0.0000000001 F).
LC resonant frequency formula
f = 1 / (2 * pi * sqrt(L * C))
omega = 1 / sqrt(L * C) (angular frequency, rad/s)
Where L is inductance in henries and C is capacitance in farads. Example: L = 1 uH (0.000001 H), C = 100 pF (0.0000000001 F) gives f = 1 / (2*pi*sqrt(0.000001 * 0.0000000001)) = 15,915,494 Hz (about 15.9 MHz).
LC circuit applications
- AM radio tuning circuits use variable capacitors to adjust the resonant frequency across the AM band (530 to 1,700 kHz).
- Crystal oscillators replace the LC tank with a quartz crystal for much higher frequency stability.
- Switch-mode power supply output filters use LC circuits to smooth the switching waveform into DC, with the resonant frequency chosen below the switching frequency.
- Wireless power transfer (inductive charging) relies on resonant coupling between transmitter and receiver LC circuits at the same frequency.
Frequently asked questions
What is LC resonance?
At the resonant frequency, inductive reactance (XL) equals capacitive reactance (XC), and they cancel each other out. The circuit oscillates with maximum energy exchange between the inductor's magnetic field and the capacitor's electric field.
What is the resonant frequency formula?
f = 1 / (2 * pi * sqrt(L * C)), where L is inductance in henries and C is capacitance in farads. The result is in hertz. This is also called the natural frequency of the LC tank circuit.
What happens at resonance in a series LC circuit?
In a series LC circuit at resonance, impedance is at its minimum (ideally zero for ideal components). Current is at its maximum for a given voltage source. This is used in bandpass filters and radio tuning.
What happens at resonance in a parallel LC circuit?
In a parallel LC circuit (tank circuit) at resonance, impedance is at its maximum (ideally infinite). Current from the source is minimized. This is used in band-stop filters and oscillator circuits.
How do I tune a radio receiver to a station?
Variable capacitor or inductor tuning adjusts the resonant frequency of the LC tank circuit to match the carrier frequency of the desired radio station. At resonance, that station's signal is amplified while others are rejected.
Official sources
- NIST: NIST SP 811, Guide for SI Units.
- OpenStax University Physics: Resonance in an AC Circuit, Vol. 2 Ch. 15.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.