LC Resonant Frequency Calculator | f=1/(2π√LC)
Calculate the resonant frequency of an LC circuit (f=1/(2π√LC)). Enter inductance L and capacitance C, or solve for L or C from a known frequency.
How to Use
- To calculate resonant frequency: enter the inductance (L) and capacitance (C) values with units.
- To calculate capacitance from frequency: enter the frequency and inductance.
- To calculate inductance from frequency: enter the frequency and capacitance.
- Click the appropriate 'Calculate' button for your chosen mode.
- Results include the resonant frequency, angular frequency ω = 2πf, and equivalent wavelength.
- Use this to design tank circuits, RF filters, and oscillators.
About LC Resonance
LC Resonance Formula
The resonant frequency of an LC circuit is f = 1/(2π√(LC)), where L is in Henries and C is in Farads. At this frequency, the inductive reactance XL = 2πfL equals the capacitive reactance XC = 1/(2πfC), and they cancel each other out. The result is purely resistive impedance (the series resistance of real components). This cancellation is the essence of resonance.
Series vs. Parallel Resonance
In a series LC circuit at resonance, impedance is minimum (ideally zero for ideal components), causing maximum current. In a parallel (tank) LC circuit at resonance, impedance is maximum, causing minimum current from the source. Series resonance is used in bandpass filters and series-tuned circuits; parallel resonance forms tank circuits in oscillators, RF amplifiers, and impedance matching networks.
Quality Factor (Q)
The quality factor Q = (1/R)√(L/C) describes the sharpness of the resonance peak. A high Q means a narrow, tall resonance peak (sharp tuning), while a low Q gives a broader, flatter response. Practical LC circuits always have some resistance (wire resistance, core losses), which limits Q. RF tank circuits may have Q values of 50–300, while quartz crystals achieve Q values of 10,000 to 100,000.
Energy Oscillation in LC Circuits
At resonance, energy oscillates between the inductor's magnetic field and the capacitor's electric field. When the capacitor is fully charged, the inductor current is zero. As the capacitor discharges through the inductor, current builds up and the magnetic field stores energy. This continues sinusoidally at the resonant frequency. In an ideal (lossless) circuit, this oscillation continues forever, forming the basis of electronic oscillators.
Key Features
- Calculates resonant frequency from L and C using f=1/(2π√LC)
- Solves for L or C from a known frequency
- Shows angular frequency ω and equivalent wavelength
- Supports nH to H and pF to µF input ranges
Common Applications
- Designing tank circuits for RF oscillators
- Tuning LC bandpass and band-stop filters
- Matching impedances in RF power amplifiers
- Designing crystal-replacement resonators
- Educational demonstration of resonance principles