LC Resonance Frequency Calculator

Calculator

Provide any two of \( f_0 \), \( L \), \( C \) — the third is solved. The angular resonant frequency \( \omega_0 \) is always shown as an additional output.

• Resonant frequency (f₀):
• Hz kHz MHz

• Inductance (L):
• H mH µH nH

• Capacitance (C):
• F mF µF nF pF

Provide any two of f₀, L, C to calculate.

Calculate

LC Resonant Frequency — Explanation

An LC circuit consists of an inductor \( L \) and a capacitor \( C \) connected together. At the resonant frequency, the energy oscillates between the electric field of the capacitor and the magnetic field of the inductor — this is also the frequency where capacitive reactance \( X_C \) equals inductive reactance \( X_L \) (see the capacitor impedance calculator to compute \( X_C \) at any frequency). The resonant frequency is: \[ f_0 = \frac{1}{2\pi\sqrt{LC}} \] Where:

• \( f_0 \) is the resonant frequency (in Hertz, \( \text{Hz} \)),
• \( L \) is the inductance (in Henrys, \( \text{H} \)),
• \( C \) is the capacitance (in Farads, \( \text{F} \)).

Purpose of the Calculator

Given any two of the three variables, the calculator solves for the third. The rearranged formulas are:

• To solve for \( f_0 \): \[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
• To solve for \( L \): \[ L = \frac{1}{(2\pi f_0)^2 \cdot C} \]
• To solve for \( C \): \[ C = \frac{1}{(2\pi f_0)^2 \cdot L} \]

If the required C is not a standard component value, combine capacitors to reach it using the capacitors in series or capacitors in parallel calculator.

Angular Resonant Frequency

The angular frequency \( \omega_0 \) is often more convenient in circuit analysis and filter design: \[ \omega_0 = 2\pi f_0 = \frac{1}{\sqrt{LC}} \] It is expressed in radians per second (rad/s). Many filter and impedance formulas use \( \omega_0 \) directly, avoiding the repeated \( 2\pi \) factor.

Applications

LC circuits are used as tuned filters, oscillators, and impedance matching networks. In radio receivers, a variable capacitor is tuned to set \( f_0 \) equal to the desired station frequency. In switching power supplies, the LC output filter is designed so that \( f_0 \) is well below the switching frequency, attenuating the ripple. In RF design, LC tanks set the operating frequency of oscillators and amplifiers.

Related Tools

• Capacitor Impedance Calculator — compute \( X_C \) at any frequency; at resonance \( X_C = X_L \).
• Capacitors in Series / Capacitors in Parallel — combine capacitors to reach a non-standard C for a target frequency.
• Inductor Impedance Calculator — compute \( X_L \) at any frequency; at resonance \( X_L = X_C \).
• Inductors in Series / Inductors in Parallel — combine inductors to reach a non-standard L for a target frequency.

More calculators: blog.hirnschall.net/tools/.