# [LC Resonance Frequency Calculator](https://blog.hirnschall.net/tools/lc-resonance-frequency/)

author: [Sebastian Hirnschall](https://blog.hirnschall.net/about/)

meta description: Calculate the resonant frequency of an LC circuit. Solve for frequency, inductance, or capacitance given the other two. Angular frequency shown as additional output.

meta title: LC Resonance Frequency Calculator — Solve for f, L, or C

date published: 01.04.2025 (DD.MM.YYYY format)
date last modified: 22.04.2025 (DD.MM.YYYY format)

---

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. 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 \( C \):
  \[
  C = \frac{1}{(2\pi f\_0)^2 \cdot L}
  \]

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.

More info
---------

Looking for more helpful tools and calculators? Explore a wide range of resources to simplify your engineering projects and calculations. Head over to our [tools section](https://blog.hirnschall.net/tools/) to find our free online calculators.  
For actual projects and informational articles head over to [blog.hirnschall.net](https://blog.hirnschall.net/).