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RLC Resonant Frequency Calculator (f = 1/(2π√(LC)))

· Last updated：2026-07-21

Compute the LC (RLC series/parallel) resonant frequency: f₀ = 1/(2π·√(L·C)). Resonant frequency is identical for series and parallel RLC; R only affects Q and bandwidth. Solves for f₀, L, or C from the other two, and returns angular resonance ω₀ and characteristic impedance √(L/C). L in H/mH/µH, C in F/µF/nF/pF, f in Hz/kHz/MHz.

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Written by the Elysia Tools team
Math502
Angular Frequency3

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category
Math & Numbers
Input types
select, number
Output type
json
Sample coverage
4
API ready
Yes

Overview

The RLC Resonant Frequency Calculator uses f₀ = 1/(2π√(LC)) to calculate resonant frequency from inductance and capacitance, or solve for L or C when the other two values are known. It also returns angular resonance ω₀ and characteristic impedance √(L/C).

When to use

  • Find the resonant frequency of an LC or RLC series or parallel circuit.
  • Calculate the inductance needed for a target frequency and known capacitance.
  • Calculate the capacitance needed for a target frequency and known inductance.

How it works

  1. 1Choose whether to solve for frequency f₀, inductance L, or capacitance C.
  2. 2Enter the available values and select units for inductance, capacitance, and frequency.
  3. 3The calculator applies the resonance formula after converting the values to base units.
  4. 4Review the calculated result, angular resonance ω₀, and characteristic impedance.

Use cases

  • Tune RF and electronics circuits to a target frequency.
  • Select an inductor and capacitor pair for a tuned LC circuit.
  • Check component values used in filters and resonant networks.

Examples

1. Calculate resonant frequency from L and C

RF designer

Background

An RF designer is evaluating a tuned circuit with a 100 µH inductor and a 100 pF capacitor.

Problem

Determine the circuit's resonant frequency and characteristic impedance.

How to use

Select Frequency f₀, enter L = 100 µH and C = 100 pF, then set the frequency unit to MHz.

solveFor: frequency; L: 100 µH; C: 100 pF; decimalPlaces: 4

Outcome

The calculator returns f₀ ≈ 1.5915 MHz, ω₀ ≈ 10,000,000 rad/s, and characteristic impedance ≈ 1000 Ω.

2. Find inductance for a 1 MHz circuit

Electronics engineer

Background

An electronics engineer needs to design a resonant circuit at 1 MHz using a 100 pF capacitor.

Problem

Calculate the inductance required to reach the target frequency.

How to use

Select Inductance L, enter C = 100 pF and f = 1 MHz, then calculate.

FAQ

What formula does the calculator use?

It uses f₀ = 1/(2π√(L·C)).

Can I solve for inductance or capacitance?

Yes. Select Inductance L or Capacitance C and enter the other two required values.

Which units are supported?

Inductance supports H, mH, and µH; capacitance supports F, µF, nF, and pF; frequency supports Hz, kHz, and MHz.

Is resonant frequency different for series and parallel RLC circuits?

No. The calculator uses the same LC resonant-frequency formula for both.

What additional values are returned?

The result includes angular resonance ω₀ and characteristic impedance √(L/C).

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solveFor: inductance; C: 100 pF; f: 1 MHz; decimalPlaces: 4

Outcome

The required inductance is approximately 253.303 µH, with characteristic impedance of approximately 1591.5494 Ω.

3. Find capacitance for known L and frequency

Circuit designer

Background

A circuit designer has a 253.3029591 µH inductor and wants the circuit to resonate at 1 MHz.

Problem

Determine the matching capacitance value.

How to use

Select Capacitance C, enter L = 253.3029591 µH and f = 1 MHz, then calculate.

solveFor: capacitance; L: 253.3029591 µH; f: 1 MHz; decimalPlaces: 4

Outcome

The calculator returns a capacitance of approximately 100 pF and verifies the 1 MHz resonant frequency.