# RLC Circuit Calculator

Created by Luciano Mino
Last updated: Jun 25, 2022

With the RLC circuit calculator, you can solve any RLC series circuit given its resistance (R), inductance (L), and capacitance (C).

• Solve any series RLC circuit problems easily;
• Calculate the resonant frequency of an RLC circuit and its bandwidth;
• Obtain the Q-factor of the RLC circuit; and
• Find the damping ratio of an RLC circuit.

All of that without using an RLC circuit formula sheet!

## Calculating the resonant frequency of an RLC circuit

An RLC circuit has three parts:

• A ($R$);
• An inductor (with inductance $L$); and
• A capacitor (with capacitance $C$).

This tool will cover only the simplest configuration: a series RLC circuit.

The resonant frequency of an RLC circuit is the frequency at which the system oscillates with minimum impedance.

At this frequency, the inductance and capacitance are equal, and the system current will be at its maximum.

The formula for resonant frequency $f_{0}$ is:

$f_{0} = \frac{1}{2\pi\sqrt{LC}}$

The RLC circuit calculator will automatically find this resonant frequency for you and more!

## Q-factor of an RLC circuit

The RLC circuit calculator can easily find the Q-factor, but what is it?

The Quality Factor, or Q-factor, gives information about the damping in an oscillating system. We can find the Q-factor of an RLC circuit with the following formula:

$Q = \frac{1}{R}\sqrt{\frac{L}{C}}$

Increasing the Q-factor is desirable in many applications since it will indicate that the losses within this system are low.

## Damping ratio of an RLC circuit

The damping ratio (ζ) in an RLC circuit describes how the oscillations decay.

Since it is related to losses, we can expect the resistance $R$ to appear in its formula:

$ζ = \frac{R}{2}\sqrt{\frac{C}{L}}$

According to this value, the system will be:

• Overdamped if $ζ > 1$;
• Underdamped if $ζ < 1$; or
• Critically damped if $ζ = 1$.

## Example with the RLC circuit calculator

Suppose we have a system with the following parameters:

• R= 30 Ω;
• L = 10 mH; and
• C = 100 μF.

We can use each of these parameters separately in each equation to find the resonant frequency, the Q-factor, and the damping ratio.

Or we can input them within the RLC circuit calculator all at once and quickly get what we need without relying on an RLC circuit formula sheet.

After typing in the values, the calculator outputs:

• f₀ = 159.15 Hz;
• Q-factor = 0.3333; and
• ζ = 1.5.

Which you can check using the respective equations!

Luciano Mino
Capacitance
F
Inductance
H
Resistance
Ω
Frequency
Hz
Q factor
Bandwidth (FWHM)
Hz
Damping ratio (ζ)
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