# RLC Circuit Calculator

URL: https://speedycalculator.com/calculators/physics/rlc-circuit/
Last updated: 2026-10-30

> The RLC circuit calculator finds the resonant frequency, quality factor, bandwidth and damping of a series or parallel RLC circuit.

## Inputs

- Circuit
- Resistance R (Ω, kΩ, MΩ, mΩ)
- Inductance L (mH, µH, nH, H)
- Capacitance C (nF, µF, pF, mF, F)

## Results

- Resonant frequency f₀
- Quality factor Q
- Bandwidth
- Damping ratio ζ
- Response

## Formula

```
f₀ = 1/(2π√(LC)) · Series: Q = (1/R)·√(L/C) · Parallel: Q = R·√(C/L) · BW = f₀/Q
```

## Explanation

Adding resistance to an LC circuit damps its oscillations. The quality factor Q measures how sharp the resonance is: high-Q circuits pick out a narrow band of frequencies, low-Q circuits respond broadly.

### How to use the RLC Circuit Calculator

- **Circuit**
- **Resistance R**
- **Inductance L**
- **Capacitance C**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose series or parallel and enter R, L and C.

### Inputs explained

FieldWhat to enterCircuitChoose one: Series RLC, Parallel RLCResistance RUnits: Ω, kΩ, MΩ, mΩInductance LUnits: mH, µH, nH, HCapacitance CUnits: nF, µF, pF, mF, F

### What each result means

- **Resonant frequency f₀** = 1÷(2×pi×sqrt([Inductance L]×[Capacitance C]))
- **Bandwidth** = 1÷(2×pi×sqrt([Inductance L]×[Capacitance C]))÷[Quality factor Q]
- **Damping ratio ζ** = 1÷(2×[Quality factor Q])

### Example values

How the main result changes when **Resistance R** changes and everything else stays at the example values above:

Resistance R (Ω)Resonant frequency f₀ (Hz)515,915.49437.515,915.49431015,915.494312.515,915.49431515,915.49432015,915.4943

## Worked example

Inputs — Circuit: Series RLC; Resistance R: 10 Ω; Inductance L: 1 mH; Capacitance C: 100 nF.

Results — **Resonant frequency f₀ = 15,915.49431 Hz**; Quality factor Q = 10; Bandwidth = 1,591.54943 Hz; Damping ratio ζ = 0.05; Response = Underdamped (rings).

## Key terms

- **Damping ratio**: ζ = 1/(2Q).

## FAQ

**What is the Q factor?**
Resonant frequency divided by bandwidth.

**Why does Q differ between series and parallel?**
Resistance damps them in opposite ways.

**What happens with very low Q?**
The circuit no longer oscillates (overdamped).

**Where are RLC circuits used?**
Filters, tuners, oscillators and impedance matching.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)