# Frequency Bandwidth Calculator

URL: https://speedycalculator.com/calculators/physics/frequency-bandwidth/
Last updated: 2026-10-30

> The frequency bandwidth calculator finds the −3 dB bandwidth and the lower and upper cutoff frequencies of a resonant circuit or band-pass filter from its centre frequency and quality factor.

## Inputs

- Centre frequency f₀ (MHz, kHz, GHz, Hz)
- Quality factor Q

## Results

- Bandwidth
- Lower cutoff frequency
- Upper cutoff frequency

## Formula

```
BW = f₀/Q,  f₁,₂ = f₀·(√(1 + 1/(4Q²)) ∓ 1/(2Q))
```

## Explanation

A resonant circuit responds strongly only near its centre frequency. The higher its quality factor Q, the narrower the band – radio receivers use high-Q circuits to pick out one station.

### How to use the Frequency Bandwidth Calculator

- **Centre frequency f₀**
- **Quality factor Q**

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

### How it works

Enter the centre (resonant) frequency and the quality factor.

### Inputs explained

FieldWhat to enterCentre frequency f₀Units: MHz, kHz, GHz, HzQuality factor QA number

### What each result means

- **Bandwidth** = [Centre frequency f₀]÷[Quality factor Q]
- **Lower cutoff frequency** = [Centre frequency f₀]×(sqrt(1 + 1÷(4×[Quality factor Q]^2)) - 1÷(2×[Quality factor Q]))
- **Upper cutoff frequency** = [Centre frequency f₀]×(sqrt(1 + 1÷(4×[Quality factor Q]^2)) + 1÷(2×[Quality factor Q]))

### Example values

How the main result changes when **Centre frequency f₀** changes and everything else stays at the example values above:

Centre frequency f₀ (MHz)Bandwidth (kHz)5.351078.02160.510.721413.38267.516.0532121.4428

## Worked example

Inputs — Centre frequency f₀: 10.7 MHz; Quality factor Q: 50.

Results — **Bandwidth = 214 kHz**; Lower cutoff frequency = 10.593535 MHz; Upper cutoff frequency = 10.807535 MHz.

## Key terms

- **Quality factor**: f₀ divided by bandwidth.

## FAQ

**What does Q measure?**
How sharply a circuit resonates – centre frequency divided by bandwidth.

**Are the cutoffs symmetric?**
Geometrically: f₁·f₂ = f₀².

**What is a typical Q?**
10–100 for LC circuits, thousands for quartz crystals.

**What does −3 dB mean?**
Half-power points.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)