Filter Q Factor Calculator

Compute Q from center frequency and bandwidth, or from damping ratio (ζ). Includes Show Work and share links.

How to Use

  1. Pick a mode: f0 & Bandwidth (most common) or Damping Ratio (ζ).
  2. Enter your values and units (Hz / kHz / MHz).
  3. Results calculate instantly (no uploads).
  4. Open Show Work to see the formulas and steps in base units.
Q
—
quality factor
ζ
—
damping ratio
BW
—
bandwidth
f0
—
center frequency
Mode
Tip: For band-pass and resonant 2nd-order filters, Q = f0 / BW is the go-to.
—
Inputs & Settings
Switch modes to calculate from bandwidth or damping ratio. Units are applied before math.
Use the filter’s resonant / center frequency.
For band-pass: BW is typically f2 − f1 at the -3 dB points.
If provided with f2, BW will be derived as f2 − f1.
If f1 and f2 are set, BW auto-derives (still no URL changes while typing).
Show Work (step-by-step)
—
Work is shown in base units (Hz for frequency) for clarity and consistency.

Formulas

Quality factor (Q) describes how “narrow” a resonant peak is (higher Q = narrower bandwidth).

  • From center frequency and bandwidth: Q = f0 / BW
  • Bandwidth from cutoffs: BW = f2 − f1
  • From damping ratio (2nd-order): Q = 1 / (2ζ)
  • Estimated bandwidth (if f0 and Q known): BW = f0 / Q
Notes: “Bandwidth” is commonly the -3 dB bandwidth for band-pass filters, depending on your design context.

FAQ

What does a higher Q mean?

Higher Q typically means a narrower bandwidth around the center frequency and a more selective response.

What is ζ (damping ratio) used for?

ζ is a standard 2nd-order system parameter. For many 2nd-order filter forms, Q and ζ are directly related by Q = 1 / (2ζ).

My BW is zero or negative — what does that mean?

Bandwidth must be positive. If using f1 and f2, make sure f2 > f1. If BW is extremely small, Q becomes very large.

Tool Info

Last updated:

Updates may include additional modes, unit handling, and edge-case validation improvements.