Filter Q ↔ bandwidth
Convert EQ Q to bandwidth in octaves, find the −3 dB edges, or the centre frequency from two edges.
Q ↔ bandwidth
octaves
Hz
Lower −3 dB edge
707.071 Hz
Upper −3 dB edge
1414.28 Hz
Bandwidth
707.214 Hz
Centre frequency from band edges
Hz
Hz
- Centre frequency (geometric mean)
- 999.849Hz
- Arithmetic mean (for comparison)
- 1060.5Hz
- Bandwidth
- 1octaves
- Q factor
- 1.41421
Audio bands are symmetric on a logarithmic scale, so the centre is the geometric mean, not the average.
How it works
Higher Q means a narrower filter. A one-octave band has Q ≈ 1.41, a third-octave band Q ≈ 4.32. Band edges are placed symmetrically on a logarithmic frequency axis.
Formulas
- Q = √(2^N) / (2^N − 1)
- N = 2 · asinh(1 / 2Q) / ln 2
- f₀ = √(f₁ · f₂)
- Q = f₀ / (f₂ − f₁)
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