MusicReasonProduction, Synthesis, and Audio Math
What Q corresponds to this bandwidth?
Enter a center frequency and an octave bandwidth or a Q value. This tool converts between them and shows the half-power frequencies the bandwidth implies.
Answer
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Understand
A wider octave bandwidth means a lower Q (a broader, gentler filter shape), while a narrower bandwidth means a higher Q (a sharper, more surgical shape). This is exact math relating the two representations; it does not describe any specific plug-in or hardware EQ's actual filter curve, which can differ in shape even at the same nominal Q.
Worked example
A one-octave bandwidth gives a Q of approximately 1.414. Converting that Q back to bandwidth returns the original one octave, within floating-point precision, since the two representations are exact inverses of each other.
Method and limitations
Q is sqrt(2^BW) / (2^BW − 1) for octave bandwidth BW. The inverse has no closed form and is solved here by numerical bisection to the same precision. Half-power frequencies are the center frequency divided and multiplied by 2^(BW/2).
Why some plug-ins show Q and others show octaves
Different EQ designers picked different conventions decades apart, and neither fully displaced the other: audio engineers who came up on analog outboard gear often think in octave bandwidth, while many digital plug-ins default to a bare Q number. Because the two are exact mathematical inverses of each other, this tool lets you move fluidly between whichever convention the gear or plug-in in front of you actually uses.