EQ bandwidth

The width behind the Q number.

Q expresses how narrow a band is relative to its center frequency. This conversion gives an equivalent octave width and the lower and upper half-power frequencies.

The formula

• $Q$ — center frequency / bandwidth in $\text{Hz}$
• $f_c$ — $f_c = \sqrt{f_{\text{low}} \cdot f_{\text{high}}}$
• $BW$ — $BW = f_{\text{high}} - f_{\text{low}}$ in $\text{Hz}$

Worth knowing

Q is independent of center frequency: the same Q spans the same number of octaves at 100 Hz or 10 kHz, but not the same number of hertz.

Assumptions

Uses a constant-Q band-pass half-power definition. Parametric equalizer bandwidth conventions can vary with gain, filter design and manufacturer. The plot shows a reference band-pass, not a boost/cut EQ.

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