## EQ bandpass filter: Q factor and bandwidth

When using the bandpass (or peak) filters of a parametric equalizer, you might be asking what is exactly the effect of the quality factor Q. You have probably noticed that a high Q curve is narrow, a low Q curve is wider and that the bandwidth is not linearly related to Q.

Here are some bandwidths in octaves and the corresponding Q.

Q | N (bandwidth in octaves) |
---|---|

0.267 | 4 |

0.326 | 3.5 |

0.404 | 3 |

0.511 | 2.5 |

0.667 | 2 |

0.920 | 1.5 |

1.414 | 1 |

1.707 | 5/6 |

2.145 | 2/3 |

2.871 | 1/2 |

4.318 | 1/3 |

8.651 | 1/6 |

*N* = LOG(SQRT((((2+(1/*Q*^2))^2)/4)-1)+(1/(2**Q*^2))+1)/LOG(2)

*Q* = SQRT(POWER(2;*N*))/(POWER(2;*N*)-1)

Thanks to
SengpielAudio
explanations and useful calculators:

Bandwidth in octaves to Q factor (filter) conversion and vice versa

Q Factor and filter center frequency - Find -3 dB cutoff frequencies

See also RaneNote 170 (2008) by Dennis Bohn:

Bandwidth in Octaves Versus Q in Bandpass Filters

November 2016