# Calculate Q factor of a Low Shelf and High Shelf filter

I'm developing an app that has an EQ using eq10q plugin. My eq has 10 bands. I'm using peaking filters for the middle bands and a low shelf filter for the first band and a high shelf filter for the last band. I calculated the Q factor for the middle bands by dividing the middle frequency by the bandwidth desired for that band but I don't know how to calculate the Q factor for the High Shelf filter and the Low Shelf Filter. How should I do it?

it looks like this eq10q uses cascaded parametric EQs, initially set up to be bell, but switchable to other types (like shelving).

i wouldn't doubt that they're using the audio EQ cookbook. if you're using that, there is a parameter called "shelf slope" or $S$ that is often set to 1, because that gets you the steepest slope without dips or lips or bumps. so it's a straight incline or decline to the shelf level. if the control is $Q$, instead, there is a relationship between $S$ and $Q$:

$$\frac{1}{Q} = \sqrt{ \left( A + \frac{1}{A} \right) \left( \frac{1}{S} - 1 \right) + 2}$$

where

$$A = 10^{dB_\text{gain}/40}$$

and $dB_\text{gain}$ is the shelf gain in dB.

i would just plug in $S=1$ and get a $Q=\frac{1}{\sqrt{2}}$.