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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?

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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 $Q=\frac{1}{\sqrt{2}}$.

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