# The Definition of Q Factor by an Equation and How to Graph

I am currently building an EQ in an music app, and it's relatively simple:

6 bands of fixed center frequency, and a Q knob to control the Q of all bands, because we do not currently have space for separate Q knobs for each individual band.

The problem is that we need to draw an EQ graph according to the user's settings like the one usually seen on a sound board.

My current understanding is that the Y axis is measured in dB's and grows linearly, and the X axis is the frequency and grows exponentially (a Lin-Log graph, that is).

I have no problem drawing this, until the Q factor comes in. I know that Q makes the affected range larger if Q is smaller, and shrinks the affected range if Q is larger.

However, I do not not how to calculate the exact staring position and end position of the "bump" of that Peak EQ filter, if I'm given a center frequency of 1 kHz and a Q of 2.0.

What is the mathematical formula to compute the beginning and end of the curve?

• I went ahead and added a few line breaks (possibly: too many) to your two questions, simply to make them easier to read (and not one wall of text). Dec 16 '18 at 1:08
• dB is a logarithmic scale. So, with respect to amplitude (or power) the described graph would be log-log, with respect to logarithmic amplitude (or power), it is indeed lin-log. Dec 16 '18 at 1:08
• If your "Q" is the Quality Factor of a filter (I'm not well-versed in the conventions of audio terminology), then it is defined to be the ratio between passband width and center frequency. That would immediately be your formula. Does this help? Dec 16 '18 at 1:10
• Thanks for your edition! But if the Q is defined that way, what is the "passband width" then? Say I have a Q of 0.5 on frequency 2K, isn't the width going to be 2K/0.5 which is 4K? How can the width be 4K? Or is there a value range of Q and it cannot be certain number? Thanks! @MarcusMüller Dec 16 '18 at 4:54
• You might find these sources helpful in this - sengpielaudio.com/calculator-bandwidth.htm and sengpielaudio.com/calculator-cutoffFrequencies.htm Dec 16 '18 at 8:19