Hi,
I don't think there is a common formula.
Overtones are mainly caused by distortions:
Let's look at two cases:
1) audio amplifier, pure sine input, close to clipping:
The overtones are very low in amplitude, maybe -80dB
Now if you increase the input signal (fundamental) amplitude by 6dB..
Then the overtones will increase rapidly, maybe up to -24dB (referenced to the fundamental amplitude. not calculated) for the first overtone
2) audio amplifier, distorted sine input, not close to clipping:
The overtones do exist
Now if you increase the input signal (fundamental) amplitude by 6dB..
Then the overtones will increase by close to 0dB (referenced to the fundamental amplitude)
In case 1 the distortion increases with amplitude, whereas in case 2 the distortion does not increase with amplitude, and there will be all other sytems inbetween.
Klaus