As far as I know, both speech and noise signal are stochastic processes, which means they both are random and change there statistical parameters over time. Therefore, it is difficult to find a single mathematical formula abstracting the classification between them. Unless of course if you use VAD to separate speech from non-speech signal, where there is no single formula to do so.

The certain SNR value for speech depends on the application. However, While I was doing my research, I found that the relative difference between whispering and moderate speech is > 20 dB. This fact could be found in 'The Audio Handbook' by Gordon J King, and old book but explains many things to me. 

You will find some useful information about both questions in the 

Article The Short-Time Silence of Speech Signal as Signal-To-Noise R...

To my knowledge a SNR > 30 dB is considered as a clean speech. Some guidelines can be found in the link.

http://www1.icsi.berkeley.edu/Speech/faq/speechSNR.html

Dear Adam,

I will suggest a practical book. Its title is "Speech Enhancement - Theory and Practice".

It is written by P.C. Loizou and published by CRC Press in 2007. If you look at Section 7.3.3 "Estimating the a priori SNR" (pp. 228-236) you will see various formulas  for calculating SNR of speech signals.

Best wishes,

NIST has been publishing SNR algorithms for about two decades.  Look there.

Hi Adam,

Am trying to do something similar.

1) Could you please point me to the different ways you found to calculate SNR of an audio file?

2) Could you also recommend the SNR ranges to be used to determine good vs less noisy vs noisy audio files?

Thanks!