Why are the top and bottom of a waveform graphic +1 and -1? In the picture, the peak amplitude is 0 db, but it’s represented on the graphic as +1. Shouldn’t it be 0?
Never mind, as soon as I posted this I found the answer. It has to be set to Waveform (db). 
The blue waves are in percent because it’s easier to see what you’re doing than in dB. You can change the blue waves to dB if you want with the little black arrow drop-down to the left.
“Waveform (dB).”
You see right away that the area of interest becomes scrunched up and hard to see. The waves then represent the whole audible range, but you usually only care about the top 20dB or so and that works in percent.
Koz
That rang alarm bells because usually the only people who worry about that are trying to do scientific research or other academic task. Audacity doesn’t lend itself very well to doing that. It’s an Audio Production Editor, not a WAV editor. There are techniques used that sound good and aren’t necessarily statistically accurate.
Koz
The conventional way to represent waveforms is with a “dB” vertical scale, which as you say would be “0” at full scale. ( 0.0 at the top and at the bottom and “minus infinity” at the centre line).
As you have discovered, Audacity does not always do things the conventional way.
I think that the main reason for the +/- 1 scale was to make it easier for people that are new to audio technology (though I don’t personally agree with the validity of that argument). However there is also a sound technical reason for the +/- 1 scale:
In digital audio, the audio is made up of “samples”. These are measurements taken in very rapid succession (typically 44100 times per second) of the analogue waveform.
These measurements are stored as binary numbers. There are different formats that those binary number can take, for example, “signed 16 bit”, or “signed 24 bit”, or, as is the default case for Audacity, “32 bit float”. Whichever number format is used, the values are “normalized” to give a common decimal representation of a “valid” signal range (-inf to 0 dB) of +1.0 to -1.0. Thus the short answer to your question is that +/- 1.0 is the (decimal) numerical range of sample values.
If you have a look at the “Sample Data Export” analysis tool (Audacity Manual) you can verify that this is the case.
For most purposes the “Waveform dB” is not very useful because it causes the waveform to appear “squashed”.
In practice, the +/- 1.0 range does not take long to get used to, even if you are more familiar with dB.
The conversion betweem “dB” and “linear” is quite simple if you remember the number “6”.
Halving the “linear” amplitude is very close to a drop of 6 dB.
Doubling the linear amplitude is an increase of 6 dB.
Thus you can easily approximate the dB value when looking at the normal “Waveform” view.
Full track height = 0 dB
1/2 track height = -6 dB
1/4 track height = 12 dB
1/8 track height = -18 dB
and so on.
Having a dB scale on the normal Waveform view is a feature request. If you’d like to vote for that feature request, please say so and I’ll add your vote. (Voting does not mean that it will be implemented any time soon, but it does provide a reference for the popularity of proposed features).
Very educational indeed. Much appreciated.