The R-390A is slightly less than 15" deep. Not sure if the non - A version is any different.
The outline dimensions for the R-390 and the R-390A are identical.
As an aside, and as most enthusiasts are aware, the electronics are significantly different between the non-A and A variants. I have both. Personally, I prefer the non-A version, as the LC IF filter section is much smoother on the ears as compared to the mechanical filters employed in the R-390A. If you are shopping for one of these receivers, I would try to hold out for the non-A unit for this reason, although due to relative scarcity nowadays and the better audio quality compared to the R-390A, the price will be somewhat higher.
In my opinion, it does'nt get any better than taking the audio off of the diode load in the R-390 (non-A version) and feeding it into a good outboard amplifier. The receiver will sing like a bird when you do this. Doing the same same thing with my SP-600 yields very close results. The internal 600 ohm output audio in the R-390 and the R-390A is for the birds; no low-end due to less than ideal-quality audio transformers, and typical coarse pentode sound.
73,
Bruce