The find command could be your friend for getting a full depth count. Something like:
find /path/name/here/ | wc -l
Or just:
find . | wc -l
for the current directory.
There's also a command called locate (often with another letter in front, but accessible by just that word) which maintains a database of filenames on a system that can be used, provided it's installed and has built that database.
Pro: Faster than churning the disk every time with find. (Though disk cache can help alleviate some of this).
Cons: Can get out of date with a changing filesystem. Harder to search for relative paths like .
locate -r '^/path/name/here/' | wc -l
... would be roughly equivalent to the first find example.