This is a hard task not not easy to solve. If you really want an exact result, copy paragraph by paragraph for your PDF viewer into a text file and check it with the
wc -w tool. The reason why not to use
pdftotext in that case is: mathematical formulas may get also into the output and regarded as "words". (Alternatively you could edit the output you get from
pdftotext). Another reason why this may fail are the headings: "4.3.2 Foo Bar" is counted as three words.
A way around is only to count words starting with a char out of [A-Za-z]. So what I usally do is a two step approach:
get the list of uniq words and check if there are too much false positives inside:
pdftotext foo.pdf - | tr " " "\n" | sort | uniq | grep "^[A-Za-z]" > words
I don't use a dictionary here, as some spelling errors would not count as words.
Get this word list and grep it within the output of pdftotext:
pdftotext foo.pdf - | tr " " "\n" | grep -f words | wc -l
I know this could be done within a one liner, but then I could not easily see the filter result from the first step.