The SciWrite site wiki recommends a free text analysis utility, but don't go there yet, I'm talking. The program can be used on the web or downloaded as a Chrome browser extension. It is easy to use, and has generous capacity -- I dumped in a 25,000 word fiction manuscript and it went right to work. It counts up words, sentences and paragraphs; Microsoft Word's spellchecker does that too, of course, but you can't consult it until you've slogged through the spellcheck. Also, there are some bonus extras, of which three sound most useful.
1. A tally and percentage of "difficult words," defined as those not found on this list of 3000 "familiar" words. My ordinary non-scientific prose runs about 22% unfamiliar; compare that with Einstein's 1905 paper "The Electrodynamics of Moving Bodies" at 43%. (This refers to the 1922 translation by W. Perrett and G.B. Jeffery.)
2. Average sentence length, which you could easily calculate from Word's report, but I like having it faster. My typical sentence runs just under 10 words in length.
3. A list of all the words you have used, in order of how often you have used them. (You can choose to view top 10, top 20, or whatever number you're curious about.) Why would you want to do this? I use it to police my overuse of certain words, notably "but." Too many buts gives my prose an argumentative tone, and I'm scary enough already.
Here is Word Count Tools' main display, giving the lowdown on this very blog post you just read.
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Testing the comments.
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