After a pair of years learning German I'm still not convinced that its number of words is finite (actually it's infinite). But as a guide to answer your question. Is there a language for which such an information is available? You might want to see in the Duden. After looking up a word there, it often appears
Dieses Wort gehört zum Wortschatz des Zertifikats Deutsch.
You can also infere a lot from the frequence it's used. For, say, the verb machen it appears
Häufigkeit:
■■■■■
Wheras for other less used words, like Unwort:
Häufigkeit:
■■□□□
There are more accurate dictionaries telling you how many inverse factors of two you need to multiply the frequency of the word you look for, so that the frequency equals that of "der".