"somewhere between 12,000 and 20,000", according to this site. They also say,
"A vocabulary of between 1500 to 2000 words should be enough for most circumstances. The more you know the better because even though you can control the words you use, you can't control the other person. Because of this, you need to learn more words to understand well than you need to speak well."
Word Origins.org says,
"The Oxford English Dictionary, the largest English-language dictionary, contains some 290,000 entries with some 616,500 word forms.
Of course, there are lots of slang and regional words that are not included and the big dictionary omits many proper names, scientific and technical terms, and jargon as a matter of editorial policy (e.g., there are some 1.4 million named species of insect alone). All told, estimates of the total vocabulary of English start at around three million words and go up from there.
Of these, about 200,000 words are in common use today. An educated person has a vocabulary of about 20,000 words and uses about 2,000 in a week's conversation. (These estimates vary widely depending on who is doing the counting, so don't take them as absolute.)
All the best.