there is no single answer, the Oxford English Dictionary containes 171476 words in constant use and 47146 obsolete words. This suggests about 250,000 words. However with other technical additions there may be as many as 750,000 in total
No one actually knows for sure. (Perhaps that is why they are called 'uncountable'! Only joking!) Everyday new and interesting things are being found. So no one can say exactly how many. But it is...