I see there’s a lot of replies all ready here, and I haven’t read them all. But I want to give my cents anyways. 
I’m currently at 37000 known words in Russian and ~800000 total words read. And I can already read High-end fantasy without a dictonary… or so it can feel sometimes. The thing is, it depends on what you mean with a dictionary and what you read. Currently I’m reading Assassins’ apprentice in Russian and it’s about 8 - 10% unknown words for me per lesson. I can read it on my kindle and get everything that is going on no problem. But on the other hand, it’s my favorite book of all time and I know it very well having read it in Danish and English. So it’s no issue to follow along. However there is still a ton of words that I don’t know, and I would have to be in the dictionary constantly if I wanted to look up all of them.
So my point is, you can probably already read a ton of books already without the use of a dictionary, as long as you know the plot.
I’m also currently reading “Дар Огня” which I’ve never read before. But so far I have no issue following along.
So again it really depends on the book, try some young adult books and see if they are possible to read.
After all, every author writes differently, some easy and some not. And you don’t have to know every word in a book to finish and enjoy it.
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