According to this slideshow (from a presentation at the 2015 IATEFL Conference), you need to know 95-98% of the words in a text to be able to read it easily.
At 90%, “For many of your students, this is where ‘fun’ starts to turn into ‘work’.”
The slideshow displays excerpts from a story in which 98% – then 95% – then 90% – then 80% of the text is in English, while the remaining words are gibberish.
Some people think 80% is enough. This is the 80% passage:
“Bingle for help!” you shout. “This loopity is dying!” You put your fingers on her neck. Nothing. Her flid is not weafling. You take out your joople and bingle 119, the emergency number in Japan. There’s no answer! Then you muchy that you have a new befourn assengle. It’s from your gutring, Evie. She hunwres at Tokyo University. You play the assengle. “…if you get this…” Evie says. “…I can’t vickarn now… the important passit is…” Suddenly, she looks around, dingle. “Oh no, they’re here! Cripett… the frib! Wasple them ON THE FRIB!…” BEEP! the assengle parantles. Then you gratoon something behind you…
The author cites two sources:
Hsueh-Chao, M. H. and Nation, P. (2000) ‘Unknown vocabulary density and reading comprehension‘, Reading in a Foreign Language, 13(1), pp. 403-30.
Schmitt, N., Jiang, X. and Grabe, W. (2011) ‘The percentage of words known in a text and reading comprehension‘, The Modern Language Journal, 95(1), pp. 26–43.