Answered at Quora.
There has been a lot of writing on this at genius.com. The man who writes that estimates that Goethe and a few others had IQ’s up to 220. That’s about the limit.
William Sidis was estimated by a psychologist who examined him to have an IQ to 250–300. This puzzled me for some time, but that estimate was based on SD +16, which can go up to 250-275. The corollary for that score on SD +15 would possibly be 200-220.
The smartest man in the world, Christopher Langan, is said to have an IQ of 200.
It gets very hard to measure very high IQ’s.
Children can have very high IQ’s because their IQ’s are measured in terms how smart they are for their age. Using that scale, childhood IQ’s of up to 400 have been calculated. Of course, once they hit 18, you start counting the scores the other way, and they can’t have much above 200.