Contrary to lay opinion, the size of a man’s vocabulary is not only an index of his schooling, but an excellent measure of his general intelligence. Its excellence as a test of intelligence may stem from the fact that the number of words a man knows is at once a measure of his learning ability, his fund of general information and of the general range of his ideas.

From the Measurement and Appraisal of ADULT INTELLIGENCE by David Wechsler 4th edition 1958

One of the great things about using vocabulary as a measure of IQ (or at least verbal IQ) is that like physical measurements, it’s a true ratio scale with an actual zero point.

So how many words does the median young adult know and how does this map to IQ?

From How Many Words Do We Know? Practical Estimates of Vocabulary Size Dependent on Word Definition, the Degree of Language Input and the Participant’s Age by Marc Brysbaert,* Michaël StevensPaweł Mandera, and Emmanuel Keuleers

According to the above study, among young U.S. adults, the 5th percentile, 50th percentile and 95th percentile, know 27,100, 42,000, and 51,700 lemmas respectively. These percentiles equate to verbal IQ equivalents of 75, 100, and 125 allowing me to equate total vocabulary to the IQ scale.

Notice how linear the relationship is? Verbal IQ appears to be a true interval scale, at least within 2 SDs from the mean.

ŷ = 0.002X + 19.35827

Verbal IQ is almost a true ratio scale too because notice how 51,700 (verbal IQ 125), is roughly 125% as large as 42,000 (verbal IQ 100). On the other hand, a vocabulary of no words equates to a verbal IQ of 19, and not zero.

It is interesting to ask what would be the verbal IQ equivalent of someone who knew every word in the English language. According to the study data cited above, the maximum number of lemmas is 61,800 which would equate to an IQ of 143. Although 143 is an exceptionally high IQ, it’s absurd to think one in several hundred Americans knows every single word (even on a very superficial level).

Reading the above study further I find:

A first limitation is the list of 61,800 lemmas we used. Although we are reasonably sure the list contains the vast majority of words people are likely to know, there are ample opportunities to increase the list. As indicated above, the Collins scrabble list could be used to more than double the number of entries. We are fairly confident, however, that such an increase will not change much in the words known by the participants (see also Goulden et al., 1990). The words we are most likely to have missed are regionally used common words and recently introduced words.

So if the maximum number of lemmas could be doubled to 123,600, that raises the ceiling of verbal IQ (as measured by total vocabulary) to 267! I doubt anyone could ever score that, unless they have some kind of autistic obsession with reading scrabble dictionaries, in which case the test would be invalid for them.