How many monosyllabic words does English have? (estimations are fine)

Solution 1:

The Phonetic Word Search website returns nearly 12,000 one-syllable words — input !* @ !* to the search function.

Some of these words have two pronunciations. For example, the database has both a one-syllable pronunciation and a two-syllable pronunciation of fire. So you should think of this as the number of words that can be pronounced with one syllable.

Further, many of these words are extremely rare, so you should probably view this as an upper bound.

Solution 2:

In the Beginning was Information by Werner Gitt may provide you with a starting point for your investigation. Gitt claims that 71.5% of English words are monosyllabic. You'll have to decide whether Gitt's sampling universe is to your liking.