I’ll admit, I wasn’t thinking of comparing the inauguration numbers to the women’s march numbers when I wrote The Art of Estimation. However, even if you can’t estimate the actual numbers in either case, it’s clear from the photographs that far, far, far more people showed up to remind President Trump that he has an obligation to work for the betterment of all Americans than showed up to celebrate his inauguration; likewise, that Trump’s inauguration crowd was significantly smaller than Obama’s.
In any case, here’s an article from the Poughkeepsie Journal about the march over the Hudson. The article quotes park officials as estimating a crowd of about 5000, which is at the low end of my estimate. Someone at the march with a counter got up to 7716, which is about the middle of the range.