A more commonly cited figure is 10%, which comes from the clearance rate of DNA testing kits. i.e. someone accuses a man of rape, there is DNA and it exonerates him. So this is an absolute lower bound because a lot of rape accusations are a bit like this article: "we had sex a bunch of times consensually, and then also when it wasn't". You can't disprove that with DNA evidence but it can still be a false accusation.
Back in the 90s when this stuff was less politicised there was a somewhat rigorous study that put the true figure at around 50% [1]. It gave pie charts of the reasons for the false accusations and other interesting bits of data. This figure causes people to freak out these days due to the "believe the victim" mentality you can see above, where there is a deliberate conflation between accusations of rape and actual rapes, so it gets attacked a lot, but modern scholarship hardly investigates the question of false reporting rates for rape unless the authors already decided their conclusion before doing the research (you can sometimes see admissions of this in the study's discussion sections). The 50% figure has some other support: when interviewed anonymously police workers, both male and female, tend to pick this figure when asked to estimate the false reporting rate.
The low prosecution success rate is usually painted these days as an obvious flaw of the justice system, but that's identity politics. When you drill into it in detail and ask OK, where do these prosecutions go, and why are they dropped, or why do they fail to win in court, the answer is: because a LOT of rape allegations are not only false but clearly false. For example, because the complainant goes to the police and admits they made it up, or because they are clearly high on drugs when making the accusation and rescind it when sober. Even if you engage in some mental gymnastics to assume rescinding an accusation is never valid, it doesn't matter. It's really hard to win in court when the "victim" themselves are claiming they're not really a victim at all.
[1] https://ia800209.us.archive.org/4/items/FalseRapeAllegations...
I wrote a bunch more and gathered some links, but Hacker News is telling me to slow down. 6 comments on this thread since 2pm, wow such spam
That is a HUGE percent of false accusations! On the high end that's 1 in 10! In the middle, it's 1 in 20. That's a LOT.