There are 10,000+ roundabouts in the US and the number is growing rapidly. One could argue they may even be overused in certain areas (exhibit: Carmel, Indiana).
So about 0.003 roundabouts per square mile, or 1 roundabouts in 380 square miles
At the same time, the US is much larger than most, so "There are 10,000+ roundabouts in the US" isn't very significant. A proportion would thus be a better metric here than an absolute number.
If you have numbers on intersections per country, and what proportion of them are roundabouts, that would be better, but I don't, so I'm using land as a proxy. I would also accept sum total road length as an option for denominator.