Tl;dr: roughly speaking, ~2 hours/week of mixed cardio and strength training may in effect raise your IQ by ~2.7 points.

I spent a few hours trying to roughly estimate the cognitive benefits of aerobic exercise. The best literature review I could find about the type/magnitude of the benefits reports the following effects:

Attention/processing speed (with combined strength training): g = .25, P = .026
Executive function: g = .123, P = .018
Working memory (with combined strength training): g = .228, P = .028
Memory: g = .128, P = .026

Working memory and attention/processing speed, but not executive function or non-working memory, appeared to benefit more from a combination of aerobic exercise and strength training than aerobic exercise alone (g = .288 versus g = -0.042, and g = .250 versus g = .098, respectively).

These are pretty substantial benefits—how much do they cost to acquire? In my favorite world, I would have found a graph depicting cognitive benefit as a function of hours of exercise per month, to get a sense of diminishing returns. In the actual world, the best I could find was this lit review of studies involving 11k old people, which reports a finding that vaguely hints at what that graph might look like: all studies which reported no cognitive benefits from exercise involved less than 52 hours of exercise over six months, while studies which did show cognitive benefit involved a median of 52 hours.

Normally I would have been skeptical these results would generalize to young people, but the first (Smith et al.) review studies relative gains in improvement between young and old populations, and finds no difference (except for working memory, where older people benefit more). So my guess is that the results of Osman et al. are at least mostly applicable across age groups.

Both studies report that neither intensity of exercise nor study length (which ranged from weeks to 1.5 years) correlated with improved cognition; Osman et al. reports that the only thing which did correlate was number of hours exercised over six months. In other words, from what I understand, you don’t have to exercise very hard to get the benefits, you just have to log a certain number of hours—maybe 52 over six months, or ~8.5/month. And while continuing to exercise after that presumably ensures these benefits continue, they probably won’t increase further.

So, to make a very crude est...

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