Serious woodworker here:

They aren't off by that much. You are further off if you assume some standard parameter ranges :)

But in the end, it depends on factors i didn't see listed.

Overall, the percents are usually calculated by swelling coefficient. Swelling coefficient is percent change in radial/tangential for each 1 percent of moisture change. There are well-known sources for these that calculated them in sane ways. The US forest service is one of them, and they publish their methodologies/etc for how they determine them. See, e.g., https://wfs.swst.org/index.php/wfs/article/download/1004/100...

Take standard flat sawn red oak. The swelling coefficient is 0.001-0.002 for radial (0.1% per 1%), and 0.004-0.005 for tangential (0.4% per 1%).

So in initial drying, which is usually 30%->15%, it will move 1.5-3% radial and 6-7% tangential.

Without humidity control, houses swing from 30%<->60%. Sometimes per day, sometimes per month, sometimes per season. So even more than initial drying. But because the swing varies, depending on thickness/etc, how much moisture change you get in the wood, and how fast, will vary a lot.

If you assume it causes a 10% change in moisture content over the year, throughout the wood, we get 1-2% radial movement, and 4-5% tangential movement for red oak. But that is both swelling and shrinking, not solely one or the other.

So the GP would be off by a factor of 2 in one, but not off in the other.

It's obviously trickier in practice to calculate the actual rates because the moisture is going to diffuse through the wood at some rate, and as long as the RH is changing faster than the diffusion rate, the wood will not really have a consistent moisture content all the way through. To be accurate, you'd have to slice it into enough pieces to capture the different moisture levels in the wood, apply the coefficients to each slice, and, etc. Worse, because boards are rarely square, and instead often much wider than they are thick (IE 12"x1") , you'd have to slice and calculate it one way to deal with this for radial, and slice and calculate it the other way to deal with tangential.

I'm too lazy to calculate how coarse/fine of a slice you'd need to get within say 5% of the "real" number.

I'm also assuming you are trying to do it by hand, since this is obviously an integral of some sort that you could also just directly solve. I'm sure it's in a paper somewhere.

This is all for bare wood too, with no topcoats. The topcoat would seriously affect absorption rates, etc, even assuming you applied it to all sides.

Nobody does any of this calculation in practice, we just accept large error bars and build floating tables :)