According to Mr. Scarlett, the amateur carpenter, “rough-cut” 2x4s (such as were used in the walls of our house) are actually 2x4. The size reduction comes when they’re planed smooth. Mr. S gives the analogy of a “quarter-pound” hamburger – the weight is before cooking, not after.
Why the system was set up that way, he doesn’t know.
IIRC, the size of a 2 x 4 has shrunk over the years (I believe it used to be 1 3/4 x 3 3/4). It was never exactly 2 x 4 due to the explanations already given, but lumber manufacturers reduced the size further in order to get a few more boards out of a log.
I worked for years as a builder of houses, and I’ve done a lot of work in houses that were older and were framed with rough-sawn 2x4’s that actually were 2" by 4", or pretty close. The story I heard many times as to why the lumber is planed nowadays makes a lot of sense if you’ve ever had to handle rough-cut lumber. OUCH! Carpenters got pretty sick of picking dozens of splinters out of their hands and other body parts every day, and their complaints got back to the sawmill owners, who detected a market opportunity to sell nicely planed boards at a considerably higher price. Any carpenter will tell you two things – rough-sawn lumber is hard on the hands and requires gloves for safety, and gloved hands just can’t pick a nail from a nail pouch.
Note also that the corners of framing lumber are somewhat rounded for the same reason – to avoid splinters.
You can, however, find true 2x4 boards. Not really practical for most people, but for woodworkers, it might be something worth looking into. We’ve got a few true 2x4s, course, they’re also oak, which is something you don’t normally find, either.
In my theatre scene shop class, the teachers told us that 2x4’s were actuall 1 3/4 x 3 3/4, a 1/4 inch less than what its supposed to be. Also, when you get to larger sizes of lumber, the sizes start to decrease by 1/2 inch. They said it had something to do with the sanding down of rough lumber.