It is an industry standard and has been since Jesus was an apprentice carpenter. Ive known it since I was about 12, family full of carpenters though. Dimension lumber size is rough cut size and finished size is after planing.
I started working as an architect (actually as a draftsman, as I hadn't gotten my degree yet) in 1966. Back then a 2x4 was 1-5/8" x 3-5/8". Then, some time in the early to mid-1970s, the industry standard shifted to 1-1/2 x 3-1/2, and there it has stayed. But it's not as simple as subtracting a half inch from the nominal dimension to get the actual dimension. Oh, no ... that would be too easy.
"Boards" and pieces of wood with a nominal thickness of one inch or less. A "one by" whatever is 3/4 of an inch thick. But a nominal 1-1/4" board ("five quarter") isn't 1-1/4" thick. They used to be 1-1/8" but now they're 1-1/16" thick.
Framing lumber, 2" or greater nominal thickness, is called "dimension lumber." A 2x4 is 1-1/2 x 3-1/2. A 2x6 is 1-1/2 x 5-1/2. But ... beyond 2x6 it gets even worse. A 2x8 is 1-1/2 x 7-1/4, a 2x10 is 1-1/2 x 9-1/4, etc.
Back in the heyday of "soft metrication" I once suggested to a lumber industry rep that we should just adopt standard metric dimensions for dimension lumber. A 2x4 would become 40mm x 90mm, for example. My suggestion was met with horror. Oh, no! That would mess up all the detailing in the field, he said. Never mind that lumber that was surfaced when green shrinks at least an eighth, maybe a quarter of an inch when it dries, so mixing "S-green" lumber with air-dried lumber with kiln-dried lumber results in a real mish-mash.
And never mind that I saw first-hand the change from a 1-5/8 x 3-5/8 "2x4" to the smaller version. In metric dimensions, the 1-5/8 x 3-5/8 "2x4" was 41.28mm x 92.08mm. The newer 1-1/2 x 3-1/2 version is 38.1mm x 88.9mm. My suggestion was to make a 2x4 40mm x 90mm. The industry had already undergone the change from the n-5/8 sizes to the n-1/2 sizes. My proposal would have fallen between the two, so very little adjusting would be needed, and that would have been less than what the industry had absorbed without a whimper in the 1970s. But no -- it was not to be.
So we still have idiot buyers and idiot lawyers who sue because industry standard, commodity-grade lumber is being sold at (oh the horror!) industry standard dimensions.
