Board Feet of Lumber

A board foot is a volume, not a length, and that is the single thing most people get wrong about it. It is 144 cubic inches: a piece 1 inch thick, 12 inches wide and 1 foot long. That is why the working formula divides by 12 — you are multiplying inches by inches by feet, and the 12 reconciles the mixed units back into a whole board foot. A 2x10x12 comes out at $2 \times 10 \times 12 / 12 = 20$ board feet, exactly.

Hardwood is sold this way, softwood framing usually by the piece, and both are priced from the nominal dimension rather than the actual one. A "2x4" measures 1$\tfrac{1}{2}$ by 3$\tfrac{1}{2}$ inches after drying and surfacing, but you pay for 2 by 4. Rough sawn hardwood is a different animal again, quoted in quarters: 4/4 is one inch, 8/4 is two inches, and the tally is taken before surfacing.

Handy shortcut worth carrying: a 2x6 yields exactly one board foot per running foot, since $2 \times 6 / 12 = 1$. A 2x12 gives two per foot, a 1x12 gives one, and everything else can be scaled off those.