The board-foot formula, and why lumber isn't priced like plywood
A board foot is a volume, not a length: one piece of wood measuring 1 inch thick by 12 inches wide by 12 inches long, equal to 144 cubic inches. For sawed lumber, the University of Wisconsin-Madison's Division of Extension forestry program gives the working formula: board feet = (thickness in inches × width in inches × length in feet) / 12. Plug in a piece's actual thickness and width in inches and its length in feet, and the /12 converts the length term so the whole thing comes out in cubic-foot-sized units instead of cubic inches.
Framing lumber (2x4s, 2x6s) skips this entirely because it's milled to standardized sizes under the American Softwood Lumber Standard (Voluntary Product Standard PS 20, administered by NIST) and sold by the piece or the linear foot: every stud is the same cross-section, so there's nothing to normalize. Hardwood and specialty lumber come in random widths and odd lengths off the saw, so board feet gives buyer and seller a volume-based price that works no matter how wide or long any individual board happens to be.
Worked examples: a hobby board and a table-top order
A single rough 1"×6"×8' pine board: board feet = (1 × 6 × 8) / 12 = 4 board feet. At $6.50 per board foot that one board runs 4 × $6.50 = $26.00.
A woodworker orders six pieces of 8/4 walnut (2 inches actual thickness), each 8 inches wide and 6 feet long, for a table build. Per piece: (2 × 8 × 6) / 12 = 8 board feet. Six pieces: 6 × 8 = 48 board feet. Add a 10% allowance for knots, checks, and cutting waste: 48 × 1.10 = 52.8 board feet. At $9.25 per board foot: 52.8 × $9.25 = $488.40.
Nominal quarters vs. what you should actually measure
Rough-sawn hardwood is traded in "quarters," a National Hardwood Lumber Association convention where the number of quarter-inches gives the nominal thickness: 4/4 is 1 inch, 5/4 is 1.25 inches, 8/4 is 2 inches, and so on. That works directly as a thickness input when a board is still rough off the saw, before any surfacing.
Once a board is surfaced (S2S or S4S), the mill has planed material off both faces, and how much varies by supplier. Retailers describe results anywhere from about an eighth to a quarter inch under nominal for 4/4 stock, and it isn't the same number everywhere. Rather than guess, measure the board with calipers and enter that actual thickness; the quarter buttons on this calculator are a rough-lumber shortcut, not a substitute for measuring surfaced stock.