The formula
Board feet = (thickness in inches × width in inches × length in feet) ÷ 12. The division by 12 converts the inch-foot mix into cubic feet divided by twelve — since one board foot is one-twelfth of a cubic foot. Three examples show the range: a 1×6 board 10 feet long is (1 × 6 × 10) ÷ 12 = 5 board feet; a 2×8 board 12 feet long is (2 × 8 × 12) ÷ 12 = 16 board feet; and a chunky 4×4 post 8 feet long is (4 × 4 × 8) ÷ 12 = 10.67 board feet.
Why lumber is sold this way
Pricing by the foot of length would punish thick boards and reward thin ones; pricing by weight would punish dense hardwoods. Board feet price the actual material, so a walnut board and a pine board of the same dimensions cost in proportion to their per-board-foot rates, and a project estimate is just total board feet times the rate, plus waste. Most yards add 10–15% for offcuts and defects when quoting a project — a habit worth copying, since no board is usable end to end.
The nominal-size trap
Shelf labels are nominal: a 2×4 is sawn 2 × 4 inches rough, then planed smooth to about 1.5 × 3.5 inches, but it keeps the 2×4 name and the board-foot math uses the nominal figures. That means the 5.33 board feet of an 8-foot 2×4 describes the rough-sawn volume, not the planed board you take home. For structural framing this hardly matters — everyone prices the same way — but if you are comparing a rough-sawn hardwood supplier against a planed softwood yard, check which dimensions each quote is based on before comparing per-board-foot prices.
For firewood, a different volume unit rules: see what a cord of wood is, and for the length and area conversions behind any project, start with the feet to metres converter.