Board feet explained: converting a cut list into lumber volume
A board foot is a volume of wood: 1 inch thick, 12 inches wide, 12 inches long. Some hardwood is priced this way; here is the arithmetic on two worked examples.
The formula
Board feet = thickness in inches x width in inches x length in feet / 12. The formula uses nominal dimensions: a 1 x 10 is counted as 1 by 10 inches even though the board you carry home is thinner and narrower. Ask the seller whether they price by nominal or actual size.
Example 1: 1 x 10 pine shelves
The 32-inch bookshelf example buys 4 boards, each 8 feet long. One board is 1 x 10 x 8 / 12 = 6.67 board feet, so the purchase is 26.67 board feet. At the example price of $13.00 per board, that works out to $1.95 per board foot.
Example 2: 2 x 4 studs
The 4-foot workbench frame buys 6 boards, each 8 feet long. One board is 2 x 4 x 8 / 12 = 5.33 board feet, so the purchase is 32.00 board feet. At the example price of $5.50 per board, that is $1.03 per board foot.
Why a cut list still matters
Board feet tell you the volume of wood; they do not tell you how many boards to buy. Parts must fit on whole boards after kerf and end trim, so the number of boards comes from the cut list, and the board-foot figure is a way to compare prices between products sold by the board and by volume.