What 4/4 means in lumber

The Handbook writes it that way

The USDA Forest Products Laboratory’s Wood Handbook labels one-inch lumber with the quarter call, and a range of thicknesses the same way:

25-mm (1-in.) (4/4) [Wood Handbook, Table 13-3, p. 13-11]

25- to 50-mm (1- to 2-in.) (4/4 to 8/4) [Wood Handbook, Table 13-3, p. 13-11]

The standard thicknesses

The Handbook lists the standard thicknesses of hardwood lumber, rough and surfaced on two sides (S2S):

Standard thickness values for hardwood lumber, rough and surfaced on two sides (S2S), are given in Table 6–4. [Wood Handbook, ch. 6, p. 6-3]

Its Table 6-4, with the quarter call for each row (the number of quarter-inches):

The last 4 rows have no planed size in the table. Its footnote:

Finished size not specified in rules. Thickness subject to special contract. [Wood Handbook, Table 6-4, p. 6-6]

The calculator reads 3/4 as three quarters of an inch, not as a quarter call: a quarter call starts at 4/4.

Which thickness counts for board feet

The Handbook says the board foot calculation is based on nominal thickness:

In practice, the board foot calculation for lumber 1 in. or more in thickness is based on its nominal thickness and width and the actual length. [Wood Handbook, Glossary, p. G-2]

Its glossary also says what nominal size means:

Nominal Size—As applied to timber or lumber, the size by which it is known and sold in the market (often differs from the actual size). [Wood Handbook, Glossary, p. G-10]

A board known and sold as 8/4 is known by 2 inches, so the calculator takes 2″ as its nominal thickness: an 8/4 board 8 inches wide and 10 feet long is 13.33 board feet, even after it has been planed to 1¾″. Counted at the planed thickness it would be 11.67. Type the quarter call, or the inches it stands for, and the calculator counts it.

A board called 4/4 is 1″ nominal and 13/16″ planed. The calculator counts anything under 1 inch as 1 inch, so a 4/4 board is 4 board feet at 6 inches wide and 8 feet long either way.

Board feet by thickness

One board, 8 inches wide and 10 feet long, at each quarter the Handbook gives a planed size for:

Board feet go up in step with the thickness, so 8/4 has twice the board feet of 4/4 at the same width and length.

Hardwood comes in random widths

The Handbook on widths and lengths:

Hardwood lumber is usually manufactured to random width. [Wood Handbook, ch. 6, p. 6-3]

Standard lengths of hardwood lumber are in 305-mm (1-ft) increments from 1.2 to 4.9 m (4 to 16 ft). [Wood Handbook, ch. 6, p. 6-3]

So each board has its own width, and you measure it. Add each board to the list in the calculator and the total is the sum of the boards.