Log board feet calculator
How many board feet a sawlog holds by each of the three log rules used in the United States, from the diameter at its small end and its length. All three are shown, because a buyer and a seller may not use the same one.
Measure across the small end, inside the bark, to the inch. The log rules are written in inches and feet.
Doyle
144 bd ft
From the standard, the Doyle rule (Purdue FNR-191)
Scribner Decimal C
160 bd ft
Only two sources publish this: Purdue University Extension and Idaho Board of Scaling Practices
International 1/4 inch
180 bd ft
From the standard, the International 1/4-inch rule (Purdue FNR-191)
Why: The three log rules assume different saw kerfs and log taper, so the same log scales 144 (Doyle), 160 (Scribner) and 180 (International) bd ft.
Why these numbers?
The situation
A log 16 in across the small end, inside the bark, and 16 ft long.
From your input: diameter and length
The number
Doyle: (16 − 4)² × 16 ÷ 16 = 144 bd ft.
Arithmetic: exact by definition , sources [1]
The number
Scribner Decimal C: the table gives 16 for 16 in × 16 ft, in tens of board feet: 160 bd ft.
Two sources: Purdue University Extension and Idaho Board of Scaling Practices , sources [1, 2]
The number
International 1/4 inch: 4 sections of 4 ft, 0.199D² − 0.642D each, the diameter growing 1/2 in per section from 16 in, rounded to the nearest 5: 180 bd ft.
Arithmetic: exact by definition , sources [1]
Sources
Three rules, three answers
A log rule estimates the lumber a sawmill will cut from a log, so it builds in an allowance for the saw kerf, slabs and edgings. The rules make different allowances, and they disagree most on small logs.
Doyle (1837) is a formula: subtract 4 inches from the diameter, square it, and multiply by the length over 16. It ignores taper and gives the least of the three for small logs. Scribner (1846) was drawn from diagrams of 1-inch boards sawn from circles; the Decimal C version rounds to the nearest 10 board feet and drops the last zero, so it is read from a table. International 1/4 inch (Clark, 1917) adds up 4-foot sections with the diameter growing half an inch per section to allow for taper, with a 1/4-inch saw kerf; it is rounded to the nearest 5 board feet, and Purdue Extension calls it probably the most accurate of the three.
Lengths here run 8 to 20 feet in 2-foot steps and diameters 8 to 40 inches, the range of the published tables. Published International tables differ from the formula by 5 board feet in a few cells; we compute it from the formula rather than copy a table.
For sawn boards, use the board foot calculator.