Log to Board Feet Calculator

How it works

A log rule estimates how many board feet of lumber a sawmill will cut from a log, from the diameter inside the bark at the small end and the length. Logs are bought and sold on these estimates, and the three rules in common US use give quite different answers for the same log (Purdue Extension FNR-191).

Doyle (in print by 1837) subtracts 4 inches from the diameter for slabs and edgings and squares the rest. It ignores taper and badly underestimates small logs. The Scribner rule was drawn from diagrams of 1-inch boards in circles; its Decimal C tables round to the nearest 10 board feet and step irregularly, so this calculator uses the smooth Scribner formula of Bruce and Schumacher (1950). The International 1/4-inch rule (Clark, 1917) allows for a 1/4-inch saw kerf and 1/2 inch of taper per 4 feet, and is generally considered the most accurate of the three.

The calculator works out all three rules for the log and multiplies the chosen one by the number of logs.

Formula

D = small-end diameter inside bark (in), L = length (ft)
Doyle          = (D − 4)² × L ÷ 16
Scribner       = (0.79·D² − 2·D − 4) × L ÷ 16
International  = 0.04976191·L·D² + 0.006220239·L²·D − 0.1854762·L·D
                 + 0.0002591767·L³ − 0.01159226·L² + 0.04222222·L
total          = chosen rule × number of logs

Example

A 16 in × 16 ft log scales (16 − 4)² × 16 ÷ 16 = 144 board feet by Doyle, matching the published Doyle table. The International 1/4-inch formula gives 180.6 board feet (the published table, rounded to the nearest 5, shows 180), and the Scribner formula gives (0.79 × 256 − 32 − 4) × 16 ÷ 16 = 166.2 board feet.

A load of 10 such logs is 1,440 board feet Doyle.

Assumptions and limitations

• These are estimates of sawn lumber, not measurements. Actual yield (overrun or underrun) depends on the mill, kerf, sawing pattern, log shape and defects; mills apply their own experience on top of the rule.
• Each log is treated as sound and straight. Deductions for rot, sweep, crook and splits, which scalers make under formal scaling rules, are not applied.
• Diameter is inside the bark at the small end and is limited to 6–40 in, the range of the FNR-191 tables. Length is limited to 4–20 ft, the range FNR-191 gives for the International formula; its printed tables cover 6–18 ft (Doyle), 6–20 ft (Scribner Decimal C) and 8–20 ft (International). Longer logs are scaled as two or more logs.
• The Scribner value comes from the Bruce and Schumacher formula and will differ from Scribner Decimal C tables, which round to the nearest 10 board feet and step irregularly; the formula can differ from Decimal C by 30% or more on logs under 12 in (a 6 in × 16 ft log is 12.4 board feet by the formula and 20 in the Decimal C table). Published International tables round to the nearest 5 board feet.
• The formulas are from Purdue University Extension publication FNR-191, Log and Tree Scaling Techniques (Cassens). Standing-tree volume (from DBH and merchantable height) is a different estimate and is not calculated here.

Frequently asked questions