Log board foot calculator (log scale)

These estimates come from log rules — the three common ones are compared below. New to this? Words explained.

The three log rules

A log rule is a formula or table that predicts lumber yield from diameter and length. Each makes different assumptions about saw kerf (the width of wood the blade turns to sawdust), slabs and edgings, and taper, so they disagree — sometimes by a lot.

Doyle:          BF = (D − 4)² × L ÷ 16
Scribner (Bruce and Schumacher formula, ≈):  BF = (0.79D² − 2D − 4) × L ÷ 16
International ¼": per 4 ft section BF = 0.905 × (0.22D² − 0.71D),
                 with D growing ½ in per 4 ft section for taper
D = small-end diameter inside bark (in) · L = length (ft)

• Doyle dates from around 1825 and is still widely used in the southern United States. Its 4 in slab allowance is about twice what a mill really loses, so it underestimates small logs and overestimates very large ones (Virginia Cooperative Extension 420-085).
• Scribner was built by drawing 1 in boards inside circles the size of the log end. It allows for a ¼ in kerf but not for taper, so it tends to underestimate, especially on long logs. It is often used in the rounded Scribner Decimal C form (volumes to the nearest 10 board feet). The Scribner rule itself is a table, not a formula; the calculator uses Bruce and Schumacher’s formula, the standard approximation, which can differ from the tables by several percent — at 16 in × 16 ft it gives 166 against 160 in the published Decimal C table. For 16 ft logs measured in whole inches, the calculator also shows the published Decimal C figure from Virginia Cooperative Extension’s table.
• International ¼-inch (1906) is a mathematical formula with a ¼ in kerf and ½ in of taper per 4 ft. The Virginia Cooperative Extension guide calls it the most consistent of the three and uses it as the yardstick for comparing the others.

Worked examples: board feet in a 12 in × 16 ft log shows Doyle at its worst, board feet in a 16 in × 16 ft log is the typical sawlog, and board feet in a 20 in × 16 ft log is where the rules start to agree.

Measuring a log

1. Measure the diameter at the small end, inside the bark, in whole inches. If the end is oval, average the long and short diameters.
2. Measure length in feet. Logs are bucked a little longer than their nominal length so the mill can square the ends, and that trim allowance is not scaled. How much is required depends on the buyer’s specification — the University of Washington’s log-measurement guide gives 8 in on a 32 ft log as an example, and the West-side Scribner scaling used in western Washington and Oregon allows up to 12 in on logs up to 40 ft. Ask before you cut to length.
3. Expect deductions. The log rules give gross scale, the volume from the log’s dimensions alone. A scaler then deducts for defects — rot, sweep, crook, splits, large knots, metal — to reach the net scale that is actually paid on. Hidden defects can cut the real volume a lot, so a log that looks big may scale well below the figures here.