Tree Board Foot Volume & Timber Scale Log Rules Guide

Defining the Board Foot Unit: 144 Cubic Inches

In forest biometrics and the hardwood lumber industry across North America, wood volume is measured in board feet (BF or bd ft, with thousands of board feet designated as MBF). One board foot represents a solid wood volume of 144 cubic inches ($1\text{ ft} \times 1\text{ ft} \times 1\text{ in}$, or $12\text{ in} \times 12\text{ in} \times 1\text{ in}$):

When converting standing timber or bucked sawlogs into board feet, foresters measure two primary dimensions: small-end diameter inside the bark (DIB, in inches) and log length (in feet, typically standardized to 8, 10, 12, 14, or 16-foot logs plus a 3 to 4-inch trim allowance).

To calculate the economic stumpage value and appraisal volume of standing trees on your property, run your forest inventory through our standing tree stumpage value calculator.

The Doyle Log Rule: Formula and Small-Log Under-Scaling

Formulated by Edward Doyle in 1825, the Doyle rule is the most widely utilized log rule for private commercial timber sales across the eastern and southern United States. It is calculated algebraically as:

Where $D$ is the small-end diameter inside bark (inches) and $L$ is the log length (feet).

The mathematical premise of the Doyle rule deducts a fixed 4 inches from the log diameter for slab and edgings waste, then assumes the remaining core is sawn into 1-inch boards with a 25% allowance for saw kerf (sawdust). Because a 4-inch diameter deduction is proportionally colossal on small-diameter logs ($D < 20\text{ inches}$), the Doyle rule severely underestimates the true lumber yield of small logs.

Modern sawmills cutting small sawlogs routinely experience an "overrun" of 25% to 50% above the Doyle scale tally, making Doyle highly favorable to sawmill buyers and unfavorable to uninformed timber landowners.

The Scribner Log Rule: Diagram Geometry

Developed in 1846 by J.M. Scribner, the Scribner rule is a classic diagram rule widely utilized on public federal timber sales (such as USDA Forest Service contracts) and across the Pacific Northwest and northern Lake States. Rather than using an algebraic formula, Scribner drafted 1-inch board cross-sections inside full-scale circles representing log diameters, assuming a 1/4-inch saw kerf.

The Bruce and Schumacher regression formula mathematically approximates the Scribner Decimal C rule:

Scribner provides intermediate accuracy for sawlogs between 14 and 28 inches. However, because the original diagram rule did not account for natural log taper (the expanding diameter from top to butt), it still moderately under-scales logs exceeding 16 feet in length.

The International 1/4-Inch Rule: The Scientific Standard

Developed in 1906 by forester J.F. Clark, the International 1/4-Inch rule is universally recognized by academic forestry extensions and research institutions as the most scientifically accurate predictor of actual sawmill lumber recovery. Clark accounted rigorously for modern sawmill physics:

• 1/8-inch saw blade kerf plus 1/16-inch lumber shrinkage allowance (total 3/16-inch kerf, adjusted to 1/4-inch in commercial trade).
• A realistic natural trunk taper deduction of exactly 0.5 inches per 4 feet of log length.
• Calculated in 4-foot sections to mirror progressive lumber breakdown.

For a standard 16-foot log, the International 1/4-Inch formula is expressed as:

Because it accounts for taper and realistic kerf, International 1/4-Inch scale closely tracks the actual green tally of lumber coming off modern thin-kerf band saws.

Direct Comparative Scale Matrix for 16-Foot Sawlogs

Comparing volume estimates across the three rules demonstrates why specifying the log rule in a timber harvesting contract is critical:

Notice that for a small 12-inch hardwood log, a landowner selling under the Doyle rule is paid for only 64 board feet, whereas the International scale credits 100 board feet—a 36% loss in paid volume.

Frequently Asked Questions

Sources & Further Reading

1. Cassens, D. L. (2010). Log Rules and Other Useful Information. Purdue University Cooperative Extension, FNR-ENV-1-W. Purdue Forestry FNR-ENV-1-W (PDF)
2. Bond, B. (2019). Log Rules: How Much Lumber is in That Log? Virginia Cooperative Extension, Publication ANR-322P. Virginia Tech Extension ANR-322P
3. Clark, J. F. (1906). The International Log Rule. The Forestry Quarterly, 4, 79–93. doi:10.1093/jof/4.1.79
4. Avery, T. E., & Burkhart, H. E. (2015). Forest Measurements (5th ed.). Waveland Press.