Log Rules Explained: Doyle, Scribner & International ¼\

Log Scaling Basics: DIB and Why It Matters

DIB (diameter inside bark) is the log's usable diameter — the measurement taken after mentally removing the bark layer. All three major log rules use DIB at the small end of the log (the narrower end) as their diameter input. Using the small end is a conservative measurement that ensures the buyer isn't paying for wood that tapers out near the top.

In practice, a log scaler uses a scale stick or calipers across the small end of a debarked or partially debarked log. For logs that are still fully barked, bark thickness tables (by species) are used to subtract an estimated bark deduction from the outside-bark diameter.

Log scaling is distinct from board foot calculation. The board foot formula (T × W × L ÷ 12) applies to rectangular lumber only — not to round, tapered logs. To estimate yield from a log, you must use one of the log rules below.

Doyle Log Rule

The Doyle rule was devised in the 1820s and is the dominant rule in the eastern and southern United States, particularly for hardwood logs. Its longevity is due to tradition and market convention — not accuracy. Many hardwood buyers and sellers in Appalachia and the South use Doyle exclusively because that's what their counterparties expect.

Formula

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

Worked Example — Doyle

A 16-inch DIB, 16-foot hardwood log:

((16 − 4)² × 16) ÷ 16 = (12² × 16) ÷ 16 = (144 × 16) ÷ 16 = 144 board feet

A 10-inch DIB, 12-foot log:

((10 − 4)² × 12) ÷ 16 = (36 × 12) ÷ 16 = 432 ÷ 16 = 27 board feet

Doyle Scale Table

Accuracy & Known Biases

Doyle underestimates small logs (under 20" DIB) — sometimes by 30–50% for logs under 12". It overestimates large logs (over 28"). For logs in the 20–24" range, Doyle comes close to actual yield under traditional thick-kerf sawing.

The underestimation of small logs effectively functions as a market discount for sellers of small-diameter timber. Despite this bias, Doyle remains prevalent in hardwood markets because of long-standing tradition — buyers and sellers both understand the implicit adjustment. Logs smaller than D=4" yield 0 board feet by the formula.

Scribner Log Rule (Decimal C)

The Scribner rule was developed by J.M. Scribner in the 1840s. It was originally based on scaled diagrams showing how boards could be laid out inside a log's cross-section — a graphical rather than formula-based approach, which is why its values come from tables rather than a clean equation. The Scribner Decimal C version (which rounds values to the nearest 10 and records them as tenths) is the version used today, particularly in the Pacific Northwest for softwood logs.

Formula (Approximate)

The authoritative Scribner values come from published tables, not a clean formula. An approximate expression for Scribner Decimal C:

⚠ This is a polynomial approximation, not the official table. Verify against the USDA Scaling Handbook before use in commercial transactions.

Worked Example — Scribner (Approximate)

A 14-inch DIB, 16-foot log:

(0.79 × 14² − 2×14 − 4) × (16 ÷ 16) = (0.79 × 196 − 28 − 4) × 1 = (154.84 − 32) = ≈ 123 BF (verify against official table)

A 10-inch DIB, 12-foot log:

(0.79 × 100 − 20 − 4) × (12 ÷ 16) = (79 − 24) × 0.75 = 55 × 0.75 = ≈ 41 BF (verify against official table)

Accuracy & Known Biases

Scribner is generally more accurate than Doyle for small-to-medium logs. It was derived empirically based on actual sawmill diagrams and reflects yield better for traditional thick-kerf sawing. Modern thin-kerf sawing typically outperforms Scribner estimates on large logs — meaning the actual yield exceeds what Scribner predicts, which benefits the buyer.

The Pacific Northwest timber trade uses Scribner as its primary scaling rule for most commercial softwood transactions. State and federal timber sales in Oregon, Washington, and California typically specify Scribner Decimal C.

International ¼-Inch Log Rule

The International ¼-inch rule was developed by L.P. Clark in 1906 and refined by L.R. Grosenbaugh in 1952. It is considered the most mathematically rigorous of the three rules for estimating actual sawn yield under modern sawmill conditions. Unlike Doyle (a single formula) or Scribner (empirical tables), the International rule explicitly accounts for log taper by computing board feet in successive 4-foot sections from the small end.

There is also an International ⅛-inch variant for thin-kerf bandsaws, which produces higher estimates because it assumes less material is lost to sawdust.

Formula (Grosenbaugh Polynomial, per 4-ft section)

Where D = small-end diameter inside bark (inches). Sum the sections for total log volume. For a 16-ft log: compute 4 sections and sum them.

⚠ The coefficients 0.22 and 0.71 are from Grosenbaugh (1952). Results may differ from official USDA tables by 10–15% for some diameters. Verify against the USDA Forest Service Scaling Handbook (EM 7133-4) before use in commercial transactions.

Worked Example — International ¼"

A 12-inch DIB, 16-foot log (four 4-ft sections, all using small-end DIB = 12"):

BF per section = 0.22 × 12² − 0.71 × 12 = 0.22 × 144 − 8.52 = 31.68 − 8.52 = 23.16 BF

Total (4 sections) = 23.16 × 4 = ≈ 92.6 BF (verify against official table)

Compare: the same 12" × 16' log gives 64 BF by Doyle — International ¼" yields ~44% more for this size.

Accuracy & Known Biases

The International rule consistently produces higher estimated yields than Doyle or Scribner for small logs and is considered most accurate for modern sawmills. It is the preferred rule for timber cruise estimates and forestry research. It is used as the standard in the US Lake States, the Northeast, Canada, and by many consulting foresters nationwide.

The International ⅛-inch rule (thinner kerf) gives even higher estimates — appropriate only for bandsaw mills where actual kerf approaches ⅛ inch.

Side-by-Side Comparison

Example values for common log sizes (verify all against USDA Scaling Handbook for commercial use):

The pattern holds across diameters: for most log sizes, Doyle < Scribner < International ¼". The gap is largest for small logs (8–12" DIB) where Doyle can be 40–50% below International ¼". All three rules converge more closely for very large logs (20"+).

→ Use the Log Scale Calculator to see all three rules side by side for any log

Which Log Rule Should You Use?

Use the rule that your buyer, seller, or state regulatory body specifies. When in doubt, International ¼" gives the most accurate estimate of modern sawmill yield but may not be accepted by counterparties who trade in Doyle or Scribner.

Legal & Commercial Context

The choice of log rule is not just a technical preference — it is a contractual matter. Timber sale contracts, state forestry board regulations, and private log purchase agreements all specify which rule governs the transaction. Misunderstanding which rule applies can result in significant financial disputes:

• A seller using Doyle expects to receive less per log than a buyer using International ¼". If the contract doesn't specify, both parties may calculate different totals from the same logs.
• State timber sales on public lands (USFS, BLM, state forestry) always specify the scaling rule. On federal timber sales, the contracting officer and a certified log scaler apply the official rule — substituting your own calculation is not permitted.
• When buying standing timber or logs from private landowners, always agree on the log rule in writing before scaling begins. This prevents post-transaction disputes about volume and payment.

Sources: USDA Forest Service General Technical Report PNW-GTR-251, Grosenbaugh L.R. (1952), NHLA Grading Rules, USDA Forest Service Scaling Handbook EM 7133-4.