Log Scaling Rules: Why the Same Log Gets Three Different Board Foot Counts
Timber buyers and sellers have relied on Doyle, Scribner, and International scaling rules for over 200 years. The same log can yield 64, 86, or 97 board feet depending on which rule you use — and that difference can mean thousands of dollars on a timber sale. ColfaxMath and forestry educators are driving renewed interest in understanding these formulas.
About This Calculator: Log Scaling — Doyle, Scribner & International Rule
Why: Timber buyers, sellers, and foresters need to understand how Doyle, Scribner, and International rules produce different board foot counts. The choice of rule can swing a sale by thousands of dollars. This calculator compares all three and shows who each rule favors.
How: Enter log diameter (small-end, inside bark), length, number of logs, price per BF, and grade. Select a single rule or compare all three. The calculator shows BF, dollar value, batch total, and which rule favors buyer vs seller.
📋 Quick Examples — Click to Load
📊 Rules Comparison — Board Feet
Doyle, Scribner, and International BF for your log
📈 Diameter vs Board Feet (16ft logs)
How each rule behaves across diameters — Doyle lags on small logs
📊 Value by Diameter ($0.50/BF, 16ft)
Dollar value per log by rule — biggest gap at 8–12"
🍩 Rule Difference — BF Share
Proportional BF from each rule for your log
⚠️For educational and informational purposes only. Verify with a qualified professional.
The same log can yield three different board foot counts depending on which scaling rule you use. Doyle (1825), Scribner (1846), and International 1/4-inch (1906) each use different formulas and assumptions. Doyle severely underestimates small logs, favoring buyers; Scribner and International give higher BF on small logs, favoring sellers. The timber industry relies on these rules for stumpage sales, mill payments, and contract disputes. ColfaxMath and forestry educators have driven renewed interest in understanding these differences.
Sources: ColfaxMath/YouTube, USDA Forest Products Lab, Global Timber, Cornell Forest Connect.
Key Takeaways
- • Doyle: BF = (D - 4)² × L/16 — underestimates small logs, favors buyers
- • Scribner: BF = (0.79D² - 2D - 4) × L/16 — middle ground, diagram-based origin
- • International 1/4-inch: formula-based, most consistent, tracks modern mill yield
- • On logs 24"+, all three rules converge; biggest differences at 8–12" diameter
Did You Know?
How Do Log Scaling Rules Work?
Doyle Rule
BF = (D - 4)² × L/16. The (D - 4) term is a slabbing allowance; for D ≤ 4 inches, BF = 0. The rule was designed for circular-saw mills with wide kerfs. It systematically underestimates logs under ~14 inches.
Scribner Decimal C
BF = (0.79D² - 2D - 4) × L/16. Derived from diagram-based Scribner tables. Does not account for taper; typically underestimates longer logs. Scribner Decimal C rounds to nearest 10 BF in some applications.
International 1/4-Inch Rule
Uses 1/4-inch kerf and 1/2-inch taper per 4 feet. Formula-based; divides log into 4-foot sections. Considered most consistent and closest to actual mill recovery. Preferred for federal and many state sales.
Expert Tips
Scaling Rule Comparison (12" × 16ft Log)
| Rule | Board Feet | Favors | Region |
|---|---|---|---|
| Doyle | 64 BF | Buyer (small logs) | East, South |
| Scribner | ~86 BF | Seller (small logs) | Pacific NW |
| International 1/4" | ~85–97 BF | Most accurate | Federal, many states |
Frequently Asked Questions
What is the Doyle log scale rule?
The Doyle Rule (c. 1825) estimates board feet as BF = (D - 4)² × L/16, where D is small-end diameter in inches and L is length in feet. It uses a 5/16-inch saw kerf and 4-inch slabbing allowance. Doyle severely underestimates small logs (under 12 inches) and favors buyers; it overestimates large logs and favors sellers.
What is the difference between Doyle, Scribner, and International rules?
Doyle underestimates small logs the most. Scribner (BF = (0.79D² - 2D - 4) × L/16) typically falls between Doyle and International. International 1/4-inch rule is the most consistent and tracks modern mill yield best. For a 12" × 16ft log: Doyle ≈ 64 BF, Scribner ≈ 86 BF, International ≈ 84–97 BF depending on formula.
Which log scaling rule favors the buyer vs seller?
Doyle favors the buyer on small logs (under ~14 inches) because it underestimates volume. Scribner and International give higher BF counts on small logs, favoring the seller. On large logs (24"+), all three rules converge. Timber sale contracts often specify which rule applies — know before you buy or sell.
What is board foot overrun in log scaling?
Overrun is the percentage by which actual sawn lumber yield exceeds the scaled (estimated) volume. Small logs often show 10–20% overrun vs Doyle because Doyle underestimates them. Mills may use overrun tables to adjust payments. International rule tends to match actual yield more closely, reducing overrun disputes.
How does log grade affect lumber value?
Grade multipliers adjust price per board foot: Grade 1 (select/clear) = 1.0×, Grade 2 (common) ≈ 0.8×, Grade 3 (utility) ≈ 0.6×. Premium species (walnut, cherry) command higher base prices. A 100 BF log at $2.00/BF grade 1 = $200; same at grade 3 = $120.
Where is each scaling rule used in the US?
Doyle dominates in the eastern and southern US. Scribner is common in the Pacific Northwest and some northern states. International 1/4-inch is used in federal timber sales and regions wanting consistency. Many states allow contract specification — check local forestry regulations.
Key Statistics
Official Data Sources
⚠️ Disclaimer: This calculator is for educational purposes only. Actual scaling practices vary by region, contract, and mill. Always specify the rule in timber sale agreements. Consult a licensed forester or timber buyer for professional advice. Board foot estimates do not guarantee actual sawn yield; species, defect, and mill efficiency affect recovery.