Doyle Log Scale Calculator: Board Feet, 3-Rule Comparison, Multi-Log Tally, and Stumpage Value for US Timber Markets
The only Doyle calculator that shows Scribner and International 1/4-inch side-by-side for the same log, auto-converts outside bark to inside bark by species, and runs a full tally session with stumpage value. Built for US foresters, timber buyers, and landowners in the eastern hardwood belt.
Measure at the small end of the log, inside the bark. Round down to nearest inch per US scaling convention.
Standard US log lengths: 8, 12, 16, or 20 ft. Use same length your mill will scale.
Select species first, then enter DOB. DIB field updates automatically with standard bark deduction.
Enter the stumpage rate your buyer quoted. Leave blank to skip value calculation.
| # | DIB | Length | Species | Doyle BF | Remove |
|---|---|---|---|---|---|
| Total BF: | 0 BF | Value: – | |||
The Doyle Log Rule: Why the American South Still Uses a 200-Year-Old Formula for Hardwood Timber
In 1825, Edward Doyle developed a log scaling formula so simple a sawmill operator could calculate board feet from a single diameter measurement using mental math or a pocket table. The formula is BF = ((D – 4)^2 times L) / 16, where D is the small-end diameter inside the bark in inches and L is the log length in feet. That formula has not changed in two centuries. Walk into any sawmill receiving yard from Georgia to West Virginia to Tennessee on any morning of the week, and there is a reasonable chance the log scaler is using a variation of this same arithmetic to determine what the logger gets paid.
The reason Doyle survived is not mathematical accuracy. Researchers at the USDA Forest Products Laboratory in Madison, Wisconsin documented as early as the 1940s that the Doyle rule systematically underestimates the board foot yield of logs under 16 inches in diameter by 20 to 50 percent compared to what a modern efficient sawmill actually produces. A 10-inch log that scales 36 board feet Doyle might yield 55 to 60 board feet of actual lumber. The Doyle rule survives because it became the legal and contractual standard across a large geographic region before better rules were widely available, and because changing a regional standard requires consensus among buyers, sellers, mills, and state forestry agencies that has never materialized in the eastern hardwood belt.
Understanding the Doyle rule and its relationship to the Scribner and International 1/4-inch rules is essential for any landowner, timber buyer, or forester operating in the United States. The stumpage price you are offered, the mill gate price on your load, and the total value of your standing timber all depend on which rule your buyer uses and how that rule compares to others. This calculator shows you all three simultaneously so you can understand the full picture before you negotiate or sign a contract.
The Doyle Formula in Plain Language
The formula works like this: take the small-end diameter inside bark, subtract 4 inches (accounting for slab loss and saw kerf), square the result, multiply by the log length in feet, and divide by 16. That division by 16 converts the result from the units of the formula to board feet based on a 16-foot standard log length. For a 12-inch log 16 feet long: (12 minus 4) equals 8, squared is 64, times 16 feet, divided by 16, equals 64 board feet. For a 16-inch log 16 feet long: (16 minus 4) is 12, squared is 144, times 16, divided by 16, equals 144 board feet.
The 4-inch constant in the formula represents the assumed slab and saw kerf loss. This was calibrated to the thick kerf circular saws and relatively inefficient milling practices common in the mid-1800s. Modern thin-kerf band saws and optimizing headrig systems recover significantly more lumber from the same log, which is why actual mill recovery consistently exceeds Doyle scale on logs under 24 inches in diameter at modern US sawmills.
Why Small-Diameter Logs Are Penalized by the Doyle Rule in Eastern US Markets
The Doyle penalty on small logs is the central economic issue in eastern US timber markets. Consider two logs: one 8 inches in diameter and one 20 inches in diameter, both 16 feet long. The 8-inch log scales at (8 minus 4) squared times 1 = 16 board feet Doyle. The 20-inch log scales at (20 minus 4) squared times 1 = 256 board feet Doyle. Now compare to International 1/4-inch scale: the 8-inch log is about 34 board feet and the 20-inch log is about 295 board feet. The ratio of Doyle to International is roughly 47% at 8 inches but 87% at 20 inches. Small logs on the Doyle scale are worth far less relative to their actual yield than large logs, which is why small-diameter timber sales in the eastern US often appear economically marginal to landowners even when the timber itself is perfectly sound.
How the Doyle Log Scale Calculator Works Through Each Input
This calculator implements the full Doyle formula with three additions that no other online Doyle calculator provides: a bark deduction tool for converting outside-bark field measurements to inside-bark scale measurements by species, a three-rule simultaneous comparison showing Scribner and International results for the same log, and a running tally session where you can accumulate multiple logs and track total board feet and stumpage value for an entire truck load or timber sale.
Small-end diameter inside bark (DIB): This is the critical measurement for all three US log rules. It is taken at the small (top) end of the log, measured on the inside of the bark. In the field, log scalers either measure inside-bark directly by pressing the graduated end of a scaling stick against the raw wood surface after the log is cut, or they measure outside-bark diameter and apply a species-specific bark deduction factor. US convention rounds the DIB measurement down to the nearest inch before applying the formula, regardless of whether the actual measurement is 11.8 inches or 11.1 inches. That rounding is built into standard US log scale tables.
Species-based bark deduction: Select the tree species and enter the outside-bark diameter, and the calculator applies the USDA Forest Products Laboratory standard bark deduction factor for that species to compute an estimated DIB. White oak with its thick, blocky bark has a deduction factor of 0.90, meaning a 12-inch outside-bark measurement becomes approximately 10.8 inches inside bark. Southern yellow pine with its thick, deeply furrowed bark has a factor of 0.86. These factors follow the tables published in USDA Miscellaneous Publication 1036 and the regional scaling manuals for major timber species in each US forest type.
Multi-log tally: Click Calculate, then Add to Tally after each log. The tally accumulates all logs entered during your session, shows the total board feet Doyle, and if you entered a stumpage price, shows the total timber value. The PDF scale ticket exports the complete tally with all log details for documentation. This mirrors the workflow a log scaler uses during a truck-weigh-in or cruise session.
Stumpage value: Enter the price per thousand board feet (MBF) that your buyer quoted and the calculator converts board feet to dollars at that rate. Timber prices in the eastern US vary widely by species, log quality, proximity to markets, and current market conditions. In the Appalachian hardwood markets, white oak sawtimber has sold anywhere from $200 to $600 per MBF Doyle in recent years depending on export market demand. Walnut consistently commands a premium. Pine sawtimber in the US South typically ranges from $150 to $350 per MBF.
Three Real Doyle Log Scale Calculations from US Timber Markets
Tennessee Landowner Evaluating a Timber Offer on Mixed Hardwoods
A landowner in Sevier County, Tennessee receives a timber bid from a local hardwood buyer offering $275 per MBF Doyle for white oak sawtimber and $180 per MBF Doyle for mixed hardwood (red maple, hickory, sweetgum). A forester helps them cruise the timber and identifies 12 white oak logs averaging 14-inch DIB at 16 feet, and 8 mixed hardwood logs averaging 10-inch DIB at 16 feet.
White oak tally: 12 logs at ((14-4)^2 x 16)/16 = 100 BF each = 1,200 BF Doyle. At $275/MBF: $330. Mixed hardwood tally: 8 logs at ((10-4)^2 x 16)/16 = 36 BF each = 288 BF Doyle. At $180/MBF: $51.84. Total stumpage value: $381.84. At International 1/4-inch scale the white oak logs would have been 132 BF each (1,584 total) and the mixed hardwoods 60 BF each (480 total), but the local market operates on Doyle.
West Virginia Logger Scaling a Load for a Panel Mill in Elkins
A logger in Randolph County, West Virginia delivers a load of mixed red oak and yellow poplar logs to a panel mill that pays on Doyle scale. The load has 6 red oak logs at 16-inch DIB, 16 feet long, and 4 yellow poplar logs at 18-inch DIB, 12 feet long. He needs to verify the mill’s scale ticket before signing.
Red oak: ((16-4)^2 x 16)/16 = 144 BF each x 6 = 864 BF. Yellow poplar: ((18-4)^2 x 12)/16 = 147 BF each x 4 = 588 BF. Total: 1,452 BF Doyle. At the mill’s posted price of $310/MBF: $450.12. He can verify the mill’s ticket against this calculation and flag any discrepancy before signing the weigh slip.
Georgia Forestry Consultant Pricing Standing Timber for a County Family Farm
A forestry consultant in Lowndes County, Georgia assesses a 40-acre stand of loblolly pine for a family farm timber sale. During the timber cruise, she identifies an estimated 180 pine logs averaging 12-inch DIB at 16 feet, representing the merchantable sawtimber volume across the stand. Local pine sawtimber markets are paying $220 per MBF Doyle at the mill, with a delivered log price of approximately $260/MBF. She uses outside-bark measurements from the cruise and applies the Southern Yellow Pine bark deduction of 0.86.
Outside-bark average: 14 inches. DIB = 14 x 0.86 = 12.0 inches. Per log Doyle: ((12-4)^2 x 16)/16 = 64 BF. 180 logs x 64 BF = 11,520 BF = 11.52 MBF Doyle. At $220/MBF stumpage: $2,534.40 gross timber value. This estimate is refined further using USDA volume tables during the formal appraisal.
Expert Tips for Accurate Doyle Log Scaling in US Timber Operations
Always Round DIB Down, Never Round Up
Standard US log scaling convention rounds the inside-bark diameter down to the nearest inch regardless of the actual measurement. A log measuring 11.7 inches DIB scales as an 11-inch log, not a 12-inch log. This is universally applied in all three log rules and all published scale tables. Using the actual decimal measurement instead of rounding down produces results that will not match a certified log scaler’s ticket and can create contract disputes at the mill receiving yard. Build this rounding step into your measurement habit: measure to the nearest half inch, then round down to the nearest whole inch before entering the diameter into any log scale calculation.
Verify Which Rule Your Buyer Uses Before Comparing Prices
A timber buyer in Georgia quoting $350 per MBF and a Pacific Northwest mill quoting $280 per MBF are not necessarily offering different prices for the same logs. The Georgia buyer almost certainly means $350 per MBF Doyle. The Pacific Northwest mill almost certainly means $280 per MBF Scribner. Because Scribner scale is typically 15 to 25 percent higher than Doyle scale on most commercial-diameter sawlogs, the $280 Scribner offer may actually represent more money per log than the $350 Doyle offer. Always ask which log rule is the basis for any timber price quote before comparing bids from different regions or different buyers who may use different scales.
Know the Break-Even Diameter Where Doyle Becomes More Favorable
At very large diameters (above 28 to 30 inches), the Doyle formula actually begins to overestimate board foot yield relative to what a modern sawmill achieves. This is because Doyle was calibrated to old-growth timber with a different taper profile than second-growth timber common today. For large-diameter logs above 24 inches, Doyle scale becomes increasingly favorable to the seller. The cross-over point where Doyle scale approaches the accuracy of International 1/4-inch scale is approximately 24 to 28 inches DIB. Below that, International scale is more accurate and more favorable to sellers. Above it, Doyle may be comparable or even slightly more favorable. The three-rule comparison in this calculator makes this dynamic visible for any log you enter.
Quick Reference: Doyle Log Scale Table for Common US Log Sizes
Board feet per log using the Doyle formula BF = ((D-4)^2 times L) / 16. Source: USDA Forest Service log scale tables and the Doyle formula as adopted in state forestry measurement standards across the US eastern hardwood belt. All values use diameter inside bark at small end, rounded to nearest inch.
| DIB (in) | 8-ft log | 10-ft log | 12-ft log | 14-ft log | 16-ft log | 20-ft log |
|---|---|---|---|---|---|---|
| 6″ | 2 | 3 | 3 | 4 | 4 | 5 |
| 8″ | 8 | 10 | 12 | 14 | 16 | 20 |
| 10″ | 18 | 23 | 27 | 32 | 36 | 45 |
| 12″ | 32 | 40 | 48 | 56 | 64 | 80 |
| 14″ | 50 | 63 | 75 | 88 | 100 | 125 |
| 16″ | 72 | 90 | 108 | 126 | 144 | 180 |
| 18″ | 98 | 123 | 147 | 172 | 196 | 245 |
| 20″ | 128 | 160 | 192 | 224 | 256 | 320 |
| 24″ | 200 | 250 | 300 | 350 | 400 | 500 |
Frequently Asked Questions About the Doyle Log Rule
Related Forestry and Timber Measurement Calculators
Legal Disclaimer and Editorial Transparency
This Doyle Log Scale Calculator implements the standard Doyle formula BF = ((D – 4)^2 times L) / 16 as published in USDA Forest Service measurement standards. Scribner Decimal C values use the standard approximation formula BF = (0.79 times D^2 minus 2D minus 4) times L/16. International 1/4-inch values use the formula BF = (0.22 times D^2 minus 0.71 times D) times L/4. All results are estimates for planning purposes. Log scale results may differ from certified mill scale tickets due to measurement rounding, bark deduction variations, log defect deductions, and scaling method differences. Species-specific bark deduction factors are based on USDA Forest Products Laboratory reference data and represent averages that may not match site-specific conditions. Stumpage price calculations are for illustration only and do not constitute a timber appraisal. For official timber sales, consult a Registered or Certified Consulting Forester and use certified log scalers. USCalculators.com is not affiliated with the USDA Forest Service or any timber company. Authority references: USDA Forest Service Forest Products Measurement; USDA Forest Products Laboratory; USDA Southern Research Station. Tool last updated August 2026.