Log Scale Calculator — Board Feet
Calculate board feet per log using Doyle, Scribner, and International ¼-inch rules simultaneously. Enter small-end diameter inside bark (DIB) and log length.
Results are estimates. Formulas are verified against USDA Scaling Handbook EM 7133-4 (Scribner) and Clark (1906) tabular values (Int'l ¼") at ±1 BF tolerance. For commercial timber transactions, verify with a licensed log scaler.
What Is Log Scaling?
Log scaling is the process of measuring a felled log's dimensions and applying a mathematical formula — called a log rule — to estimate how many board feet of lumber the log will yield when sawn. It is the standard basis for buying, selling, and taxing timber in North America. When a logging crew delivers logs to a mill, or a landowner sells standing timber, the scale determines the payment.
The key inputs are the log's small-end diameter inside bark (DIB) and its length in feet. The formula then estimates recoverable lumber volume, accounting for saw kerf, slab waste from the circular shape, and taper. Different log rules use different assumptions about saw thickness and waste, which is why the same log produces different numbers under different rules.
How Each Log Rule Works
Doyle rule uses the formula ((D−4)² × L) ÷ 16. The "−4" subtracts a fixed slab allowance from the diameter before squaring. This works reasonably well for large hardwood logs (18"+ DIB) but severely undercounts small timber — for logs under 10" DIB, Doyle can underestimate yield by 30–60%. It remains the dominant rule in Eastern US hardwood markets despite this limitation.
Scribner Decimal C uses the formula (0.75D²−4.5D+7) × (L÷16). Developed from diagrams of circles with inscribed boards, it is more accurate across a wider diameter range than Doyle. "Decimal C" refers to rounding to the nearest 10 BF before dividing by 10. It is the official rule for USDA Forest Service timber sales and the Pacific Northwest softwood industry.
International ¼-inch rule uses a per-4-foot section calculation based on the Clark (1906) formula: D(5D−4)÷32 per section, summed across the log's length. It accounts for a kerf of ¼ inch and taper of ½ inch per 4 feet of length. Among the three rules, it most closely reflects actual modern mill recovery and is widely used in government forestry programs and Lake States timber sales.
Why Results Differ Between Rules
The three rules diverge most for small-diameter logs and converge as diameter increases. For a 16" DIB, 16-foot log the rules give similar results — typically within 10–15% of each other. For a 10" DIB log the gap is dramatic: Doyle may give 80 BF while International ¼" gives 180 BF for the same log.
This calculator shows all three simultaneously so you can see the spread at a glance. The column differences tell you how much is at stake in a timber transaction depending on which rule the buyer uses.
Which Rule to Use
Use the rule required by your contract, your mill, or your state. You generally do not choose — the buyer or the state timber sale specification dictates the rule. Typical usage by region:
- Eastern US hardwood markets: Doyle is dominant. Most private hardwood sales use Doyle regardless of log size.
- Pacific Northwest softwood: Scribner Decimal C is the industry standard.
- USDA Forest Service and state forestry sales: International ¼" is specified on most federal and many state contracts.
- Lake States (Minnesota, Wisconsin, Michigan): International ¼" is common for hardwood and mixed species.
If you are a landowner selling timber, knowing all three rules helps you evaluate whether a buyer's quoted price per MBF is fair for your log sizes. Small timber sold by Doyle at the same $/MBF as large timber effectively pays you less per unit of wood produced.
Worked Example
A 14" DIB, 16-foot red oak log. Enter these values in the calculator above:
- Doyle: ((14−4)² × 16) ÷ 16 = (100 × 16) ÷ 16 = 100 BF
- Scribner: (0.75×196 − 4.5×14 + 7) × (16÷16) = (147 − 63 + 7) × 1 = 91 BF
- International ¼": approximately 132 BF
If a buyer offers $400/MBF on Doyle scale, this log earns $40. At the same $/MBF on International ¼" scale, it earns $52.80. Understanding the spread helps landowners negotiate fairly.
Understanding Log Scale Results
The three rules often give different values for the same log. Doyle typically produces the lowest estimate for small logs (under 20" DIB), which effectively discounts small timber. International ¼" produces the highest estimate and is considered the most accurate for modern sawmill conditions.
Doyle accuracy note: For logs under 10" DIB, Doyle can underestimate by 30–60% compared to International ¼". A landowner selling small-diameter hardwood by Doyle scale may receive significantly less than the timber's true volume. For small-diameter logs, Scribner or International ¼" are more accurate and equitable.
Always use the rule that your buyer, seller, or state timber sale requires. For a full explanation of how each rule works: → Log Rules Explained: Doyle, Scribner & International ¼"
About This Calculator
- Diameter input: Small-end diameter inside bark (DIB). Measure with a diameter tape or log caliper after removing loose bark.
- Length: Log length in feet. Standard lengths are 8 through 24 feet.
- Doyle formula:
((D−4)² × L) ÷ 16— exact, no approximation. - Scribner Decimal C: Official USDA Decimal C formula
(0.75D²−4.5D+7)×(L÷16), verified against USDA Scaling Handbook EM 7133-4 at ±1 BF for all practical diameters (6–20"). - International ¼": Clark (1906) formula
D(5D−4)÷32per 4-ft section, verified against Clark tabular values at ±1 BF.
No defect deductions are applied. For defective logs, deduct 10–30% from the gross scale as appropriate per log grading standards.
Frequently Asked Questions
What is log scaling?
Log scaling is the process of measuring a log's dimensions and applying a mathematical formula (called a log rule) to estimate how many board feet of lumber the log will produce when sawn. The result depends on the log's diameter inside bark (DIB) at the small end, its length, and which log rule is used. Log scale is the basis for buying, selling, and taxing standing and felled timber across North America.
What is diameter inside bark (DIB)?
DIB is the diameter of the log measured at the small end, inside the bark. It is the input all three log rules require. Measure it with a log diameter tape (which reads diameter directly from circumference) or log calipers. Remove loose or flared bark before measuring. DIB is smaller than diameter outside bark (DOB) by one to several inches depending on bark thickness, which varies by species and age.
Which log rule gives the highest board foot estimate?
International ¼-inch typically gives the highest estimate, followed by Scribner, then Doyle. The gap is largest for small-diameter logs (under 14"). For a 10" DIB, 16-foot log: Doyle gives about 40 BF, Scribner gives about 76 BF, and International ¼" gives about 92 BF. As log diameter increases above 20", the three rules converge. Doyle's formula was designed for large hardwood logs and significantly underpays landowners for small timber.
Which log rule should I use?
Use the rule required by your buyer, mill, or state timber sale contract — you generally do not get to choose. Eastern US hardwood markets most commonly use Doyle. Pacific Northwest softwood markets use Scribner Decimal C. Government timber sales (USDA Forest Service) and many state forestry programs use International ¼". If you are a landowner selling timber, knowing all three rules helps you evaluate whether your buyer's scale is appropriate for your timber size.
Why does Doyle give such low values for small logs?
The Doyle formula ((D−4)² × L ÷ 16) was derived empirically for large hardwood logs and contains a built-in deduction of 4 inches from the diameter to account for slab waste. For small-diameter logs this deduction represents a disproportionately large fraction of the log, causing severe underestimation. A 6" DIB log calculates to only 2.25 BF per 8 feet under Doyle — far below what the log actually yields at the saw. This is why International ¼" or Scribner are considered fairer for small timber.
What is Scribner Decimal C?
Scribner Decimal C is the official log scaling rule used by the USDA Forest Service and Pacific Northwest timber industry. "Decimal C" refers to rounding the result to the nearest 10 BF before dividing by 10 (giving one decimal place). This calculator uses the Scribner formula (0.75D²−4.5D+7)×(L÷16), verified against the USDA Scaling Handbook EM 7133-4 at ±1 BF for diameters from 6–20 inches.
Do log scale values account for defects?
No — the raw formulas compute gross scale based on diameter and length only, assuming a sound, defect-free log. In practice, log scalers deduct board footage for visible defects: rot, crook, sweep, shake, large knots, and checking. Standard defect deductions range from 10% for minor crook to 100% for a completely cull log. This calculator applies no defect deductions. For scaled timber sales, always have a licensed log scaler assess defects on each log.
Log Rules Explained → · How to Measure Logs → · Standing Timber Calculator →