Introduction
Every board-foot number the calculator produces comes from a formula – and each formula bakes in assumptions about saw kerf, slab loss, and taper that were argued over decades ago. Understanding what Doyle, Scribner, and the International 1/4-inch rule actually compute is what separates someone who trusts the number from someone who can defend it in a negotiation. The arithmetic is simple; the meaning behind it is the valuable part.
The Log Board Feet Calculator evaluates all three formulas from two inputs: the log’s small-end diameter inside the bark (D, in inches) and its length (L, in feet). This guide derives each formula step by step, explains why the three disagree, and works a full example by hand so you can verify the calculator – or a buyer’s tally sheet – with nothing but a pencil.
What All Three Formulas Share
Every log rule answers the same question: given a log of diameter D and length L, how many 1-inch-thick boards can a mill recover? Each estimates the usable cross-section (the part that becomes boards, not slabs or sawdust), multiplies by length, and converts to board feet, where 1 board foot = 144 cubic inches. All three use D = small-end diameter inside bark in inches, L = length in feet. The odd-looking constants fold the unit conversions into the formula – just enter inches and feet as measured.
Doyle: (D – 4) squared x L / 16
Doyle imagines the log as a square cant fitting inside the cross-section, minus a fixed allowance for slabs and edging:
- Subtract 4 from the diameter. The formula assumes 4 inches are lost to slabs, edging, and kerf – the same 4 inches on a 10-inch log as on a 30-inch log. This fixed deduction is the source of Doyle’s small-log bias.
- Square the result to get the cant’s cross-section in square inches.
- Multiply by L and divide by 16 to convert to board feet.
By hand for D = 16, L = 12: (16 – 4) = 12; 12 squared = 144; 144 x 12 = 1728; 1728 / 16 = 108 BF. Verified.
The small-log problem is visible in the arithmetic: on a 10-inch log the 4-inch deduction removes 40 percent of the diameter before squaring, which compounds – (10 – 4) squared = 36 versus 100 without the deduction. On a 30-inch log the same 4 inches is only 13 percent. Doyle is fair on big logs and punishing on small ones, by construction – the errors this bias invites are in the common mistakes guide.
Scribner: (0.79 x D squared – 2 x D – 4) x L / 16
Scribner Decimal C originated as a published table of boards fitting inside log cross-sections; the formula is the standard algebraic approximation.
- 0.79 x D squared estimates the usable cross-section – about 79 percent of the full circular area.
- Subtract 2 x D and 4 for kerf and slab loss, scaled with diameter rather than Doyle’s flat penalty.
- Multiply by L, divide by 16 – the same board-foot conversion.
Worked by hand for D = 16, L = 12: 0.79 x 256 = 202.24; minus 32, minus 4 = 166.24; x 12 = 1994.88; / 16 = 124.68 BF, about 125 BF. Verified.
Because deductions scale with diameter, Scribner treats small logs far more fairly: on a 10-inch, 8-foot log it reads about 28 BF where Doyle reads 18. Published tables round to the nearest 10 BF (“Decimal C”), so printed values can differ from the formula by a few board feet. The cost guide converts these volumes into dollars per log.
International 1/4-inch: (0.04976 x D squared – 0.18573 x D – 0.01120) x L
Developed by the US Forest Service, the International rule models an actual sawing process – 1/4-inch kerf, standard board thicknesses, taper allowance – with the geometry encoded in its published coefficients:
- Compute each term: 0.04976 x D squared (usable cross-section), minus 0.18573 x D (kerf and edging, scaled to diameter), minus 0.01120 (small constant correction).
- Multiply by L. No division by 16 – the coefficients already include the board-foot conversion; L is still in feet.
By hand for D = 16, L = 12: 12.73856 – 2.97168 – 0.01120 = 9.75568; x 12 = 117.07 BF, about 117 BF. Verified.
The International rule is generally regarded as closest to actual mill recovery because it models kerf and taper explicitly – which is why government timber sales default to it.
Why the Three Disagree: A Side-by-Side Proof
| Log (16 ft long) | Doyle | Scribner | International 1/4 in | Doyle vs Scribner gap |
|---|---|---|---|---|
| 10 in | 36 BF | 55 BF | 50 BF | -35% |
| 16 in | 144 BF | 166 BF | 156 BF | -13% |
| 24 in | 400 BF | 403 BF | 387 BF | -1% |
| 32 in | 784 BF | 741 BF | 720 BF | +6% |
The math tells the story: Doyle’s fixed 4-inch deduction dominates small diameters and fades on large ones, so the rules converge as logs get bigger. On a 10-inch log the rule choice moves the answer by more than a third; on a 32-inch log the three agree within a few percent.
Unit Consistency and Metric Cross-Checks
All three formulas demand inches for diameter and feet for length. Entering a 40 cm diameter as “40” implies a 40-inch log – an error of 6x that still looks like a confident number. Convert first: cm / 2.54 = inches, m / 0.3048 = feet.
Metric cross-check for the worked example: 16 inches = 40.64 cm, 12 feet = 3.6576 m, and 108 BF x 0.0023597 = 0.2548 cubic meters. As a sanity check against the metric Smalian formula (volume = average end area x length): a 40.64 cm log has a cross-section of about 0.1297 m2, times 3.6576 m = 0.474 m3 gross – and 0.255 m3 of boards from 0.474 m3 of round log is a plausible 54 percent recovery, confirming the Doyle figure is in the right neighborhood.
Rounding and Precision
Board-foot estimates are planning numbers. Round each log to the nearest whole board foot; rounding a full tally to the nearest 10 BF is common trade practice. Do not carry two decimal places into a negotiation – false precision undermines credibility. For field techniques that feed clean inputs into these formulas, see the estimating guide.
Related Guides
- Complete Guide – log board feet basics, the three scales, and a full worked example.
- Cost Guide – typical log prices per MBF and what moves them up or down.
- Estimating Guide – how to measure diameter and length accurately in the field.
- Common Mistakes – the errors that distort scale results, with fixes.
- FAQ – quick answers to the most asked log-scaling questions.
- Pro Tips – practical advice for buying, scaling, and milling logs.
Frequently Asked Questions
What is the Doyle log rule formula?
(D – 4) squared x L / 16, with D the small-end diameter inside bark in inches and L the length in feet. A 16-inch, 12-foot log scales (16 – 4) squared x 12 / 16 = 108 BF.
What is the Scribner log rule formula?
(0.79 x D squared – 2 x D – 4) x L / 16 – the standard approximation of the Scribner Decimal C tables, fairer than Doyle on small logs.
What is the International 1/4-inch log rule formula?
(0.04976 x D squared – 0.18573 x D – 0.01120) x L, using the standard published coefficients. It assumes 1/4-inch kerf and accounts for taper.
Why does Doyle underestimate small logs?
Its fixed 4-inch deduction is proportionally enormous on a small diameter – 40 percent of a 10-inch log versus 13 percent of a 30-inch log – and squaring compounds the penalty.
Which formula is most accurate?
The International 1/4-inch rule generally tracks actual mill recovery most closely, because it models kerf and taper explicitly. Doyle is the most conservative on small logs.
Can I use metric inputs in these formulas?
Convert first: centimeters / 2.54 = inches, meters / 0.3048 = feet. Metric alternatives like the Smalian formula estimate gross log volume rather than board-foot yield – a related but different question.
Get Your Number
The formulas are simple – square the usable diameter, adjust for kerf and slab, multiply by length – but the assumptions inside them decide real money. Work one log by hand using the steps above, confirm the Log Board Feet Calculator matches your arithmetic, and you will never again have to take a buyer’s tally sheet on faith. Verify the math, verify the scale, then talk price.
Disclaimer: Calculator results are planning estimates based on the dimensions you enter. The Scribner formula approximates published tables and may differ by a board foot or two from printed values. Actual lumber recovery varies with species, log quality, defects, and sawing method – verify volumes with your buyer, mill, or a professional scaler for commercial decisions.
