International ¼-inch Log Rule
Judson Clark's International ¼-inch rule (1906) is widely considered the most accurate log-to-lumber predictor for modern band-saw mills. It divides the log into 4-foot segments and models taper — unlike Doyle or Scribner.
International ¼" processes the log as 4-foot segments with taper: each successive segment loses ½ inch of diameter. Modern band-mill overrun on International is typically under 5% — the most accurate prediction of the three major rules.
The International ¼-inch Formula
For each 4-foot segment of a log:
BF_segment = 0.22 D² − 0.71 D
Where D is the diameter (inside bark) at the small end of that segment. Successive segments add ½" of diameter (moving up the taper). The formula assumes a ¼-inch saw kerf and a 6% shrinkage allowance — hence "¼-inch" in the name.
Worked example (16" × 16-ft log)
Break into four 4-ft segments. Small end = 16"; next up = 16.5"; next = 17"; largest = 17.5":
- Seg 1 (D=16): 0.22×256 − 0.71×16 = 56.32 − 11.36 = 44.96 BF
- Seg 2 (D=16.5): 0.22×272.25 − 0.71×16.5 = 59.90 − 11.72 = 48.18 BF
- Seg 3 (D=17): 0.22×289 − 0.71×17 = 63.58 − 12.07 = 51.51 BF
- Seg 4 (D=17.5): 0.22×306.25 − 0.71×17.5 = 67.38 − 12.43 = 54.95 BF
- Total: ~200 BF International ¼"
(Published tables typically round this to 180 BF for a 16" × 16-ft log; the difference comes from segment-by-segment table lookups vs. formula computation.)
International ¼-inch BF Table (Standard ½" Taper)
| SED (in) | 8 ft | 10 ft | 12 ft | 14 ft | 16 ft | 18 ft | 20 ft |
|---|---|---|---|---|---|---|---|
| 8 | 25 | 32 | 40 | 47 | 55 | 63 | 72 |
| 10 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
| 12 | 60 | 75 | 90 | 105 | 120 | 135 | 150 |
| 14 | 85 | 105 | 130 | 150 | 175 | 195 | 220 |
| 16 | 115 | 145 | 175 | 205 | 235 | 265 | 295 |
| 18 | 150 | 190 | 230 | 270 | 310 | 350 | 390 |
| 20 | 195 | 245 | 295 | 345 | 395 | 445 | 495 |
| 24 | 295 | 370 | 445 | 520 | 595 | 670 | 745 |
| 28 | 415 | 520 | 625 | 730 | 835 | 940 | 1,045 |
| 32 | 555 | 695 | 835 | 975 | 1,115 | 1,255 | 1,395 |
International vs Doyle vs Scribner
For the same 16" × 16-ft log:
| Rule | BF | vs Actual Yield |
|---|---|---|
| Doyle | 144 | ~25% low (overrun) |
| Scribner | 166 | ~10% low |
| International ¼-inch | 180 | within 2-5% of actual sawn |
| Actual sawn (modern band mill) | ~185 | — |
The gap widens on smaller logs: for a 10" × 16-ft log, Doyle predicts 36 BF vs International's 80 BF — a 120% difference driven entirely by which rule you use.
Where International ¼" Is Used
- Northeast US / Appalachia — Vermont through Georgia, hardwood-heavy region.
- USDA Forest Service inventories — most FIA (Forest Inventory Analysis) data uses International.
- Academic and research forestry — the preferred scale when accuracy matters.
- Modern band-sawmill contracts — some sellers negotiate International-only pricing to avoid Doyle-driven mill overrun.
International ¼-inch FAQ
Who invented the International rule?
Judson F. Clark in 1906, in Ontario. The rule was refined for US use and standardized as "International ¼-inch" (matching typical band-saw kerf).
Why is it the most accurate?
Because it accounts for taper (unlike Scribner) and uses a modern kerf assumption (unlike Doyle's over-conservative deduction). On a well-formed log sawn on a band mill, International predicts within 5% of actual yield.
What's the ⅛-inch variant?
Same underlying method but assumes ⅛-inch kerf (extremely thin blade). Rare in commercial use; produces ~7% higher BF than the ¼-inch version.
Should I always use International if it's most accurate?
Depends on your buyer/seller. Every scale is legally valid; use whatever the contract specifies. International is best when you're paying for what actually comes out of the log.
Does it work for softwood too?
Yes — International handles softwood well, though softwood mills often quote in ⅛-inch or in cubic scale (m³) rather than board feet.
How is the ½-inch taper chosen?
It's an average for hardwood species over their merchantable stem length. Fast-growing softwood may taper less; over-mature hardwood more. Adjust in the calculator for atypical logs.