How to use it
Scaling a log
Measure the small end
Inside the bark, twice at right angles, and average the two: logs are seldom round. Purdue notes that how fractions are rounded is a decision buyer and seller must agree; the rules here take whole inches.
Measure the length
With a tape, in whole feet. Purdue warns that a log just short of a full foot is tallied at the next lower foot in hardwoods and the next even foot in softwoods. Scale a log over 20 ft as two or more logs.
Enter the number of logs
Logs of the same size; scale different sizes separately and add them.
Read all three rules
Use the one your buyer, seller or sawyer uses. If you are comparing a price in one rule with a scale in another, convert first — the rules are not interchangeable.
The three rules
| Rule | How it is made | Taper | Rounding here |
|---|---|---|---|
| Doyle | Formula: (D − 4)² × L ÷ 16; a 4-in slab allowance and, by Virginia Tech, a 5/16 in kerf | Ignored | Nearest board foot |
| Scribner Decimal C | Diagram rule: 1-in boards drawn in circles with a 1/4 in kerf; Decimal C rounds to tens | Ignored | As tabulated, nearest 10 bd ft |
| International ¼-inch | Formula from an analysis of sawing losses; 1/4 in kerf | 1/2 in of diameter per 4 ft | Nearest 5 bd ft |
From Purdue FNR-191 and Virginia Tech CNRE-201. D is small-end diameter inside bark (in); L is length (ft).
Doyle and International ¼-inch
Doyle bd ft = (D − 4)² × L ÷ 16
International ¼ (16 ft) = 0.796 D² − 1.375 D − 1.230
International ¼ (any L) = 0.04976191 L D² + 0.006220239 L² D − 0.1854762 L D + 0.0002591767 L³ − 0.01159226 L² + 0.04222222 L
- D
- small-end diameter inside bark (in)
- L
- log length (ft)
The third line is Grosenbaugh's integrated formula as Purdue gives it; the calculator uses it for every length from 4 to 20 ft and rounds to the nearest 5. Purdue's printed International table differs from it by one 5-bd-ft step in about a tenth of its cells.
Why the answers differ
| Diameter | International ¼-inch | Scribner Decimal C | Doyle |
|---|---|---|---|
| 8 in | 40 | 30 | 16 |
| 12 in | 95 | 80 | 64 |
| 16 in | 180 | 160 | 144 |
| 20 in | 290 | 280 | 256 |
| 24 in | 425 | 400 | 400 |
| 30 in | 675 | 660 | 676 |
From Virginia Tech CNRE-201, Table 1; the calculator returns the same values.
Doyle's fixed 4-in deduction for slabs and edgings is too large for small logs and too small for large ones, so it seriously underscales small logs and catches up with the others only around 30 in. Scribner, drawn board by board, rises in steps and ignores taper. International ¼-inch, which allows for taper and was built on studies of sawing losses, is the one Purdue calls probably the most accurate and Virginia Tech uses as the basis for comparison. A seller is paid more under the rule that scales the logs higher, which is why both extension guides say to agree on the rule before agreeing on a price.
A log scale is not a lumber tally
- Overrun. The lumber a mill actually saws beyond the log scale is called overrun (underrun if it is less). It depends on the rule, log size and taper, kerf, sawing practice, board thickness and more, and mills judge it from their own records.
- Defects. Rot, splits and sweep are scaled out by rules of their own; a log scale here is for a sound, straight log.
- Standing trees. Estimating board feet in a standing tree needs form-class volume tables, which this calculator does not apply.
- After sawing. Once the log is boards, measure them: board feet of sawn lumber are on the board foot calculator, and the lumber's weight while it dries on the wood weight calculator.
Before scaling a log
- Small-end diameter measured inside the bark
- Two diameters at right angles, averaged
- Rounding of fractions agreed with the other party
- Length measured with a tape, trim allowance noted
- The log rule agreed before the price
- Logs over 20 ft scaled as two or more logs
Grades and surfacing of the sawn boards are in the lumber guide, and how the sawing pattern sets the grain in wood grain. The lumber family is mapped in choosing lumber.
Sources
Formulas and tables are the extension services' own. Purdue's printed tables contain apparent misprints (for example Doyle 21 in × 15 ft printed 217 against 270.9 by its formula); the calculator uses the formulas for Doyle and International and Purdue's Scribner Decimal C table, cross-checked against Virginia Tech's 16-ft values.
- 1.
Daniel Cassens. Log and Tree Scaling Techniques (FNR-191). Purdue University Cooperative Extension Service.
Used for: Doyle, Scribner and International as the three rules in current use; the Doyle formula (D − 4)² × L ÷ 16 with D the small-end diameter inside bark and L the length in feet, ignoring taper; the Scribner diagram rule for 1-in boards with a 1/4 in kerf and no taper, Scribner Decimal C rounding to the nearest 10 bd ft (Table 2); Bruce and Schumacher's Scribner formula; the International ¼-inch rule with 1/2 in of taper per 4 ft, its equations by length rounded to the nearest 5 bd ft, lengths over 20 ft scaled as two or more logs, and Grosenbaugh's integrated formula; measuring the small end inside bark in two directions at 90° and averaging; overrun; Tables 1–3.
- 2.
James E. Johnson; revised by Jennifer Gagnon. Forest Landowner’s Guide to the Measurement of Timber and Logs (CNRE-201NP). Virginia Cooperative Extension, Virginia Tech, 2025.
Used for: The three rules compared for 16-ft logs 6–40 in (Table 1): for example 95, 80 and 64 bd ft for a 12-in log by International ¼-inch, Scribner Decimal C and Doyle; Doyle's 5/16 in kerf and 4-in slab allowance; Scribner Decimal C rounding (392 → 390); International's 1/4 in kerf and 1/2 in per 4 ft taper allowance; agreeing on the rule before trading.
About this calculator
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