Log board feet calculator: Doyle, Scribner and International ¼″

Small-end diameter (in)Log length (ft)Number of logsPrice per MBF ($)

The three log rule formulas

A log rule predicts how many board feet of 1-inch lumber a sawmill can cut from a log of a given small-end diameter D (inches, inside bark) and length L (feet). They disagree because each one assumes a different sawing loss.

Rule	Formula	What it assumes
Doyle	(D − 4)² × L ÷ 16	A flat 4-inch allowance for slabs and edgings, and a wide saw kerf. No taper.
Scribner	0.0494·D²·L − 0.124·D·L − 0.269·L (formula fit)	Boards drawn as 1-inch diagrams inside a cylinder the size of the small end, with a 1/4-inch kerf. No taper. Scribner Decimal C rounds to the nearest 10 BF.
International ¼″	0.905 × (0.22·d² − 0.71·d) for each 4-ft section	A 1/4-inch kerf, shrinkage allowance and ½ inch of taper per 4 feet: d grows by ½ inch for each section after the first.

Scribner was originally a diagram rule — its values were read off drawings, not a formula. This calculator uses the official Scribner Decimal C table values for 8, 12 and 16-ft logs of 6–30 inches, and the regression formula above (rounded to 10 BF) for other sizes, so treat Scribner results at odd lengths as close estimates. The International ¼″ results here match the published tables, which round to the nearest 5 BF; a final part-section shorter than 4 ft is counted in proportion to its length.

Worked example: one 16-inch, 16-foot log

Doyle: (16 − 4)² × 16 ÷ 16 = 12² = 144 BF. Scribner Decimal C: 160 BF (the table value 16). International ¼″: four 4-ft sections at 16, 16½, 17 and 17½ inches give 0.905 × (0.88·16² − 1.52·16 − 1.36) = 180.6, rounded to 180 BF. At $500 per MBF the same log is worth $72.00, $80.00 or $90.00 — a 25% difference that depends only on the rule in the contract.

Comparison table: 16-foot logs

Small-end diameter	Doyle	Scribner Dec. C	International ¼″	Int'l vs Doyle
6 in	4	20	20	400%
8 in	16	30	40	150%
10 in	36	60	65	81%
12 in	64	80	95	48%
14 in	100	110	135	35%
16 in	144	160	180	25%
18 in	196	210	230	17%
20 in	256	280	290	13%
22 in	324	330	355	10%
24 in	400	400	425	6%
26 in	484	500	500	3%
28 in	576	580	585	2%
30 in	676	660	675	-0%

Doyle gives a fraction of the other rules on small logs — the 4-inch slab deduction is a third of a 12-inch log — and catches up near 26–30 inches, where its square term overtakes the others. Scribner sits between them on most sizes; because it ignores taper, it falls behind the International rule more on long logs.

Board feet by length

International ¼″

Diameter	8 ft	10 ft	12 ft	14 ft	16 ft
8 in	15	20	25	35	40
12 in	45	55	70	85	95
16 in	85	110	130	155	180
20 in	135	175	210	250	290
24 in	205	255	310	370	425

Doyle

Diameter	8 ft	10 ft	12 ft	14 ft	16 ft
8 in	8	10	12	14	16
12 in	32	40	48	56	64
16 in	72	90	108	126	144
20 in	128	160	192	224	256
24 in	200	250	300	350	400

Scribner values for 10 and 14-ft logs come from the formula; 8, 12 and 16 ft use the Decimal C table.

Scribner

Diameter	8 ft	10 ft	12 ft	14 ft	16 ft
8 in	10	20	20	30	30
12 in	40	50	60	70	80
16 in	80	100	120	150	160
20 in	140	170	210	240	280
24 in	210	250	300	350	400

Why the log rules differ — and which one to use

The three rules answer the same question with different assumptions about how much of the log ends up as sawdust and slabs. Doyle (1825) is the simplest and the most conservative; it is still the standard for hardwood logs in much of the southern and midwestern United States, which is why log buyers there often pay for more lumber than they are charged for. Scribner (1846) is the official rule in much of the western United States in its Decimal C form. The International ¼″ rule (Clark, 1906) was built from mill studies, includes taper and is the closest to what a modern band or circular mill really saws, so foresters and many state agencies use it for timber sales and inventories.

The practical rule: use whatever rule the buyer, mill or timber-sale contract names, and compare prices only within the same rule. A price of $500 per MBF Doyle is worth more per log than $500 per MBF International. When you saw your own logs, expect to beat the Doyle scale on small logs — that surplus is overrun.

Metric logs

The rules work in inches and feet only. Convert a diameter in centimeters by dividing by 2.54 (40 cm ≈ 15.7 in, round down to 15) and a length in meters by multiplying by 3.281 (4.9 m ≈ 16 ft). Board feet from a log rule are a lumber-yield estimate, not the solid volume of the log; one cubic meter of sawn lumber is about 424 board feet.

How to use the calculator

1. Measure the small end. Measure the diameter inside the bark at the small end of the log, rounding down to the nearest inch. Average two diameters at right angles if the end is oval.
2. Measure the length. Measure the length in whole feet, not counting the 3–6 inch trim allowance.
3. Pick the rule. Use the rule your buyer or mill uses — compare all three here.
4. Price the log. Enter the price per thousand board feet (MBF) to see the value of the log under each rule.

Once the boards are sawn and dried, total them with the board foot calculator, convert prices with the board foot price calculator and read board feet explained.

FAQ

Which log rule gives the most board feet?

For most logs the International 1/4-inch rule gives the highest scale, then Scribner, then Doyle. Doyle catches up only on very large logs, around 26–30 inches, where it can exceed the others.

Why does Doyle underestimate small logs?

The Doyle formula subtracts 4 inches from the diameter for slabs and edgings before squaring it. On a 12-inch log that removes a third of the diameter, so Doyle scales 64 BF for a 12 × 16 ft log that will actually saw out close to 95 BF.

Where do I measure a log for scaling?

Measure the diameter inside the bark at the small end, rounded down to the nearest inch, and the length in whole feet not counting the 3–6 inch trim allowance. If the end is oval, average the long and short diameters.

What is overrun?

Overrun is the lumber a mill actually saws beyond the log scale. A log scaled at 144 BF Doyle that yields 180 BF of lumber has 25% overrun. Doyle logs often show large overrun; International 1/4-inch logs show little.