Log rule · 1837

Doyle Log Rule

The Doyle log rule, published in 1837, remains the dominant scale for US Midwest and Southern hardwood mills — even though it undervalues small logs by up to 40%. Here's the formula, the full BF table, and why the industry still uses it.

Calculate Now ↓

Doyle formula: BF = ((D − 4) ÷ 4)² × L — where D is small-end diameter inside bark (inches) and L is log length (feet). The formula is deliberately conservative to favor the sawmill buyer.

Formula

The Doyle Formula

BF = ((D − 4) ÷ 4)² × L

Where:

D = small-end diameter inside bark, in inches
L = log length in feet
BF = predicted lumber yield in board feet

The formula treats the log as if it were a rectangular block with sides of (D − 4)/4 inches — essentially assuming a 1-inch slab is lost per side to slabs, kerf, and shrinkage. That deduction is proportionally huge on small logs and negligible on large ones, which is why Doyle famously under-scales anything under 16".

Worked example

For a 16" × 16 ft log:

D − 4 = 12
12 ÷ 4 = 3
3² = 9
9 × 16 = 144 BF Doyle

The same log actually mills out closer to 180–220 BF on a modern band saw — this is the famous "Doyle overrun."

Full Table

Doyle BF Table — by Diameter and Length

SED (in)	8 ft	10 ft	12 ft	14 ft	16 ft	18 ft	20 ft
8	8	10	12	14	16	18	20
10	18	22	27	32	36	40	45
12	32	40	48	56	64	72	80
14	50	62	75	88	100	112	125
16	72	90	108	126	144	162	180
18	98	122	147	171	196	220	245
20	128	160	192	224	256	288	320
22	162	202	243	283	324	364	405
24	200	250	300	350	400	450	500
28	288	360	432	504	576	648	720
32	392	490	588	686	784	882	980

History

Why the Industry Still Uses Doyle

Doyle's under-scaling of small logs feels like a bug — but it's the reason mill buyers love it. When a mill buys logs on Doyle and sells lumber on International ¼-inch, the difference (called overrun) becomes pure margin.

The Doyle overrun ratio

10" small-end log: Doyle predicts 36 BF; modern mill actually saws ~85 BF. Overrun = ~135%.
16" small-end log: Doyle predicts 144 BF; mill saws ~180 BF. Overrun = ~25%.
24" small-end log: Doyle predicts 400 BF; mill saws ~455 BF. Overrun = ~14%.
32" small-end log: overrun drops toward zero — Doyle becomes accurate at very large diameters.

Regional dominance

Doyle is the standard scale in:

Ohio, Indiana, Kentucky, Tennessee, West Virginia
Missouri, Arkansas, most of the Ozarks
Alabama, Mississippi, Georgia, the Carolinas (traditional hardwoods)

Sawmills in these regions grew up on Doyle, invoicing formats are built around it, and switching would require rewriting how every buyer, seller, and forester communicates.

Landowner's rule of thumb

If you're selling logs and the buyer scales in Doyle, expect to see a much lower BF number on the ticket than you'd get from a tape measure. That's not the buyer cheating — it's the rule doing what it was designed to do. Ask about payment on International ¼-inch if you want a scale that more closely matches sawn output.

FAQ

Doyle Rule FAQ

Who invented the Doyle rule?

Edward Doyle published the formula in 1837 as part of a scaling manual. The rule takes his name and has stayed essentially unchanged for nearly 200 years.

Why does Doyle undervalue small logs?

The formula deducts (D − 4)/4 inches from each side of the log to account for slab and kerf. On a 10" log that deduction is 60% of the diameter; on a 30" log it's only 20%.

What is Doyle overrun?

The extra lumber a modern band-saw mill produces beyond the Doyle prediction. Typical: 25–40% on 16" logs, 100%+ on 10" logs, single digits on 30" logs.

Is Doyle used in Canada?

Rarely. Canada mostly uses metric cubic-meter scaling for softwood and Ontario Rule / International for hardwood.

Is Doyle better or worse than Scribner?

Neither — different assumptions. Doyle is more conservative on small logs; Scribner is closer on medium-large logs. International ¼-inch beats both for accuracy on modern mills.

How do I convert Doyle BF to actual sawn BF?

Multiply by 1.25–2.0 depending on log size. Small logs (10-12") need ~1.8-2.0; large logs (24"+) need ~1.1-1.2. For budgeting, use 1.5× as a middle estimate.

Scribner Log Rule
International ¼-inch Log Rule
Main Board Feet Calculator — Log mode with all rules
Standing Tree BF Estimator
MBF Calculator

SED (in)	8 ft	10 ft	12 ft	14 ft	16 ft	18 ft	20 ft
8	8	10	12	14	16	18	20
10	18	22	27	32	36	40	45
12	32	40	48	56	64	72	80
14	50	62	75	88	100	112	125
16	72	90	108	126	144	162	180
18	98	122	147	171	196	220	245
20	128	160	192	224	256	288	320
22	162	202	243	283	324	364	405
24	200	250	300	350	400	450	500
28	288	360	432	504	576	648	720
32	392	490	588	686	784	882	980

SED (in)	8 ft	10 ft	12 ft	14 ft	16 ft	18 ft	20 ft
8	8	10	12	14	16	18	20
10	18	22	27	32	36	40	45
12	32	40	48	56	64	72	80
14	50	62	75	88	100	112	125
16	72	90	108	126	144	162	180
18	98	122	147	171	196	220	245
20	128	160	192	224	256	288	320
22	162	202	243	283	324	364	405
24	200	250	300	350	400	450	500
28	288	360	432	504	576	648	720
32	392	490	588	686	784	882	980