Log Scale Rules Explained: Doyle, Scribner Decimal C and International 1/4 Inch

Lumber math · Log scaling · Updated 2026-09-13

A log rule estimates how much lumber a log will give up once it has been through a saw. It is not a measurement of the wood in the log, and it is not geometry. Three rules are in common use in North America, and on the same log they return three different answers.

Doyle, Scribner Decimal C and International 1/4 inch each assume something different about saw kerf, taper and slabbing. This guide takes each rule in turn with its exact definition, puts the three side by side, and shows how far apart they land on the same log.

What a log rule actually is

A log rule is a table or a formula that predicts the board feet of sawn lumber a round log will yield, which is a different question from how much wood is in the log. A cylinder 16 in across and 16 ft long holds far more cubic volume than any rule credits it with, because the rule has already written off the sawdust, the slabs and the edgings. For the unit itself, see how to calculate board feet. Because a rule is a prediction rather than a measurement, it can be built generous or stingy, and the three in circulation disagree on three things.

• Saw kerf. How much of each cut is lost as sawdust. A rule that assumes a thick kerf predicts fewer boards from the same log.
• Taper. Whether the log is treated as a plain cylinder of its small-end diameter, or as a shape that grows toward the butt and carries extra lumber in its back half.
• Slabbing and edging. How much of the round outside is written off before the first full-width board starts.

None of the three is correct in an absolute sense. International 1/4 inch is the most accurate of them and is used as the yardstick the other two get judged against, which is why it is the reference column in the comparison table below.

Doyle: a formula, clamped at 4 in

Doyle is the simplest of the three and the only one you can do in your head. The scale in board feet is ((D - 4) squared divided by 16) multiplied by L, where D is the small-end diameter inside bark in inches and L is the length in feet. A 16 in log 12 ft long: 16 minus 4 is 12, 12 squared is 144, divided by 16 is 9, times 12 ft is 108 bf.

That flat 4 in is the whole story of the rule. On a 10 in log the subtraction removes 40 percent of the diameter before anything gets squared; on a 30 in log it removes 13 percent. The penalty is fixed in inches but logs are not, so small logs get hammered and big ones get off lightly. Doyle is the common rule in the US South and East.

Scribner Decimal C: an 1846 table, never a formula

Scribner Decimal C is a published table dating to 1846. It is not a formula, it was never derived from one, and it must never be approximated or interpolated. Every published value is a multiple of 10 board feet. If a diameter or a length falls outside the printed table, the honest answer is that the log is outside the published table, not a number you worked up on the tailgate.

The table is also not smooth, which is the second reason interpolating it fails. In the 10 in row below, 8 ft, 10 ft and 12 ft all scale at the same 30 bf, then 14 ft jumps to 40 and 16 ft to 60. Any curve you fit through those points disagrees with the printed values somewhere.

International 1/4 inch: taper built in, issued in 5 bf steps

International 1/4 inch is a formula, but unlike Doyle it does not pretend the log is a cylinder. It cuts the log into 4 ft sections and adds 1/2 in of taper to each one working from the small end toward the butt. Each section contributes 0.199 times d squared minus 0.642 times d board feet, where d is that section's own diameter, and a section that would come out negative contributes 0. The sections are added up and the result is issued in 5 board-foot steps.

1. Split the log into 4 ft sections: A 16 ft log is four sections. Work from the small end, where the scaling diameter was taken.
2. Step the diameter up by 1/2 in per section: For a 16 in small end the four section diameters are 16.0, 16.5, 17.0 and 17.5 in.
3. Score each section: 0.199 d squared minus 0.642 d gives 40.67, 43.58, 46.60 and 49.71 board feet for those four diameters.
4. Add them and round to the nearest 5: The four sections total 180.56 bf, so the log is issued at 180 bf.

The three rules on the same log

Read the last column top to bottom and the shape of the Doyle rule is plain. On a 16 ft log with a 10 in small end it credits 36 bf where International credits 65, so the seller is paid on a little over half the lumber. The gap closes as the log grows, the two cross at around 30 in, and past that Doyle runs ahead: a 16 ft log with a 40 in small end scales 1296 bf on Doyle against 1215 on International. Scribner sits between the two for most of the table, then falls behind both on the largest logs.

That is the practical consequence, and the only reason any of this matters: the rule the buyer scales on decides what the seller is paid. Sell small logs on Doyle and you are paid for roughly half of what comes off the saw. Buy large logs on Doyle and you pay for more lumber than the log holds. A mill scaling on Doyle is not cheating anyone, since the rate it quotes per thousand board feet is set with its own rule in mind. But a scale and a rate only mean something together, so find out which rule a mill scales on before you agree a price.

Three rules, one log, no arithmetic. Board Foot Calculator₊ takes a small-end diameter (or a tape measurement around the log) plus the length and returns Doyle, Scribner Decimal C and International 1/4 inch together, every result carrying its own unit label so no bare number can be misread. The log input form is free; the three scale results come with the one-time Shop Unlock, which is a purchase and not a subscription. Learn more about Board Foot Calculator₊.

How to measure a log for scaling

All three rules take the same input: diameter at the small end, inside the bark, in inches, plus length in feet. Getting that input wrong moves all three at once, so it deserves more care than the choice between them.

1. Work at the small end: A board cannot be wider than the narrowest part of the log it came out of, which is why every rule scales the small end and not the butt.
2. Measure inside the bark: Bark is not lumber. Take the reading across the wood face on the end of the log, not over the bark outside it.
3. Take two readings on an oval end: Log ends are rarely round, so a single diameter depends on where you happen to hold the stick. Two readings at right angles, averaged, is steadier.
4. Or use a tape and divide: Measured around the log, the diameter is the circumference divided by pi. A tape runs over the bark, so that figure is an outside-bark diameter and the bark has to come off it. How much depends on the species and on the log in front of you, so take it from the log rather than from a chart.
5. Record the length in feet: Diameter is inches and length is feet in all three rules. Mixing the units is the same trap that catches people in ordinary board-foot math.

Length, trim and rounding

Published log tables are printed in even 2 ft steps, which is why the Doyle and Scribner columns above run 8, 10, 12, 14 and 16 ft. Logs are commonly bucked with a few extra inches of trim so the ends can be squared, and that trim is not scaled: the scaling length is the nominal length the log was cut to, in whole feet. What happens to an odd foot is a mill convention rather than something the rules settle. Doyle is a formula and takes 13 ft happily. Scribner has no 13 ft column, and International is built on whole 4 ft sections, so somebody decides whether that log is scaled as 12 ft or as 14 ft. Ask which, and ask before the logs are on the truck.

What to settle before you agree a price

1. Which rule is being used: Doyle, Scribner Decimal C or International 1/4 inch. There is no default, and on small logs the answer moves the scale by tens of percent.
2. Where the diameter is taken: small end, inside bark, and how an oval end is averaged.
3. How length is handled: which lengths are scaled, how much trim is dropped, and which way an odd foot goes.
4. How defects are deducted. Rot, sweep and shake come off the gross scale, and how that is figured is worth hearing before it lands on your load.
5. Whether the rate quoted per thousand board feet is quoted on that same rule. A rate on one rule and a scale on another is not a comparison.

Once the logs are sawn the arithmetic turns back into ordinary board feet and no rule enters into it. The reference tables for finished lumber are in the board foot chart, and comparing one supplier's number against another is covered in lumber price per board foot. Boards and logs both run in Board Foot Calculator.

Frequently asked questions

Which log rule gives the most board feet?

For most of the sizes in the tables above, International 1/4 inch returns the most and Doyle the least. On a 16 ft log with a 10 in small end the three read 36 bf on Doyle, 60 bf on Scribner Decimal C and 65 bf on International. The order changes on very large logs: at a 30 in small end and 16 ft, Doyle reads 676 bf against 675 for International and 660 for Scribner.

Why is the Doyle rule so low on small logs?

Because Doyle subtracts a flat 4 in from the diameter before it squares anything, and 4 in is a far bigger bite out of a 10 in log than out of a 30 in one. On a 10 in log that deduction removes 40 percent of the diameter; on a 30 in log it removes 13 percent. That one fixed number is why Doyle under-scales small logs heavily and over-scales the largest ones.

Is there a formula for the Scribner log rule?

No. Scribner Decimal C is a published table from 1846 and it must not be derived, approximated or interpolated. The approximation in wide circulation, (0.79 x D squared - 2D - 4) x L/16, returns 41.25 bf for a 12 ft log with a 10 in small end, which rounds to 40 bf, while the published table says 30 bf. If your log is off the table, the correct answer is that it is outside the published table.

Do you scale a log at the big end or the small end?

The small end, measured inside the bark. All three rules are defined on the small-end diameter because a board cannot be wider than the narrowest part of the log. Measuring the butt end instead inflates every rule at once.

How do I get log diameter from a tape measure?

Divide the circumference by pi. A tape reading of 50-1/4 in around the log works out to just under 16 in of diameter. A tape runs over the bark, so deduct the bark before you scale, since all three rules want the diameter inside bark.

What does Decimal C mean in Scribner Decimal C?

Decimal C is the rounded form of the Scribner table and the one in general use. Every published value in it is a multiple of 10 board feet, which is why the 10 in row reads 30, 30, 30, 40 and 60 for 8, 10, 12, 14 and 16 ft logs instead of climbing smoothly. That rounding is part of why the table should never be interpolated.

Which log rule does my mill use?

Ask, because there is no national default. Doyle is the common rule across the US South and East, while International 1/4 inch is the most accurate of the three and is the one the other two are judged against. The choice can change the scale by tens of percent on small logs, so settle it before you agree terms rather than after the load is scaled.

Keep reading

• How to Calculate Board Feet: The Formula, Worked Examples and the Traps
• Board Foot Chart: Common Hardwood and Softwood Sizes
• Lumber Price Per Board Foot: How Hardwood Is Quoted and How to Compare Two Quotes