Three rules, one log, very different answers
A log rule is an estimate of what a log will saw out, and the three in
use were built on different assumptions in different centuries. On an
ordinary 16 inch sawlog they differ by around a fifth. Which one your
buyer scales by is worth more than how carefully you measure.
16 ft logs, gross scale
From this calculator. Scribner is the Bruce and Schumacher approximation; the other two are computed exactly and reproduce their published tables.
Read down the Doyle column. It is 45% below International on a
10 inch log and catches up as the log gets bigger — that is the rule's
known behaviour, not a quirk of this page: it takes a flat 4 inches off
the diameter for slabs, which is far too much on a small log.
Scribner is a table, not a formula
This is the part every other calculator gets quietly wrong. Doyle and
International are formula rules — real equations you can
evaluate. Scribner is a diagram rule: somebody drew sawing
patterns onto circles, one diameter at a time, counted the boards, and
published a table. There is no exact formula to compute.
So what you see labelled "Scribner" online is an approximation to that
table. Ours is named — the Bruce and Schumacher approximation — and it
can sit around 10 board feet off the published Decimal C figure. It is
here so you can compare rules. Scale a sale from the printed table.
How the two exact rules work
Doyle — squares the log into a cant
BF = [(d − 4) ÷ 4]² × L
International ¼ in — 4 ft cylinders, each ½ in larger
per cylinder: 0.22 d² − 0.71 d
× 19/21 for the ¼ in kerf, rounded to 5 bf
d = small-end diameter inside bark, inches
L = length, feet
The International construction matters. The simplified form that
circulates — 0.20 d² − 0.71 d — misses the published table at 10, 16 and
20 inches. Building it from the 1/8-inch formula and applying the kerf
factor reproduces every diameter checked.
What this does not do
- Defects. Gross scale only. A scaler deducts for rot, sweep and crook, and the net can be far lower.
- Odd lengths. International scales whole 4 ft sections; the remainder is trim.
- Bark. Measure inside it, at the small end.
The rest of the job
Once the log is boards, the
board foot calculator
handles what you are billed for and converts between square feet and
board feet. The
lumber weight calculator
tells you what the stack weighs by species and moisture, and the
cut list optimiser lays
sheet goods out. Firewood rather than lumber? The
cord calculator
measures stacked wood instead.
Common questions
How do you calculate board feet in a log?
You do not calculate it, you scale it — and which rule you scale by changes the answer by a fifth. Measure the diameter at the small end, inside the bark, and the length; then apply Doyle, Scribner or International 1/4-inch. Doyle takes 4 inches off the diameter for slabs and squares what is left. International treats the log as 4-foot cylinders that each grow half an inch, which is why it is the rule the others get compared against. This page runs all three at once, because the difference between them is the thing worth knowing.
Which log rule should I use?
The one your buyer uses — you rarely get a choice, and it is worth more than any measurement you take. Doyle is common in the US South and badly under-scales small logs: on a 10 inch log it comes out about 45% below International. Scribner sits in the middle. International 1/4-inch is the most consistent and is the usual basis of comparison. If you are selling on Doyle, bucking to fewer, larger logs is worth real money; if you are selling on International, it matters much less.
Is Scribner really an approximation here?
Yes, and it is worth being blunt about it because nobody else is. Scribner is a diagram rule, not a formula: sawing patterns were drawn on circles for each diameter and tabulated, then rounded to the nearest 10 board feet. There is no exact formula to compute. Every online calculator that offers "Scribner" is running an approximation to the table, and this one names which — Bruce and Schumacher. At 16 inches and 16 feet it returns about 170 board feet against a published Decimal C figure of 180. Use it to compare rules; scale an actual sale from the printed table.
Is the International figure exact?
It reproduces the published table at every diameter checked. It is built from the 1/8-inch formula multiplied by 19/21 for the wider kerf, which is how the rule is actually constructed — not from the simplified "0.20 d² − 0.71 d" that circulates online. That simplification misses the published table at 10, 16 and 20 inches on a 16 foot log, returning 60, 175 and 285 against a published 65, 180 and 290. Small errors, but errors in a number somebody is paid on.
Why does my 15 foot log scale as 12?
Because International scales in whole 4-foot sections, and so does a scaler. The remaining 3 feet is trim allowance rather than volume. If you have length to spare, bucking to a clean multiple of 4 feet is free board feet.
Does this account for defects?
No. This is gross scale. A real scaler deducts for rot, sweep, crook, shake and every other defect, and the net figure can be a great deal lower than the gross. Treat this as the ceiling for a sound log of that size.
Sources
Doyle and International are FORMULA rules and are computed exactly. Scribner is a DIAGRAM rule — a sawing pattern mapped onto a circle and tabulated, not a formula — so what every calculator on the web calls Scribner is really an approximation to it. This one is named: Bruce and Schumacher. At 16 in and 16 ft it returns about 166 board feet against a published Decimal C figure of 180, so it is offered as an approximation and labelled as one; a sale should be scaled from the printed table. The International 1/4-inch figure is built from the 1/8-inch formula multiplied by 19/21 (0.904762) for the wider kerf, NOT from the simplified 0.20 d2 - 0.71 d form that circulates. The simplified version misses the published table at 10, 16 and 20 in on a 16 ft log (60, 175 and 285 against a published 65, 180 and 290); the construction used here reproduces all four checked diameters exactly.
Unit conversions are exact by definition and need no source.
How we choose and cite these figures
