Every log-scale calculator online plugs a diameter and a length into a published rule and prints one number. That number is an estimate of what a mill would pay you for, not what comes off the mill. LogYield lays real boards across the small end of your log at your thickness and your saw's kerf, drops the ones too narrow to bother with, and reports the board feet that actually result β then puts that figure next to Doyle, Scribner Decimal C and International ΒΌ-inch so you can see the overrun. A 12-inch, 16-foot log scales 64 board feet on Doyle and gives 107 sawn 4/4 on a standard-kerf band mill. That two-thirds gap is the whole argument, and it is why Doyle is the rule the buyer prefers on small logs.
The log on your deck
Enter a diameter and a lengthThe cut
Left: the small end with the sawing plan laid on it. Right: the taper you are not being paid for, and where the cubic feet of the log actually go.
Board tally
Every board the pattern produces, by finished width.
Against the scale rules
Overrun is (mill tally − log scale) Γ· log scale. Positive means the log gave you more lumber than the rule said it held. Two things to know about the figure below: it is against gross scale, so a log with rot or shake would show more overrun against its lower net scale; and the tally is constant-width boards governed by the small end, so the taper bonus reported above is not in it.
Where to put the opening face
Board feet against the position of the cut lattice, swept through one full pitch. The flat steps are where a board is either fully in or fully out.
Why a log rule and a mill tally disagree
A log rule is a nineteenth-century prediction of how much lumber a log would give on the equipment of the day. Three of them are still in daily use in the United States, they disagree with each other by a factor of two and a half on an 8-inch log, and none of them knows what saw you own. The difference between what the rule says and what you stack is overrun when you get more and underrun when you get less β one formula, not two, with a negative answer being the underrun case.
The three rules
BF = ((D − 4) / 4)Β² Γ L
BF = 0.905 Γ Ξ£ (0.22Β·Dα΅’Β² − 0.71Β·Dα΅’), Dα΅’ = D + 0.5Β·i
table lookup, rounded to the nearest 10 board feet
Doyle subtracts 4 inches from the diameter before it does anything else. That deduction was meant to cover slabbing, and on a 30-inch log it is a small fraction of the log. On a 10-inch log it is nearly half the diameter, and because the term is squared the error compounds. Doyle is not wrong so much as calibrated for one log size and applied to all of them β which is why the practitioner complaint about Doyle is always about small logs and never about big ones.
Scribner is the oldest of the three and was drawn rather than derived: circles of board cross-sections sketched inside circles of log diameter, with an allowance for the saw. Because it was drawn per diameter it has no smooth behaviour between sizes, which is why it is always published as a table and never as an equation. Decimal C is the version that rounds every value to the nearest 10 board feet so scalers could tally in tens in the woods. Note that a second, genuinely different Scribner exists β the Northwest Log Rules Advisory Group's West Side rule β and it disagrees with the table used here in a handful of small-log cells. If you scale on the Pacific coast, check which one your buyer means.
International ΒΌ-inch is the only one of the three built from a real volume model: it scales each 4-foot section as its own cylinder, adds Β½ inch of taper per section going up from the small end, and subtracts a specific saw kerf, a specific shrinkage allowance and a slab allowance proportional to diameter. The 0.905 factor converts the original β -inch-kerf form to the ΒΌ-inch one β at ΒΌ-inch kerf a 1-inch board eats 21/16 of an inch of log instead of 19/16, and 19/21 is 0.905.
It is the rule forest researchers use as the yardstick, and this tool gives an unusually direct demonstration of why. Across every diameter from 8 to 32 inches, the pattern yield here sits 7 to 12 % above International and never drifts outside that band β while the same comparison against Doyle swings from +167 % to +6 %. A volume model written in 1906 and a board-packing model written from scratch agree to within about a tenth over a four-fold range of log size. Neither was tuned to the other.
What this tool does instead
It draws your log's small end as a circle and lays a lattice of cuts across it. Each cut removes a slice of wood the width of your kerf. Between the cuts sit boards of your sawn thickness. For each board it asks the only question that matters:
w = 2Β·β(rΒ² − yfarΒ²), yfar = max(|yβ|, |yβ|)
BF = tnominal Γ w Γ L / 12
The far face governs, and this is the one piece of geometry the whole tool rests on. A square-edged board is a rectangle in cross-section. For that rectangle to sit inside the log, all four of its corners must be inside the circle β and the binding corners are the two on the face farther from the centre. Using the board's centreline, which is the intuitive choice, overstates every board that is not centred on the pith.
Boards narrower than your minimum are drawn in grey and left out of the tally. The leftovers outside the outermost boards are slab; the material between the sawn width and the full chord is edging. Both are shown, because on a small log they are a bigger share of the volume than most people expect.
Kerf is not a rounding error
A 0.085-inch band kerf and a 9/32-inch circular kerf sound like the same order of thing until you count the passes. Sawing a 20-inch log into 4/4 takes fifteen cuts on the circular saw. Fifteen passes at 9/32 inch is over four inches of solid wood turned into sawdust, and every inch of it comes out of the middle where the wide boards live β the model puts it at 20 % of the cross-section against 7 % for the band. The kerf figure in the results is the volume the blade removed, expressed in board feet so it is directly comparable to the tally beside it.
Why the opening-face offset matters
The cuts are a fixed-pitch lattice: thickness plus kerf, repeating. Sliding that lattice sideways by a fraction of an inch does not change the pitch, but it changes where the outermost board falls relative to the edge of the log β and that board is often the one that is just barely wide enough, or just barely not. The scan below the tally sweeps the lattice through one full pitch so you can see the steps. This is the practical core of the Forest Products Laboratory's Best Opening Face work: the same log, the same saw, and several percent of yield decided by where the first cut lands.
What this tool does not do
It models one pattern β through-and-through, every cut parallel, the log never turned. Real sawyers grade-saw: they open a face, read it, rotate the log and chase the clear wood. Grade sawing usually yields fewer board feet and considerably more money. Treat the number here as the yield of this pattern on this log, not as the yield of the log. There is also no price output anywhere in this tool, deliberately β log and lumber prices are local, seasonal and species-specific, and a calculator that pretended otherwise would be quoting you a market it cannot see.
Log rule reference
The three rules side by side for standard log lengths, with the pattern yield your current mill and thickness settings would give on the same log.
| Dia (in) | Doyle | Scribner C | Int'l ΒΌ | This pattern | Overrun vs Doyle |
|---|
Board feet. Scribner Decimal C values are the published table, which is rounded to the nearest 10 board feet by construction β that rounding is the rule, not an approximation of it.
Kerf by saw type
| Saw | Kerf (in) | Typical range | Note |
|---|
Questions sawyers actually ask
Why does Doyle scale so low on small logs?
Because it subtracts a flat 4 inches from the diameter and then squares the result. On a 24-inch log that deduction removes a sixth of the diameter; on an 8-inch log it removes half, and squaring turns half into a quarter. A 10-inch, 12-foot log scales 27 board feet on Doyle and 45 on International β the rule is claiming the log holds barely more than half of what a volume model says it holds. Run both in the table above and watch the gap close as the diameter grows: the two rules cross at about 30 inches, and above that Doyle reads high. Doyle is not broken; it is calibrated for large logs and still applied to small ones. Its documented fault is that the 4-inch slab deduction is a constant, while real slab and edging waste grows with diameter.
How many boards will I get out of a 20-inch log?
On a standard-kerf portable band mill sawing 4/4 through-and-through, a 20-inch small-end log gives 16 boards 3 inches wide or better, about 235 board feet, with the widest running 19 inches. Change one thing and that changes. Load a 9/32-inch circular saw instead and you are down to 14 boards and 203 board feet β two boards and 32 board feet eaten by the blade. Saw 8/4 rather than 4/4 and you get eight thicker boards and slightly more total footage, 242, because you make half as many kerfs. Enter your own numbers above rather than trusting the round figure: board count is sensitive to thickness first, kerf second, and where the first cut lands third.
Is my saw's kerf really worth worrying about?
Yes, and it scales with the number of passes rather than with the size of the log. Every cut costs you the kerf width times the full chord of the log at that height, and the cuts near the middle are the widest. The published Forest Service figure is about 2 to 3 % of yield per 1/32 inch of kerf, and this tool's geometry reproduces it without being told to: on a 20-inch log, dropping from a 0.085 in band to a 0.062 in band gains 2.1 %, and going the other way to a 9/32 in circular saw loses 13.6 % β 2.9 and 2.2 % per 1/32 respectively. A chainsaw mill at a quarter inch of kerf turns roughly a fifth of a small log into sawdust. That is the honest price of milling on the ground with no mill.
What overrun should I expect, and can I use it to argue a price?
Against Doyle on small logs, large positive overrun is normal and well documented β 50 % and more under about 14 inches. Against International ΒΌ-inch the gap is usually small in either direction, because International was built as a volume model rather than as a mill estimate. That is the useful framing in a negotiation: not "your scale is wrong" but "this log is below the diameter where Doyle tracks yield, so the rule you are quoting has a known bias here, and here is the size of it." Bring the number, not the grievance. And note this tool models a through-and-through pattern, so your real tally will differ if you grade-saw.
Should I measure the diameter over the bark or under it?
Under. Every log rule in North America scales the small end inside the bark, and using an over-bark measurement inflates the scale on every rule at once β on a small log, by more than the difference between the rules you are comparing. If your only measurement is over bark, put the total bark deduction in the field above: roughly Β½ inch for thin-barked species like poplar and soft maple, an inch for most oaks, and up to 1Β½ inches on rough old-growth bark. If the end is oval, average two diameters taken at right angles rather than picking the flattering one.