Doyle, Scribner and International 1/4-inch, side by side

A board foot is a unit of sawn lumber: a piece one foot by one foot by one inch. A log rule is somebody's estimate of how many of those a round log will yield once the slabs, the sawdust and the taper have been taken out of it. Estimate is the operative word - each of the three was built on a different idea of how a log gets broken down, and each is wrong in its own direction.

Doyle subtracts four inches from the diameter before squaring, as a flat allowance for slab and kerf. On a 24-inch butt log that allowance is a small share of the diameter. On a 10-inch top it is nearly half of it, and the rule squares what is left. That one design choice - a fixed deduction applied to logs of every size - is the entire reason Doyle and International part company on small wood. It is arithmetic written into the rule in the 1800s, and it does the same thing to every log, on every tract, for every buyer and every seller alike.

Scribner began as diagrams: boards drawn inside circles, counted, tabulated. It is properly a table rather than an equation, and the formula on this page is the version used to reproduce it. Because it started as drawings, it steps between sizes rather than curving smoothly, and the widely used decimal-C variant rounds to the nearest ten board feet on top of that.

International 1/4-inch was worked out from the geometry of a tapering log with a stated quarter-inch saw kerf. It is the closest of the three to what a mill actually recovers, which is why this page uses it as the benchmark the other two are measured against - not because it is the rule you will be paid on.

A buyer quoting a price per thousand board feet Doyle knows exactly how Doyle scales, and prices accordingly - which is why Doyle rates per thousand sit above International rates for the same wood in the same week. The rule and the rate are set together, and neither one means much without the other.

The mistake worth guarding against is not the rule. It is comparing across rules without noticing. A price per thousand on Doyle and a price per thousand on International are prices for two different quantities of wood. Set the two rates side by side and the Doyle rate will look higher for exactly the same timber, because each thousand board feet Doyle is more wood than each thousand board feet International.

So: know which rule your contract specifies before you sign it, and never compare a rate quoted on one scale with a rate quoted on another without converting the volume first. That is the whole lesson of this page, and the calculator above exists to make it concrete with your own log.

A buyer scaling accurately on Doyle is doing nothing wrong. Doyle is the customary scale across the South, written into contracts, printed on scale sticks and built into the price structure of every mill that uses it. Scaling a log on the rule the contract names is exactly what a buyer is supposed to do, and doing it well is a skill.

What a consulting forester tells a client is not 'watch out for the buyer'. It is: know your rule, know your units, and don't compare across scales. The rule, the unit and the point of measurement are the three things a seller should be able to state about his own sale without looking them up - and a seller who can state them is easier to do business with, not harder.

Almost every dispute over scale that reaches a phone call started as a surprise rather than as arithmetic. Somebody expected board feet and got tons, or expected International volume against a Doyle rate, or did not know the scale happened at the mill rather than at the landing. An informed seller and an honest buyer want precisely the same conversation, and they want it before the timber moves.

This calculator compares volume with volume and stops there. It will not tell you that a Doyle scale 'cost' you a figure in dollars, because such a figure would be arithmetically wrong, not merely impolite.

Here is why. Prices per thousand board feet Doyle run higher than prices per thousand board feet International precisely because Doyle counts fewer board feet in the same log. The scale and the rate move together. Take the board-foot difference between the two rules, multiply it by a rate quoted on one of them, and you have multiplied a quantity in one unit by a price in another - the number that falls out describes nothing that exists. It is the same error as pricing a tract in tons using a per-thousand-board-foot rate.

The useful comparison is the one shown above: the same log, the same day, expressed in three different units of measure. What that volume is worth is set by the mills within hauling distance of your gate in the week you sell, on the rule your contract names - and the way to find it is to have several buyers answer at the same time.

All three formulas fall apart at the bottom of the diameter range. Doyle reaches exactly zero at a 4-inch top, because that is what subtracting four inches does. The Scribner and International polynomials cross zero a little below that and then go negative.

Rather than print a negative board-foot count with a straight face, this calculator declines anything under a 5-inch small end and says why. Wood with a top that small is pulpwood, and pulpwood is bought by weight or by the cord - it is not scaled for lumber at all.