Lumber Yield Calculator

Lumber Yield Calculator for landowners and small sawmills. Enter log diameter, length, saw kerf and board thickness to see the log yield in sawn board feet beside three log scales.

Lumber Yield Calculator for Sawing Your Own Logs

The Lumber Yield Calculator estimates how many board feet of sawn lumber a stack of logs will give you. It also compares that figure to the Doyle, Scribner and International log scales and prices the job. That makes it a log yield check for landowners with a downed walnut, hobby bandmill owners and small mills buying logs by the scale.

Enter the small-end diameter inside the bark, the log length, the number of logs, your saw kerf and the rough green thickness you plan to saw. A 4/4 entry means boards sawn a full 1 inch thick, not a planed size. Prices, board width and metric units sit in the accordion below.

Measuring is where most estimates go wrong. Purdue Extension's Log and Tree Scaling Techniques (FNR-191) tells scalers to measure the small end twice at 90 degrees and average the two. A log just short of a full foot is tallied at the next lower foot, so tape the length rather than guessing.

The same publication describes 14 experienced timbermen scaling the same 11 logs. Their Doyle totals ran from 1,434 to 1,795 board feet, a spread of 361. Careful measurement changes the answer more than the choice of formula does.

Log Yield by Doyle, Scribner and International Rules

The first card shows the log scale, which is the board-foot estimate that logs are bought and sold on. All three rules use the small-end diameter D in inches and the length L in feet. Purdue gives the Doyle rule as follows.

$$B{F}_{Doyle}=(D-4{)}^2\times \frac{L}{16}$$

Doyle takes 4 inches off the diameter for slabs and edgings at every size. Purdue notes the result seriously underscales small logs and overscales large ones. Scribner is a diagram rule, and the tool uses the Bruce and Schumacher formula for it that Purdue reproduces.

$$B{F}_{Scribner}=(0.79D^2-2D-4)\times \frac{L}{16}$$

The International 1/4 inch rule is the only one of the three that allows for taper. It assumes 1/2 inch of diameter growth per 4 feet of length. Purdue calls it probably the most accurate, and the tool uses Grosenbaugh's integrated form of it.

$$B{F}_{Intl}=0.04976191L{D}^2+0.006220239L^{2}D-0.1854762LD+0.0002591767L^3-0.01159226L^2+0.04222222L$$

The table compares the rules on 12-foot logs. The last column shows Doyle as a share of the International figure, which is where the difference between rules is clearest.

Doyle only catches up with International near 30 inches. Gene Wengert explained on WOODWEB that the low Doyle figures on small logs offset the extra handling those logs need. That lets a mill pay one price per board foot across log sizes.

Which rule applies is mostly local custom. Purdue notes Doyle is the most widely used rule, especially on private timber in the East and South, while Scribner was long used by the Forest Service in the Lake States and the West. Pick the rule your buyer or seller uses so the log price and the scale match.

Turning the Scale into Sawn Board Feet

The hero figure is the lumber you should saw, not the scale. The tool starts from the International 1/4 inch figure and adjusts it for your kerf and board thickness. Thicker boards need fewer cuts, and thinner kerfs waste less wood per cut.

$$F=\frac{t\times (1+0.25+0.0625)}{t+k+0.0625}$$

Here t is the sawn thickness and k is the kerf, both in inches. At 4/4 and a 1/4 inch kerf, F equals 1 and the hero matches the International scale exactly. At a 1/8 inch kerf, F is 1.105. That matches the step between Clark's own 1/8 and 1/4 inch versions of the rule, whose 4-foot formulas in Purdue's bulletin open with 0.22 and 0.199.

For the default four 16-inch logs, a 1/16 inch thin bandmill gives about 611 board feet and a 1/4 inch circular mill gives 523. A 3/8 inch chainsaw mill drops to 478. Sawing 8/4 instead of 4/4 at a 1/8 inch kerf raises the total from 579 to about 628 board feet. To see the kerf loss on a single cut list, use the Kerf Spacing Calculator.

The second card reports overrun, the lumber sawn beyond the scale you paid on. Purdue defines it as the lumber tally divided by the log scale, minus one, times 100. The default logs show 33.9% overrun on Doyle, and one Fine Woodworking forum member reported bandmills reaching 125% to 150% of Doyle on careful sawing.

Log Recovery in the Lumber Yield Calculator

The third card compares the lumber to the round log itself. Log volume uses the average of the two end areas, with the large end grown by the International rule's taper of 1 inch per 8 feet. Recovery is the lumber's cubic feet, board feet divided by 12, as a share of that volume.

The USDA Forest Products Laboratory puts typical hardwood mill recovery at 50% to 60% for logs up to 24 inches. Logosol, the sawmill maker, gives the same 50% to 60% range for its customers. The tool's default of 65.5% is higher because it assumes sound, straight logs sawn at a 1/8 inch kerf.

Recovery also climbs with diameter, because slabs take a smaller share of a big log. At a 1/8 inch kerf and 4/4, a 12-foot log recovers about 49% at 8 inches, 60% at 12 inches, 69% at 20 inches and 74% at 30 inches. Scale sweep, rot and crook out of the length before you trust any of these numbers.

A companion row gives board feet per cubic foot of log, which the Forest Service calls the lumber recovery factor. A Forest Service study of Alaska sawmills found values from 4.8 to 10.05, averaging 6.38. The default logs work out near 7.9.

Log Cost, Sawing Cost and Margin

The fourth card prices the job. Log cost is your dollars per thousand board feet applied to the scale you buy on, and sawing cost is charged on the lumber actually cut. Lumber value uses your price per board foot on the sawn total.

With the defaults, 579 board feet at $1.50 is worth about $868. The logs cost $216 on the Doyle scale, and sawing at $0.45 adds about $260, which leaves roughly $392. Switch the rule to International and the log bill rises, because the same logs scale larger.

Enter $0 for a log you already own or a mill you run yourself. The margin then shows what the lumber is worth over your sawing bill alone. Once the boards are cut, the Board Foot Calculator handles individual boards and dealer tallies.

Sawyer and Log Buyer Questions

What log yield should I expect from a chainsaw mill?

Less than from a bandmill, mostly because of the kerf. A chainsaw mill cuts about 3/8 inch, so every 1 inch board costs more than a third of an inch in sawdust. The default four 16-inch logs give about 478 board feet at 3/8 inch against 579 at 1/8 inch, roughly 17% less.

Sawing thicker slabs narrows the gap because there are fewer cuts. A LumberJocks thread on milling a log makes the same point about losses in the cut.

Does a sawyer charge on the log scale or on the lumber cut?

Both happen, so ask before the saw starts. In a Woodworking Talk thread, one member found a traveling sawyer at $0.50 per board foot who billed on the log scale regardless of waste. A bandmill owner in the same thread charged on the lumber milled and bought his own logs by the scale.

The tool assumes billing on lumber cut. If your sawyer bills on scale, multiply the first card's scale by the rate instead. On the default logs, $0.45 on 432 Doyle board feet is $194, compared with about $260 on the sawn tally.

How do I handle a log longer than 20 feet?

Purdue says International-rule logs over 20 feet are scaled as two or more logs. Scribner ignores taper, so the University of Tennessee's log rule guide notes it underestimates logs longer than 16 feet. The tool warns you above 20 feet.

The integrated International formula already builds taper in 4-foot steps. A 24-foot, 16-inch log gives the same 290 board feet whether you enter it whole or as two 12-foot logs at 16 and 17.5 inches. For Doyle and Scribner, scale each section separately and add them.

Can I use it on a standing tree?

Only after estimating the log. Purdue explains that buyers measure diameter at breast height, 4.5 feet up, then deduct taper and bark to estimate the top diameter of the first log. Enter that estimated small-end diameter and the merchantable length.

Foresters use form class tables instead. Purdue gives an example of a tree with a 16-inch first-log diameter and a 20-inch breast-height diameter, which is form class 80. Each unit of form class changes the volume by about 3%.