This board foot log calculator estimates how much gross wood volume a single log contains before it reaches a sawmill. A board foot is the volume of a board 1 inch thick, 12 inches wide, and 12 inches long, making it a familiar unit for discussing lumber. Enter the small-end diameter, large-end diameter, and overall log length to produce a quick estimate from field measurements. Whether you are comparing logs, planning a milling run, checking a timber purchase, or learning about log scaling, the same three measurements provide a consistent starting point without a spreadsheet.
The board-foot estimate uses Smalian’s formula. This log-scaling method approximates a tapered log by averaging the cross-sectional areas at its two measured ends and multiplying that average by length. It is useful when both ends can be measured directly. The page reports board feet and cubic feet, letting you view the same gross geometric volume in a lumber-oriented unit or a general volume unit. Neither figure guarantees finished lumber recovery; both are consistent estimates for comparing logs measured under the same convention.
Measurements needed for a Smalian log-volume estimate
For this Smalian log-volume calculation, measure the small-end diameter in inches, the large-end diameter in inches, and the usable log length in feet. Consistency is especially important when measuring a group of logs. If one end is measured outside bark and another inside bark, or one recorded length includes trim while another excludes it, the results will not be directly comparable even though the calculation still runs. Careful field measurements matter more than extra decimal places.
For round logs, diameters are often taken across the end face. When an end is noticeably out of round, averaging two diameters taken at right angles can provide a more representative diameter to enter. If you use a local scaling convention, follow its directions for bark and measurement location, then apply that convention to every log you compare here. This calculator does not assign bark deductions or defect deductions; it converts the dimensions you enter into a geometric volume estimate.
- Use inches for both diameters. Log-end area is based on diameter squared, so even a modest diameter error can noticeably affect board feet.
- Use feet for log length. Convert a length recorded in inches before entering it.
- Measure both ends under the same convention. Outside-bark diameters generally give a larger gross-volume estimate than inside-bark diameters.
- Account for trim once. When an entered length already excludes trim, do not make another deduction while interpreting the result.
- Either diameter can occupy either end field mathematically. Smalian’s formula averages both end areas, though the labels help keep log notes organized.
The blank log-volume fields are deliberate: enter measurements from the log you are evaluating rather than copying a stock example. When assessing alternative bucking choices, test a shorter and longer version of the same log. With its diameters unchanged, the estimated gross volume changes directly with the entered length.
How Smalian’s log formula produces board feet
This board-foot calculator first finds the area of each circular log end. An end with diameter d has area πd2/4. It averages the two areas, multiplies by log length after converting feet to inches, and divides by 144 to convert cubic inches to board feet. Since a board foot contains 144 cubic inches, the unit conversion is essential. The cubic-foot output is the board-foot result divided by 12.
For a Smalian log estimate, these equations show why length and diameter do not influence the result in the same way. With both diameters fixed, each added foot contributes the same amount of gross volume. Increasing either end diameter has a stronger effect because the end area depends on the square of that diameter. Check diameter units and decimal placement particularly carefully when a result seems surprising.
The formula uses only the two entered end measurements and the entered length. It does not model changing diameter at intermediate points, hidden defects, bark thickness, kerf, or a particular sawing pattern. Those factors can matter greatly for recovered lumber, but they are separate from the gross geometric volume calculated here.
Worked Smalian example for a tapered log
Consider a log that is 12 inches at the small end, 16 inches at the large end, and 10 feet long. The small-end area is about 113.1 square inches and the large-end area is about 201.1 square inches. Their average is about 157.1 square inches. Over 120 inches of length, that gives roughly 18,852 cubic inches. Dividing by 144 produces a gross estimate of about 130.9 board feet, or about 10.91 cubic feet.
This log-volume example also illustrates the connection between the two outputs. Board feet are often easier to use for lumber planning, while cubic feet express the same geometry in a general volume unit. If an output looks implausible, verify dimensions before questioning the formula. Entering 1.2 instead of 12 inches changes end area sharply because the diameter is squared; treating an inch measurement as feet causes a similarly large length error.
| Scenario |
Small end |
Large end |
Length |
Estimated volume |
What it shows |
| Shorter cut |
12 in |
16 in |
8 ft |
104.7 bf |
With the diameters fixed, reducing log length reduces gross volume proportionally. |
| Baseline |
12 in |
16 in |
10 ft |
130.9 bf |
This is the gross Smalian estimate from the example above. |
| Longer cut |
12 in |
16 in |
12 ft |
157.1 bf |
Adding 2 feet adds about 26.2 bf because volume per foot is unchanged for these end diameters. |
Now change the diameters rather than the length. A 10-foot log measuring 14 inches and 18 inches at its ends estimates to about 170.2 board feet. That increase of roughly 39.3 board feet exceeds the gain from extending the original 12-by-16-inch log by two feet. The comparison captures the central behavior of this calculator: length changes volume steadily, while diameter changes affect the squared end-area terms.
Reading the board-foot and cubic-foot results
After you submit log dimensions, the result panel reports the estimated board feet and cubic feet for those exact measurements. For milling, ordering, or preliminary yield discussions, board feet will often be the primary number. Cubic feet offer a geometric cross-check and can be useful when comparing log volume with forestry, transport, or biomass measures. The Copy Summary button provides a short text version of the displayed estimate for notes, email, or a work order.
A Smalian log-volume result should pass three simple checks. Confirm that the displayed unit answers your question, consider whether the magnitude is reasonable for the log, and alter one input at a time to confirm the direction of change. A longer log should produce more volume, and enlarging either end diameter should also produce more volume. When behavior seems unexpected, a unit mismatch or misplaced decimal is more likely than a problem with the calculation.
Keep gross log volume distinct from saleable lumber yield. A sawmill cannot recover every cubic inch of a log as finished boards. Bark, taper between the measured ends, saw kerf, edging, trim, crook, sweep, rot, and knots all reduce recovery. This calculator intentionally does not forecast those losses, which depend on species, log quality, mill equipment, and sawing practice. Use the output as a consistent geometric volume, then apply recovery assumptions appropriate to your operation when needed.
Smalian log-scaling assumptions and limits
Smalian’s formula is most informative for a log whose measured end areas reasonably represent a tapered shape between them. Severe sweep, an irregular oval cross-section, concealed rot, or damage that changes where the log should be bucked can make the gross estimate less representative of usable material. In those situations, the calculation remains a useful planning reference, but it is not a promise of mill recovery.
This gross-volume method also differs from rule-based log scales. Some buyers and mills use Doyle, Scribner, or International 1/4-inch rules. Those systems are not the same as a Smalian geometric calculation: they incorporate their own assumptions about sawing and lumber recovery. A different number from a buyer’s rule scale does not automatically mean either figure is incorrect; the methods are answering related but different volume questions.
The board-foot log calculator is most valuable when used consistently across several measurements. Compare logs before a milling day, check whether a truckload estimate is in a reasonable range, or see the gross-volume effect of removing a damaged foot. Enter one set of dimensions, change a single measurement, and observe the result. That disciplined comparison is generally more useful than treating a rough field estimate as exact to the final tenth of a board foot.
Board-foot log volume questions
Does the large end really need to be larger on this log calculator?
Usually it will be larger on a real tapered log, but Smalian’s board-foot formula is symmetric. If a 16-inch and 12-inch measurement are accidentally entered in opposite end fields, the average end area and final volume remain unchanged. The field labels are still useful for orderly recordkeeping when measuring multiple logs.
Why does this Smalian calculator also show cubic feet?
Board feet suit lumber conversations, while cubic feet provide a general geometric volume unit. Showing both makes it easier to check and compare the gross log estimate. One cubic foot equals 12 board feet, so the calculator converts between the two without changing the underlying log geometry.
What is the best field use for this gross log-volume estimate?
Use the Smalian result as a planning and comparison number. When selecting logs to mill, it highlights how strongly end diameter affects gross volume. When deciding where to buck a log, compare the original length with a trimmed length to see the gross volume removed with a defect. For a timber lot, measure every log under the same convention so the comparisons remain meaningful.