Board Foot Log Volume Calculator

Estimate rough log volume in board feet

A board foot is a lumber volume equal to a board that is 1 inch thick, 12 inches wide, and 12 inches long. That sounds like a shop measurement, but it is also a practical way to think about how much wood is contained in a log before the sawmill turns it into boards. This calculator estimates the gross volume of a single log from three field measurements: the diameter at the small end, the diameter at the large end, and the overall log length. If you are comparing logs, planning a milling run, checking a timber purchase, or simply learning how log scaling works, those three numbers give you a fast estimate without a spreadsheet.

The math used here is Smalian's formula. In plain language, Smalian's method treats the log as a tapered shape whose volume can be approximated by averaging the cross-sectional area at both ends and multiplying by length. That makes it a good fit when you can measure each end directly. The result on this page is shown in both board feet and cubic feet so you can read it in the language of lumber planning or in the broader language of geometric volume. Neither output promises finished lumber yield; instead, it gives you a consistent gross-volume estimate that you can use to compare one scenario with another.

What to measure before you calculate

The small-end diameter is the diameter of the thinner end of the log, measured in inches. The large-end diameter is the thicker end, also measured in inches. The length is the usable log length in feet. In many real forestry and milling situations, the most important habit is consistency. If you measure outside bark at one end and inside bark at the other, or if one length includes trim allowance while another does not, the formula will still return a number, but that number will not represent the same thing from log to log. Good inputs matter more than fancy rounding.

For round logs, diameters are often taken across the end face. If the end is noticeably out of round, a common practice is to average two measurements taken at right angles, then enter that average. If you already work from a local scaling rule, follow your local convention for where and how you measure, then use the same convention every time you compare logs with this tool. The calculator itself does not enforce a bark rule or a defect rule; it simply converts the measurements you provide into a geometric estimate.

• Use inches for both diameters. The board-foot formula depends on area, so diameter errors get squared and can move the answer more than you expect.
• Use feet for log length. If your notes are in inches, convert length before entering it.
• Measure both ends the same way. Outside-bark measurements usually produce a larger estimate than inside-bark measurements.
• Trim only once. If your length already excludes trim waste, do not subtract it again mentally when you read the result.
• Do not worry if the ends are reversed. Smalian's formula averages both end areas, so the math is symmetric, even though the labels help you stay organized.

Blank fields on this page are intentional. You are meant to enter your own measurements rather than work from generic sample values. That reduces the chance of copying a demonstration scenario into a real estimate by accident. If you are exploring several possibilities, it is worth running a short, medium, and long version of the same log, because length affects the answer in a very clean way once the diameters are fixed.

How the formula turns measurements into board feet

Smalian's formula starts by finding the area of each log end. Because each end is approximated as a circle, the area of an end is πd²/4. The calculator averages those two end areas, multiplies by the log length converted to inches, and then divides by 144 to convert cubic inches into board feet. That final conversion matters because one board foot contains 144 cubic inches. The same calculation can also be expressed in cubic feet by dividing the board-foot result by 12.

If you substitute the end-area expressions into the first equation, the whole estimate collapses into a simple relationship between both diameters and the length. That is why the calculator responds so smoothly when you test scenarios. Keep the diameters fixed and volume rises almost linearly with length. Increase either diameter and the result jumps faster, because area depends on the square of diameter rather than the diameter alone.

Some readers like to see a tool first in general notation before tying it to a specific forestry formula. The two MathML blocks below are preserved from the original page because they describe that broader pattern correctly: a result can be expressed as a function of inputs, and many practical tools can be understood as a weighted combination of several terms. In this calculator, the weights come from geometry and unit conversion rather than from finance, medicine, or some other domain.

Worked example with realistic measurements

Suppose a log measures 12 inches at the small end, 16 inches at the large end, and 10 feet in length. The small-end area is about 113.1 square inches, and the large-end area is about 201.1 square inches. Average those two end areas and you get about 157.1 square inches. Multiply by 120 inches of length, and the log contains roughly 18,852 cubic inches. Divide by 144, and the gross estimate is about 130.9 board feet. Divide that by 12 if you want cubic feet, and the same log is about 10.91 cubic feet.

That example is useful because it shows how the calculator's two outputs relate. Board feet is often the more intuitive number for lumber planning, while cubic feet is a more universal volume measure. If a result feels too small or too large, pause and check the dimensions before assuming the formula is wrong. A diameter typed as 1.2 instead of 12 changes the end area dramatically, because the area calculation squares the number. The same kind of error can happen if a length recorded in inches is entered as though it were in feet.

Now compare that length change with a diameter change. If the same 10-foot log measured 14 inches and 18 inches instead, the estimate would jump to about 170.2 board feet. That increase of roughly 39.3 board feet is larger than the gain from simply making the original 12-by-16 log two feet longer. This is the key intuition behind the calculator: length matters steadily, while diameter often matters more sharply because it controls area.

How to interpret the result on this page

When you submit the form, the result panel shows the estimated board feet and cubic feet for the exact dimensions entered. The board-foot figure is usually the headline number for milling, ordering, or rough yield discussions. The cubic-foot figure is helpful if you want a pure geometric cross-check or if you are comparing the log against other volume measures used in forestry, transport, or biomass planning. The copy button creates a short text summary so you can paste the estimate into notes, email, or a work order.

A sensible result should pass three quick checks. First, the unit should match the question you are trying to answer. Second, the magnitude should look plausible for a log of that size. Third, the output should move in the direction you expect when you change one input at a time. If you make the log longer, the answer should rise. If you thicken either end, the answer should rise. If the calculator does not seem to behave that way, the usual cause is a unit mistake or a misplaced decimal point rather than a failure in Smalian's formula.

It is also worth separating gross log volume from saleable lumber yield. A sawmill never turns every cubic inch of a log into finished boards. Bark, taper between the measured ends, saw kerf, edging, trim allowance, crook, sweep, rot pockets, and knots all reduce what can actually be recovered. This calculator does not attempt to predict those losses because they vary by species, mill setup, sawing pattern, and log quality. Use the result as a consistent geometric estimate, then apply your own local recovery expectations if you need a closer yield forecast.

Assumptions, limits, and good practice

Smalian's formula is strongest when both end areas are known and the log behaves reasonably like a tapered frustum between those ends. It is less informative when a log has severe sweep, an irregular oval shape, rot hidden under bark, or a damaged section that would force you to buck the log differently in the yard. In those cases the number on the screen still has value, but it should be treated as an upper-level planning estimate rather than as a promise about what the mill will recover.

Another common source of confusion is the difference between geometric volume and rule-based log scaling. Some mills buy logs using rules such as Doyle, Scribner, or International 1/4-inch. Those rules are not identical to Smalian volume. They embed assumptions about sawing patterns and lumber recovery, so they can be higher or lower than a simple geometric estimate depending on log size and local practice. If your buyer quotes a rule scale and this page gives a different result, that does not mean either one is wrong; it means the two systems answer related but different questions.

In practice, this calculator is most useful when you want consistency. You might compare several logs before a milling day, check whether a truckload estimate is in the right range, or see how much volume changes if you trim off a damaged foot from one end. Because the inputs are straightforward and the outputs are immediate, it is a good scenario-testing tool. Enter one case, adjust a single number, and watch how the estimate moves. That kind of structured comparison is often more valuable than pretending any single rough estimate is exact down to the last tenth of a board foot.

Common questions

Does the large end really need to be larger?

Usually yes in the physical sense, but the formula itself is symmetric. If you accidentally place the 16-inch measurement in the small-end field and the 12-inch measurement in the large-end field, the average of the two end areas is unchanged, so the final volume is unchanged as well. The labels still matter because they help you keep measurements tidy, especially when you are recording many logs in sequence.

Why does the page also show cubic feet?

Board feet is ideal for lumber conversations, but cubic feet is a universal volume unit that makes geometric checking easier. Seeing both values together helps you confirm that the estimate is internally consistent. Because one cubic foot equals 12 board feet, you can always move between the two without changing the underlying log geometry.

What is the best way to use this estimate in the field?

Use it as a planning number and as a comparison tool. If you are choosing which logs to mill first, the calculator can show how strongly diameter affects potential yield. If you are deciding where to buck a log, run the original length and then a trimmed length to see how much gross volume you give up by removing a defect. If you are reviewing a timber deal, use consistent measurements across the whole lot so the comparisons are fair. The more consistent your measuring habit, the more useful the calculator becomes.