Using Smalian's Formula

The lumber industry often measures logs in board feet. One board foot represents a volume of wood that is 12 inches long, 12 inches wide, and 1 inch thick. Log rules, such as Doyle, International, and Scribner, attempt to predict how many board feet of lumber can be sawn from a log, accounting for taper and saw kerf. This calculator uses Smalian's formula to estimate log volume before applying the board foot conversion. Smalian's approach averages the cross-sectional areas of the small and large ends and multiplies by the log length:

Here $\mathrm{D\_1}$ is the small-end diameter in inches, $\mathrm{D\_2}$ is the large-end diameter, and $L$ is the log length in feet. Converting this volume from cubic inches to board feet involves dividing by 144, because a single board foot equals 144 cubic inches.

Foresters measure logs in the field using diameter tapes or calipers. While methods vary by region, most professionals round to the nearest inch for diameter and the nearest foot for length. Smalian's formula is convenient because it remains accurate even when logs taper irregularly, as it averages both ends. To use the calculator, simply enter the small-end and large-end diameters along with the log length. The script computes volume in cubic inches and then converts it to board feet, providing a quick estimate of the lumber that could be milled from that log.

Why Board Feet Matter

Board feet serve as a common currency in the timber trade. Sawmills purchase logs based on estimated board foot yield, and landowners sell standing timber according to board foot volume. The more accurate the estimate, the better each party can plan harvests and budgets. Although log scaling rules differ, Smalian's formula often provides a reliable starting point. This calculator uses a simplified version to keep the math accessible. For large logging operations, professional scalers or laser measurement systems may provide more precise results.

Example Volume Table

Small End (in)	Large End (in)	Length (ft)	Board Feet
10	12	8	56
12	14	10	96
14	16	12	150

The table above demonstrates how diameter and length influence volume. Larger logs produce exponentially more lumber as diameter increases. Keep in mind that real yields depend on mill practices, saw kerf width, and log quality—factors not captured in this simple estimate.

From Forest to Mill

Timber harvest planning involves more than just counting trees. Foresters assess species composition, tree health, market demand, and environmental considerations such as soil stability and wildlife habitat. Once a harvest area is selected, estimating the board foot volume helps determine the number of truckloads needed and the overall value of the timber. Accurate measurements are also important for forest inventory reports that track growth and yield over time.

When logs arrive at the sawmill, they are often remeasured and sorted by size and quality. Bark thickness, knots, and curvature all affect how much finished lumber can be produced. Many mills use electronic scanners to optimize cutting patterns and reduce waste. By comparing the estimated volume from the field with the actual yield from the mill, companies refine their scaling practices and improve profitability.

Managing Resources Wisely

Sustainable forestry balances timber production with ecological health. Leaving buffer strips along streams, protecting sensitive habitats, and replanting harvested areas are crucial to maintaining the productivity of forest lands. Knowing the board foot volume before a harvest makes it easier to plan regeneration and to monitor how much wood is removed from the ecosystem. Landowners who understand the long-term growth potential of their stands can better time harvests to maximize both income and environmental benefits.

Even hobbyists or small woodlot owners can use board foot estimates to budget for home projects or to sell a few logs to local sawmills. Tracking growth over time provides insight into how management choices—like thinning or selective cutting—affect the volume available for future use. Accurate calculators help demystify these processes and encourage responsible stewardship.

Conclusion

Whether you manage large tracts of forest or a small stand behind your house, estimating board foot volume empowers you to make informed decisions about harvesting and lumber sales. This calculator is designed to be straightforward and educational, giving you a quick approximation of log yield without complex conversion tables. By comparing multiple logs of varying sizes, you can gauge which trees might be worth cutting now and which are better left to grow for a higher yield later. Keep in mind that the lumber market fluctuates with supply and demand, so consider both economic and ecological factors before making final decisions.