Formula For Calculating Board Feet In A Log

Estimate log volume fast with standard log scaling rules. Enter the small-end diameter inside bark, the usable log length, your preferred rule, and quantity. The calculator returns total board feet and compares Doyle, Scribner, and International 1/4-inch outputs on a live chart.

Chart bars compare estimated board feet for the same log under all three rules. This helps you see how scaling method alone can change volume estimates.

Expert guide to the formula for calculating board feet in a log

If you buy, sell, harvest, or mill logs, understanding the formula for calculating board feet in a log is essential. Board feet are the standard commercial unit used to estimate how much lumber a log can produce. One board foot is equal to a piece of wood that is 1 inch thick, 12 inches wide, and 12 inches long. In lumber terms, that is a volume of 144 cubic inches. In log scaling, however, you usually do not calculate raw cylindrical volume and stop there. Instead, you apply a log rule that estimates recoverable lumber after saw kerf, slabs, taper, and practical milling limitations are considered.

That distinction matters. A standing tree or a bucked log contains more total wood than can actually be sawn into boards. A proper log rule converts log dimensions into an estimated lumber tally. In North America, the three most recognized rules are Doyle, Scribner Decimal C, and International 1/4-inch. Each uses a different mathematical approach, which is why the same log can have three different board foot values depending on the method used.

The calculator above is designed to make those comparisons easy, but it is equally important to understand what is happening behind the scenes. Once you know how the formulas work, you can judge whether a scale ticket, log purchase quote, or timber appraisal looks reasonable.

What is the basic formula for board feet?

The basic lumber formula is straightforward:

Board feet = (Thickness in inches × Width in inches × Length in feet) ÷ 12

This is the standard formula used for sawn boards, timbers, and lumber packs. For example, a 2 × 10 board that is 12 feet long contains (2 × 10 × 12) ÷ 12 = 20 board feet. Logs are different because they are round, tapering, and contain waste from conversion to rectangular boards. For that reason, professionals usually use a log rule formula rather than the simple board formula.

Common formulas for calculating board feet in a log

1. Doyle Rule

The Doyle rule is common in many hardwood markets, especially in the eastern and central United States. It is easy to compute and is still widely used in timber sales and sawmill buying.

Doyle board feet = ((D – 4)² × L) ÷ 16

Where:

• D = small-end diameter inside bark, in inches
• L = log length, in feet

The Doyle formula heavily discounts smaller logs because it assumes a large amount of slab loss and saw kerf. As a result, it often underestimates volume for small and medium diameters while becoming more favorable on larger logs.

2. Scribner Decimal C Rule

Scribner was developed from diagrams of boards sawn from round logs. The Decimal C version is a formula-based simplification used in many commercial settings.

Scribner board feet = ((0.79 × D²) – (2 × D) – 4) × L ÷ 16

This rule usually gives a somewhat higher estimate than Doyle for smaller logs, though actual relationships vary by diameter and length.

3. International 1/4-inch Rule

The International 1/4-inch rule is often considered the most technically consistent of the three because it accounts more realistically for taper and a 1/4-inch saw kerf.

International 1/4-inch board feet = (0.199 × D² – 0.642 × D – 1) × L

This formula usually produces higher estimates than Doyle and often tracks actual recovery more closely across a broad range of diameters and lengths.

How to measure a log correctly before using the formula

A good formula only works if your field measurements are sound. The most important measurement is the small-end diameter inside bark. In most scaling systems, you measure the diameter at the small end because it represents the limiting size for sawing. If bark is still on the log, you either estimate the inside-bark dimension directly or deduct bark according to local practice.

1. Measure the usable log length in feet.
2. Measure the small-end diameter inside bark in inches.
3. Select the log rule required by your buyer, contract, or regional market.
4. Apply the formula and round according to local scaling conventions.

Some mills require logs to be scaled to the nearest even inch diameter and nearest whole foot or standard log length increment. Others accept decimals. Always confirm the expected convention before relying on a private estimate.

Example calculation using all three log rules

Suppose you have a log with a small-end diameter of 18 inches and a merchantable length of 12 feet. Using the formulas built into this calculator:

• Doyle = ((18 – 4)² × 12) ÷ 16 = 147 board feet
• Scribner = ((0.79 × 18²) – (2 × 18) – 4) × 12 ÷ 16 = about 162 board feet
• International 1/4-inch = (0.199 × 18² – 0.642 × 18 – 1) × 12 = about 621 board feet

These differences show why the chosen rule matters so much. If a landowner expects one rule and the buyer pays on another, the value discussion can become confusing fast. The best practice is to identify the log rule in writing before pricing timber, veneer logs, or sawlogs.

Small-end diameter	Log length	Doyle estimate	Scribner estimate	International 1/4-inch estimate
12 in	8 ft	32 bf	41 bf	173 bf
14 in	10 ft	62.5 bf	74.1 bf	288.7 bf
16 in	12 ft	108 bf	120.6 bf	458.7 bf
18 in	12 ft	147 bf	162.2 bf	621.1 bf
20 in	16 ft	256 bf	276 bf	1073.6 bf

Why different rules give different board foot totals

Log rules are not simply geometry formulas. They are yield estimators based on assumptions about how logs are converted into boards. Those assumptions include kerf width, slab loss, edge trimming, and taper. Older rules were created in eras of thicker saw kerf and less efficient milling technology, so they can understate recoverable lumber compared with modern mill performance.

Doyle, in particular, is known to undervalue small logs. That can make it attractive to some buyers when small-diameter timber dominates a sale. International 1/4-inch was developed to be more consistent across log sizes and usually aligns better with modern understanding of sawing losses. Scribner sits between them in many practical settings.

This is one reason experienced foresters and timber buyers always identify the rule first, then discuss price. A high price per thousand board feet under one rule can be less favorable than a lower price under another rule if the actual scaled volume changes significantly.

Board feet in logs versus cubic volume

It is helpful to separate two concepts:

• Cubic volume measures the total wood space within the log.
• Board foot volume estimates how much lumber can be sawn from it.

A log can have a large cubic volume but still produce fewer board feet than expected if it has heavy taper, sweep, crook, defect, or if the scaling rule is conservative. Conversely, a straight, sound, high-quality log may outperform a rough estimate in actual mill recovery. In field buying and timber appraisal, board foot rules remain popular because they tie more directly to lumber output and market pricing.

What measurements and defects affect the estimate?

The formulas above assume a reasonably sound log. Real-world yields can be reduced by several factors:

• Bark thickness and errors in estimating inside-bark diameter
• Excess taper from butt flare or poor form
• Sweep, crook, or ovality
• Rot, shake, seams, and insect damage
• Metal contamination, such as wire or nails
• Scaling deductions required by mill policy or state rules

Because of these factors, your calculator result should be seen as a scaling estimate, not a guarantee of final lumber tally. In sales contracts, deductions and log grade can influence final settlement as much as the board foot formula itself.

Rule	Best known use case	Typical behavior on small logs	Typical behavior on large logs
Doyle	Traditional hardwood buying regions	Conservative, often low	Becomes more favorable
Scribner Decimal C	General sawlog scaling and regional trade	Moderate	Moderate to favorable
International 1/4-inch	More technical yield estimation	Usually more consistent	Often highest of the three

When should you use each formula?

Use the rule required by the market in which the log will actually be sold. In many local timber transactions, that means using whatever the buyer or receiving mill posts on its scale tickets. For landowners comparing bids, however, it is wise to standardize all offers to the same rule before deciding which bid is better.

For educational purposes, comparing all three rules is valuable because it reveals how sensitive the board foot estimate is to methodology. If your log values change sharply between rules, that is a signal to slow down and verify the assumptions before pricing standing timber or roadside logs.

Practical tips for landowners, foresters, and sawyers

1. Measure twice, especially the small-end diameter.
2. Confirm whether bark deduction is included.
3. Know the accepted rule in your local market.
4. Separate butt logs, veneer candidates, and lower-grade sawlogs.
5. Use log quality and defect deductions along with the formula.
6. Compare multiple loads or multiple logs, not just one sample stem.

If you are managing timber for sale, it can also help to work with an extension forester or consulting forester who understands local scaling customs. They can interpret not only board foot estimates, but also grade, utilization standards, and market timing.

Authoritative references for further reading

For deeper technical guidance, review materials from forestry agencies and universities:

• USDA Forest Service
• Penn State Extension
• University of Minnesota Extension

Final takeaway

The formula for calculating board feet in a log depends on the scaling rule you use. For actual boards, the classic formula is thickness times width times length divided by 12. For logs, the more useful approach is a log rule such as Doyle, Scribner Decimal C, or International 1/4-inch. Each formula starts with log diameter and length, but each produces different board foot estimates because each models sawing losses differently.

If you need the quickest answer, use the calculator above with your measured small-end diameter, log length, and selected rule. If you need the most reliable business answer, match the formula to the market standard, verify your measurements carefully, and document the rule used in every timber transaction.

These estimates are educational and planning tools. Actual scale tickets can vary by mill rules, defect deductions, trimming allowances, bark assumptions, and local scaling standards.