Board Foot Calculator for Tree: How to Estimate Lumber

This board foot calculator for tree estimates the volume of usable lumber in a standing tree or log. You enter the tree’s diameter at breast height (DBH) and the number of 16-foot logs (or the total log length), and you get back the estimated board feet using the Doyle Log Rule, the most common scaling method in the eastern United States. The result is an estimate, not a precise measurement—actual yield depends on taper, defects, and milling method.

Formula

The Doyle Log Rule estimates board feet from the small-end diameter of a log, not the DBH. For a standing tree, you first estimate the small-end diameter of each 16-foot log section, then apply the formula. The standard Doyle formula for a single 16-foot log is:

Board feet = ((small-end diameter in inches − 4)² × length in feet) / 16

For a 16-foot log, this simplifies to ((d − 4)²) / 4, where d is the small-end diameter in inches. The calculator above uses DBH as a proxy for the small-end diameter of the first log, which overestimates slightly; for the second log, subtract about 2 inches of taper, and for the third, subtract 4 inches. Each variable: d = diameter at breast height (inches), logs = number of 16-foot logs (or fractions thereof). The result is in board feet (1 board foot = 1 ft × 1 ft × 1 in = 144 cubic inches).

Worked Example

Using the default values: a tree with DBH = 20 inches and 2 logs (32 feet of usable trunk). The calculator applies the Doyle formula directly to the DBH, giving:

• Step 1: Subtract 4 from the diameter: 20 − 4 = 16
• Step 2: Square the result: 16² = 256
• Step 3: Multiply by the number of logs: 256 × 2 = 512
• Step 4: Divide by 4: 512 / 4 = 128 board feet

The calculator shows 128 board feet. For a more realistic field estimate, you would reduce the diameter for each additional log: first log at 20 in, second at 18 in, giving ((20−4)² + (18−4)²)/4 = (256 + 196)/4 = 113 board feet. The difference shows why the Doyle rule is considered conservative for small logs and generous for large ones.

Why Use the Doyle Rule?

The Doyle Log Rule was developed in the 19th century and remains the standard for hardwood timber in the eastern U.S. It assumes a 4-inch saw kerf (the width of the saw cut) and a minimum 4-inch slab, which makes it underestimate small logs (under 15 inches) and overestimate large logs (over 30 inches). Despite its quirks, it is widely used because it is simple and has been the basis for timber sales for generations. Other rules exist—Scribner and International 1/4-inch—but Doyle is the default for most private forest landowners and sawmills in the East.

For softwoods in the western U.S., the Scribner rule is more common. The International rule is the most accurate but requires a table. If you are selling timber, the buyer will likely use Doyle; if you are buying, you may want to ask which rule they use.

How to Measure a Standing Tree

Accurate input is the key to a useful estimate. Follow these steps:

1. Measure DBH at 4.5 feet above ground on the uphill side. Use a diameter tape (which reads diameter directly) or wrap a regular tape around the trunk and divide by π (3.1416).
2. Estimate the number of usable 16-foot logs. A “log� is a straight, defect-free section of trunk. Look for the first major branch, a fork, or a visible rot pocket—that ends the merchantable length.
3. Account for taper: subtract 2 inches from the diameter for each additional 16-foot log beyond the first. The calculator above does not do this automatically, so adjust the diameter you enter to reflect the average small-end diameter of all logs.
4. If the trunk is only 10 feet long, enter 0.625 logs (10/16). The formula works with fractions.

For example, a tree with DBH 24 inches and 2.5 logs (40 feet) would have approximate small-end diameters of 24, 22, and 20 inches. The Doyle estimate would be ((24−4)² + (22−4)² + (20−4)²)/4 = (400 + 324 + 256)/4 = 245 board feet. Entering 24 inches and 2.5 logs in the calculator gives ((24−4)² × 2.5)/4 = 250 board feet—close, but the taper adjustment makes the manual version more accurate.

Common Mistakes and Misconceptions

The biggest mistake is using DBH as the small-end diameter for every log. Trees taper, and the Doyle rule is very sensitive to diameter because it squares the difference. A 2-inch overestimate on a 20-inch log changes the result by about 20 board feet per log. Another common error is mixing units: the formula requires inches and feet, so if you measure diameter in centimeters, convert to inches (divide by 2.54) before calculating.

A widespread misconception is that board feet equals the actual volume of wood in the tree. It does not—it is the estimated volume of sawn lumber after accounting for saw kerf, slab waste, and edging. A 20-inch diameter, 16-foot log contains about 35 cubic feet of wood, but the Doyle rule says it yields only 64 board feet (which is 5.3 cubic feet of lumber). The rest is sawdust and bark. Also, the Doyle rule is not a legal standard; it is a convention. Two different buyers may scale the same log differently, so always get a written scale before agreeing on a price.

When to Use This Calculator vs. a Log Scale

Use this calculator for a quick, ballpark estimate when you are considering a timber sale, planning a small milling project, or just curious about a tree in your yard. It is not a substitute for a professional timber cruise or a mill’s official scale. If you are selling timber, the buyer will use a calibrated scale stick (like a Doyle stick) on each log after felling. If you are milling your own lumber, the actual yield will vary with the saw blade width, the skill of the operator, and the shape of the log. For a single tree, the difference between the calculator and the mill scale can be 20–30% either way.

For a more precise estimate, you can use the International 1/4-inch rule, which accounts for saw kerf and shrinkage more accurately. The formula is: board feet = 0.905 × (d² − 3d) for a 16-foot log, where d is the small-end diameter in inches. For a 20-inch log, that gives 0.905 × (400 − 60) = 307 board feet, versus 64 for Doyle—a huge difference. The International rule is closer to actual mill output for logs over 15 inches, but it is rarely used in private sales because it favors the seller.

Safety and Practical Tips

Measuring a standing tree is safe if you keep your feet on the ground. Do not climb a tree to measure the upper logs; estimate from the ground using a clinometer or a simple visual assessment. If you are felling a tree for lumber, always hire a professional logger or arborist—felling is one of the most dangerous jobs in forestry. Never stand under a tree being cut, and always wear a hard hat and eye protection when near logging operations. Also, be aware of local regulations: some municipalities require a permit to cut trees over a certain size, and timber sales may need a licensed forester’s appraisal for tax purposes.

Frequently Asked Questions

How many board feet are in a 20-inch diameter tree?

Using the Doyle rule with a single 16-foot log, a 20-inch DBH tree yields about 64 board feet. With two logs (32 feet), the estimate is 128 board feet, but if you account for taper, it drops to about 113. The actual number depends on the number of logs and the taper.

What is the difference between DBH and small-end diameter?

DBH is measured at 4.5 feet above ground and includes the bark. Small-end diameter is the diameter of the top of a log after felling and trimming, measured inside the bark. The small-end diameter is always smaller than the DBH for the same tree because of taper, and it is the number used in log rules.

Can I use this for a tree that is already cut?

Yes, but you should measure the small-end diameter of the log directly instead of using DBH. Enter that diameter and the number of 16-foot sections (or the length divided by 16) into the calculator. This will be more accurate than using a standing-tree DBH.

Why does the Doyle rule give such low numbers for small trees?

The Doyle rule subtracts 4 inches from the diameter before squaring, which heavily penalizes small logs. A 10-inch log gives only 9 board feet per 16 feet, while a 30-inch log gives 169 board feet. This is because the rule assumes a fixed 4-inch slab and saw kerf, which is a larger fraction of a small log.

What is a board foot in cubic feet?

One board foot is 1 foot long × 1 foot wide × 1 inch thick, which equals 144 cubic inches, or 1/12 of a cubic foot (0.00236 cubic meters). So 100 board feet is 8.33 cubic feet of solid lumber.

Do I need a professional forester for a timber sale?

For a single tree, probably not. But if you are selling multiple trees or an entire woodlot, a professional forester can help you get a fair price, negotiate the contract, and ensure the logging is done safely and legally. The cost of a forester is usually a percentage of the sale, often 10–15%, but it can pay for itself in better pricing.

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in d | Diameter at breast height (DBH) | in | 20 | 6
in logs | Number of 16-ft logs | - | 2 | 1
out bf | Estimated board feet (Doyle) | bd ft | ((d - 4)^2 * logs) / 4 | 0
out m3 | Estimated cubic meters | m³ | ((d - 4)^2 * logs * 0.00236) / 4 | 2