Board Foot Calculator From Log: How to Estimate Lumber

This calculator estimates the number of board feet you can expect to get from a log, based on its small-end diameter and length. You enter the log’s diameter (in inches) and length (in feet), and the calculator returns the estimated board foot yield using the Doyle Log Rule, the most common scaling method in the eastern United States. It also shows the same volume in cubic feet for comparison.

Formula

The Doyle Log Rule is the standard formula used by sawmills and timber buyers in much of North America. It estimates the number of board feet (1 board foot = 1 inch thick × 12 inches wide × 12 inches long) of lumber a log will produce after sawing.

The formula is:

Board Feet = ((d – 4) / 4)² × L

Where:

• d = small-end diameter of the log, measured in inches (inside the bark).
• L = length of the log in feet.

This rule assumes a 4-inch allowance for saw kerf (the width of the saw blade) and slab waste. It is intentionally conservative for small logs but becomes more accurate for larger diameters.

Worked Example

Using the default values from the calculator above (d = 18 inches, L = 12 feet):

1. Subtract 4 from the diameter: 18 – 4 = 14.
2. Divide by 4: 14 / 4 = 3.5.
3. Square the result: 3.5² = 12.25.
4. Multiply by the length: 12.25 × 12 = 147 board feet.

The calculator returns 147 board feet, matching the manual calculation. The cubic foot volume (using the full cylinder formula) is about 21.2 cubic feet, which shows that the Doyle rule gives a much lower volume than the geometric volume of the log.

Why the Doyle Rule? (And Its Alternatives)

The Doyle rule is one of several log scaling methods. The two most common alternatives are:

• Scribner Log Rule: Developed in the 1840s, it estimates yield by drawing the cross-section of a 1-inch board and subtracting saw kerf. It gives higher estimates than Doyle for small logs (under about 28 inches) and is common in the western US.
• International 1/4-Inch Rule: Uses a more detailed mathematical model with a 1/4-inch kerf allowance. It is considered the most accurate for estimating actual lumber recovery, but it requires a table or a more complex formula.

For a quick, conservative estimate, Doyle is widely used because it is easy to compute in the field. However, if you are buying or selling logs, the choice of rule can change the volume by 20-30%, so always confirm which rule is being used.

How to Measure a Log Correctly

Getting the right numbers is more important than the formula itself. Here are the key measurement rules:

• Diameter: Measure the small end of the log, inside the bark, in inches. This is the standard practice because the small end limits the size of the largest board you can saw.
• Length: Measure in feet, typically to the nearest foot. Most sawmills round down to the nearest 2-foot increment (e.g., a 12.5-foot log is scaled as 12 feet).
• Use a diameter tape: A regular tape measures circumference, not diameter. A diameter tape (or a caliper) measures the actual diameter. If you only have a regular tape, divide the circumference by 3.1416.
• Average the diameter: If the log is not perfectly round, take two measurements at right angles and average them.

Common Mistakes and Misconceptions

Even with the right formula, people often make these errors:

• Using the large end diameter: Always use the small end. Using the large end can overestimate by 20% or more.
• Forgetting the bark: The diameter must be inside the bark. A thick-barked log can lose 1-2 inches of diameter.
• Mixing units: Diameter in inches, length in feet. If you use diameter in feet, the result will be off by a factor of 144.
• Thinking board feet equals cubic feet: A board foot is 1/12 of a cubic foot. A log that is 10 cubic feet will yield roughly 60-80 board feet, not 10.
• Forgetting that this is an estimate: The Doyle rule assumes a certain sawing efficiency. Actual yield depends on log taper, defects, and the sawmill’s equipment.

What the Result Actually Means

The number you get from this calculator is the gross board foot volume before any deductions for defects (rot, cracks, knots) or sawing losses. A sawmill will usually deduct for visible defects, so the usable yield is often 10-20% lower. When buying logs, you should ask whether the price is per gross or net board foot.

Also note that the Doyle rule is most accurate for logs 20 inches and larger. For small logs (under 15 inches), it tends to underestimate. If you are working with small-diameter logs, the Scribner or International rule will give a more realistic estimate.

When to Use This Calculator

Use this calculator when you need a quick, field-ready estimate for:

• Estimating how much lumber a single tree or log will produce.
• Comparing the value of different logs before buying or selling.
• Planning a sawing project (e.g., how many logs do I need for a shed?).
• Understanding a sawmill’s quote (they will usually state which rule they use).

For a more precise estimate, you would need a log scale stick or a detailed software program that accounts for taper and defects. But for most hobbyists and small operators, the Doyle rule is a reliable starting point.

Frequently Asked Questions

What is a board foot exactly?

A board foot is a unit of lumber volume equal to a board that is 1 inch thick, 12 inches wide, and 12 inches long (144 cubic inches). It is the standard unit for selling rough lumber in the US and Canada.

Why do I subtract 4 from the diameter in the Doyle rule?

The 4 represents the combined allowance for saw kerf (the material removed by the saw blade) and the unavoidable slab waste (the rounded outer edges that are cut off to make square boards). It is a rough approximation that works well for medium and large logs.

Can I use this for a log that is not round?

Yes, but you should measure the small-end diameter at its narrowest point, or average two perpendicular measurements. The formula assumes a round log, so an irregular log will give a less accurate result.

How many board feet are in a typical tree?

It varies enormously by species and size. A 20-inch diameter, 16-foot log yields about 256 board feet by the Doyle rule. A 30-inch, 16-foot log yields about 676 board feet. A full tree with multiple logs can easily produce 1,000+ board feet.

What is the difference between Doyle and Scribner?

Doyle subtracts 4 inches from the diameter before calculating, which penalizes small logs. Scribner uses a more realistic sawing pattern and gives higher estimates for logs under about 28 inches. For larger logs, the two are closer.

Does the calculator account for defects like rot or knots?

No. The result is the gross volume. You should deduct 10-20% for visible defects, or more if the log has large rot or cracks. A professional scaler will make these deductions on site.

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in d | Small-end diameter (inches) | in | 18 | 0
in l | Log length (feet) | ft | 12 | 0
out bf | Estimated board feet (Doyle) | bd ft | ((d - 4) / 4) * ((d - 4) / 4) * l | 0
out cf | Cubic feet | ft^3 | (3.14159 * (d/2) * (d/2) * (l * 12)) / 1728 | 1