How to Calculate Board Feet in a Log

Accurately estimate timber volume using the industry-standard Doyle, Scribner, and International 1/4″ scaling rules.
Learn how to calculate board feet in a log for milling, buying, or selling timber.

Log Scale Reference Table (Length: 12‘)

Diameter (in)	Doyle (BF)	Scribner (BF)	Int. 1/4 (BF)

What is How to Calculate Board Feet in a Log?

Understanding how to calculate board feet in a log is a fundamental skill for sawyers, woodworkers, and foresters. A board foot is a unit of volume measurement for lumber in the United States and Canada, defined as the volume of a board that is 12 inches wide, 12 inches long, and 1 inch thick. When dealing with raw logs, we use scaling rules to estimate how many of these 12″x12″x1″ units can be sawn from a round, tapered cylinder.

Who should use this? Anyone involved in the timber supply chain—from the landowner selling standing trees to the hobbyist with a portable sawmill. A common misconception is that all rules provide the same result. In reality, different mathematical formulas account for sawdust (kerf), log taper, and slab waste differently, often leading to significantly different values for the same log.

How to Calculate Board Feet in a Log: Formulas and Mathematical Explanation

The math behind how to calculate board feet in a log varies by the “Scale Rule” used. Here are the three most common methods used in North America:

1. The Doyle Log Rule

The Doyle rule is one of the oldest and most widely used. It is known for underestimating small logs and overestimating very large ones. Its formula is simple:

BF = ((D – 4) / 4)² × L

2. The Scribner Rule

The Scribner rule is based on diagrams of how boards fit into a circle. It doesn’t follow a pure mathematical curve as strictly as the others but is standard in many regions. Our calculator uses the standard Scribner formulaic approximation.

3. The International 1/4-Inch Rule

This is considered the most accurate mathematical rule because it accounts for log taper (1/2 inch per 4 feet of length) and a 1/4-inch saw kerf. It provides the closest estimate to what a modern sawmill will actually produce.

Variables Used in Log Scaling

Variable	Meaning	Unit	Typical Range
D	Small End Diameter	Inches	6″ – 40″
L	Log Length	Feet	8′ – 24′
BF	Board Feet	Volume	10 – 2,000+
Kerf	Saw Blade Width	Inches	1/8″ – 1/4″

Practical Examples (Real-World Use Cases)

Example 1: The Small Oak Log

Suppose you have a Red Oak log with a 14-inch diameter at the small end and a length of 12 feet. If you use the [board foot calculator](/board-foot-calculator/) logic for logs:

• Doyle: ((14-4)/4)² * 12 = 75 BF
• International 1/4: 100 BF

In this case, the Doyle rule underestimates the yield by 25%. If you are selling this log by the board foot, the rule used matters immensely for your profit.

Example 2: The Large Pine Log

Consider a 24-inch diameter Pine log that is 16 feet long. Using the how to calculate board feet in a log methodology:

• Doyle: ((24-4)/4)² * 16 = 400 BF
• International 1/4: 405 BF

As logs get larger, the gap between the rules narrows significantly.

How to Use This Calculator

1. Measure the Diameter: Find the small end of the log. Measure the diameter inside the bark (average of two measurements if the log is oval).
2. Measure the Length: Determine the usable length of the log in feet.
3. Input Data: Enter these values into the fields above.
4. Interpret Results: Compare the three rules. If you are a buyer, you might prefer Doyle for small logs. If you are a sawyer aiming for precision, use International 1/4″.
5. Consider Weight: Use a [lumber weight calculator](/lumber-weight-calculator/) to estimate if your truck can handle the load.

Key Factors That Affect How to Calculate Board Feet in a Log

• Log Taper: Logs aren’t perfect cylinders. Rules like International 1/4″ assume a standard taper, but highly tapered logs will yield more than calculated.
• Saw Kerf: The thickness of your sawmill blade. Thin-kerf bandsaws (1/8″) will yield more lumber than large circular saws (1/4″).
• Log Defects: Sweep (curvature), rot, and knots reduce the actual yield. Our calculator assumes “clear” logs.
• Scaling Accuracy: Always measure the small end inside the bark. Measuring the large end will drastically overestimate yield.
• Species: While the volume is the same, hardwood vs. softwood value varies. You might use a [tree value calculator](/tree-value-calculator/) to determine market prices.
• Mill Efficiency: How the sawyer “opens” the log and cuts for grade vs. volume affects the final tally.

Frequently Asked Questions (FAQ)

1. Which log rule is the most accurate?

The International 1/4″ rule is widely accepted as the most accurate for modern milling because it accounts for taper and standard kerf losses.

2. Why is Doyle so popular if it’s less accurate?

Doyle is simple to calculate and historically favored buyers because it under-scales smaller logs, compensating for the extra labor and waste involved in milling them.

3. How do I handle an oval-shaped log?

Take two measurements—the narrowest diameter and the widest—and use the average of the two as your input.

4. Does the length include the “trim”?

Usually, no. Loggers often add 3-6 inches of “trim allowance” to ensure a clean final board length, but you should only calculate based on the target length (e.g., 8′, 10′, 12′).

5. What is “overrun”?

Overrun is when the actual lumber produced by the mill exceeds the log scale estimate. This is common with thin-kerf saws.

6. Can I use this for standing trees?

Yes, but you must estimate the diameter at the top of the first log (usually 16 feet up), which is harder. Use a [tree value calculator](/tree-value-calculator/) for standing timber.

7. How does wood shrinkage affect these numbers?

Freshly cut logs (green) will shrink as they dry. You may want to check a [wood shrinkage calculator](/wood-shrinkage-calculator/) to see how much your boards will change dimensionally.

8. Is there a rule for firewood or pulpwood?

Firewood is typically measured in cords (128 cubic feet of stacked wood) rather than board feet, which is reserved for sawlogs.