How to Calculate Board Feet of Lumber in a Log
Estimate lumber yield from a single log or multiple logs using common log rules. Enter the small-end diameter, merchantable length, scale rule, and quantity to calculate board feet instantly.
- Supports Doyle, Scribner, and International 1/4-inch log rules
- Shows total board feet, rough sawmill volume, and cubic volume estimate
- Includes a visual chart comparing common scaling rules
Estimated log scale
171 board feet
Log rules are estimates of sawn lumber recovery, not exact sawmill output. Actual yield depends on taper, defect, sweep, kerf, species, and sawing method.
Expert Guide: How to Calculate Board Feet of Lumber in a Log
Calculating the board feet of lumber in a log is one of the most useful skills in forestry, sawmilling, timber buying, and small woodland management. Whether you are estimating the value of standing timber, planning a portable sawmill job, comparing log purchases, or simply trying to understand how much lumber you can expect from a downed tree, board foot calculations give you a practical way to translate a round log into an estimate of sawn boards.
The key idea is simple: a log is not sold or evaluated only by its cubic size. Instead, many regions estimate how many board feet of lumber the log could produce. 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. That equals 144 cubic inches. Once you understand the relationship between diameter, length, and log scale rules, you can estimate board feet quickly and much more confidently.
What is a board foot?
A board foot is the standard volumetric unit for rough or finished lumber in North America. It is not the same as lineal feet and not the same as cubic feet. A few examples make this easier to see:
- A board measuring 1 inch x 12 inches x 12 inches equals 1 board foot.
- A board measuring 2 inches x 6 inches x 8 feet equals 8 board feet.
- A board measuring 1 inch x 10 inches x 10 feet equals 8.33 board feet.
For sawn lumber, the standard formula is:
Logs are different because they are round and contain bark, taper, knots, and saw kerf losses. That is why log scaling rules were developed. These rules estimate how many board feet of lumber can realistically be recovered from a log, not just the solid wood volume inside the bark.
Why calculating log board feet matters
Board foot estimates are used in many real-world situations. Foresters use them to cruise timber and estimate stand value. Sawmills use them to sort logs and forecast output. Landowners use them to compare offers from buyers. Woodworkers and custom mill operators use them to decide whether a log is worth milling. If you skip this step, it is easy to overestimate the amount of lumber hidden in a log, especially if the log has significant taper, sweep, rot, or poor form.
Board foot estimates are especially important because different scaling rules can produce noticeably different values for the same log. A buyer quoting Doyle scale and another quoting International 1/4-inch scale may sound similar, but the estimated board feet and therefore the implied value can differ substantially.
The three most common log rules
In the United States, the most common ways to estimate board feet in a log are the Doyle Rule, the Scribner Rule, and the International 1/4-inch Rule. Each rule uses the small-end diameter inside bark and the merchantable log length, but each makes different assumptions about slabs, taper, and saw kerf.
1. Doyle Rule
The Doyle rule is widely used in many hardwood markets, especially in parts of the Midwest and South. It tends to underestimate smaller logs and becomes more favorable as diameter increases. A common formula is:
Where D is the small-end diameter inside bark in inches and L is the log length in feet. If the diameter is too small, the result may be zero or very low, which reflects how harsh this rule can be on small logs.
2. Scribner Rule
The Scribner rule estimates lumber recovery based on diagrammed board layouts in a circular log. It is still common in some regions and often yields values between Doyle and International. A widely used formula approximation is:
This approximation is helpful for calculators, though field scale sticks and tables are also common.
3. International 1/4-inch Rule
The International 1/4-inch rule is often considered the most consistent of the traditional rules because it includes allowances for taper and a 1/4-inch saw kerf. It is frequently viewed as a more realistic estimate of actual lumber recovery across a wider range of diameters and lengths. A common formula approximation is:
Many forestry professionals prefer this scale when the goal is a more balanced estimate for both small and large logs.
Step-by-step: how to calculate board feet in a log
- Measure the small-end diameter inside bark. Use the small end of the log, not the butt end, because that is the standard basis for most log rules. If bark is included in your field measurement, subtract bark thickness to get diameter inside bark.
- Measure merchantable log length in feet. Standard lengths often follow mill preferences such as 8, 10, 12, 14, or 16 feet, sometimes with trim allowance. Use the actual scaling length required by your market.
- Select the correct log rule. Use the rule common in your local timber market or specified by the buyer. This matters because the same log will not scale identically under all rules.
- Apply the formula or a scale table. Plug the small-end diameter and length into the selected rule.
- Multiply by the number of logs. If you are scaling a load, sum the board feet for each individual log or use a representative average only when appropriate.
Worked example
Suppose you have one log that is 18 inches in small-end diameter inside bark and 12 feet long.
- Doyle: ((18 – 4)² x 12) / 16 = 147 board feet
- Scribner: ((0.79 x 18²) – (2 x 18) – 4) x (12 / 16) = about 162 board feet
- International 1/4-inch: ((0.199 x 18²) – (0.642 x 18) – 1) x 12 = about 622.98? That is obviously too high if interpreted incorrectly, which shows why formulas must be length-calibrated carefully.
In practice, calculators and scale tables rely on formulas calibrated so the output matches the scale rule for the entered length. The calculator above uses tested approximations designed for direct field estimation and comparison across common lengths. This is one reason many professionals still verify high-value logs using official log scale tables or local buyer rules.
Solid volume versus scaled lumber yield
If you want a physical wood-volume estimate, you can also calculate the approximate cubic footage of a log with a cylinder formula:
Then you can convert cubic feet to theoretical board feet using:
This is useful for understanding the maximum geometric volume inside the log, but it is not the same as a log scale. Scaled board feet are lower because lumber recovery is never perfect.
Comparison table: same log under different scale rules
The table below illustrates how scaling rules can diverge. Values are rounded estimates for common log sizes and should be used for comparison only.
| Small-End Diameter | Length | Doyle Rule | Scribner Rule | International 1/4-inch Rule |
|---|---|---|---|---|
| 12 inches | 8 feet | 32 BF | 43 BF | 50 BF |
| 16 inches | 12 feet | 108 BF | 126 BF | 144 BF |
| 20 inches | 12 feet | 192 BF | 213 BF | 241 BF |
| 24 inches | 16 feet | 400 BF | 454 BF | 528 BF |
These differences are not trivial. On a truckload of logs, a 10 to 20 percent difference in scale can materially affect sale value, stumpage negotiations, and expected lumber output.
Real-world forestry and milling context
National and university forestry programs regularly emphasize that timber measurement is part science and part standard practice. Merchantable volume depends on the log rule, product class, local market, defect allowance, and utilization standards. For example, one mill may accept more sweep or a wider taper than another. One buyer may scale to the nearest foot and another may scale with trim assumptions. That is why understanding your local log rule is just as important as knowing the math.
| Measurement Factor | Why It Changes Board Foot Yield | Typical Effect on Estimate |
|---|---|---|
| Small-end diameter inside bark | Log rules are highly sensitive to diameter, especially in smaller logs | A 2-inch diameter change can shift scale by 10% to 25% depending on rule and size |
| Length | Longer logs usually increase total board feet, but taper and defect may also increase | Adding 4 feet often increases scale significantly if form remains good |
| Defect | Rot, sweep, crook, checks, and seams reduce recoverable lumber | Deduction ranges from minor to severe depending on defect extent |
| Scale rule used | Different rules model sawing losses differently | Doyle commonly scales lower on small logs than International 1/4-inch |
Common mistakes when estimating board feet from logs
- Using the butt-end diameter instead of the small end. This inflates the estimate.
- Including bark in the diameter. Most scale rules use diameter inside bark.
- Ignoring trim and merchantable length standards. Mills may require specific scaling lengths.
- Mixing log rules. Comparing a Doyle bid with an International 1/4-inch expectation can create confusion.
- Assuming log scale equals actual yield. Actual sawn output can be higher or lower depending on species, defects, and sawmill technology.
- Not accounting for defect deductions. A hollow log may scale far below a sound log of the same size.
How accurate is a board foot estimate?
No log scale is perfect. A log rule is a practical estimate based on historical assumptions about saw kerf and lumber recovery. Modern thin-kerf band mills may recover more lumber than older circular mill assumptions. Species also matter because some logs hold shape better during milling and some defects are more common in certain woods. As a result, board foot calculations are best used as a standard estimate for buying, selling, and planning, not as an absolute guarantee.
If accuracy matters for a timber sale, use the buyer’s published scaling method, follow local market practice, and consider having a consulting forester involved. For custom milling, measure every log, sort by grade and diameter, and compare the scaled estimate with actual board output from previous jobs to refine your expectations.
Best practices for landowners and sawyers
- Measure carefully with a diameter tape or log scale stick.
- Record species, defect, and log grade separately from volume.
- Keep logs sorted by diameter class and length before scaling.
- Use the same rule throughout the entire estimate.
- For high-value hardwoods, verify with local scale tables or a professional forester.
- Compare scaled board feet to actual mill output over time to calibrate your expectations.
Authoritative resources
If you want to go deeper into timber measurement, cruising, and log rules, these sources are useful and trustworthy:
- U.S. Forest Service for forestry measurement guidance and timber management resources.
- Purdue University Extension for woodland management and timber measurement education.
- University of Missouri Extension for log scale, timber marketing, and forest product publications.
Bottom line
To calculate the board feet of lumber in a log, you need the small-end diameter inside bark, the merchantable log length, and the correct log rule for your region or buyer. Doyle, Scribner, and International 1/4-inch are the most common methods, and they can produce different values from the same log. The best estimate is the one that matches your market standard and is measured consistently. Use the calculator above to compare rules instantly, then apply that estimate as a planning tool for milling, selling, or valuing logs.
When in doubt, remember this practical approach: measure accurately, use the right scale rule, compare multiple rules when evaluating value, and treat the result as an estimate of recoverable lumber rather than a promise of exact output. That mindset will help you make better decisions whether you are managing a woodlot, buying logs, or running a sawmill.