Calculate Board Feet in a Log
Estimate lumber yield from a single log or a batch of logs using common log rules. Enter diameter, length, quantity, and your preferred rule to calculate board feet instantly and compare Doyle, Scribner, and International 1/4-inch estimates visually.
Tip: Diameter is usually measured at the small end inside bark for log scaling.
Chart compares the estimated total board feet under Doyle, Scribner, and International 1/4-inch rules for the same log dimensions.
Expert Guide: How to Calculate Board Feet in a Log
Calculating board feet in a log is one of the most practical skills in sawmilling, timber buying, forestry, and woodlot management. Whether you are estimating the value of standing timber, pricing delivered logs, planning your own milling project, or simply trying to understand how much lumber a tree might yield, the concept of board foot volume is the standard language used across much of North America. A board foot is a unit of lumber volume equal to a piece of wood measuring 1 inch thick, 12 inches wide, and 12 inches long. That means 144 cubic inches of solid wood equals 1 board foot.
However, when people ask how to calculate board feet in a log, they are often not asking for pure geometric volume. In practice, they usually want a log scale estimate, which predicts how many board feet of sawn lumber a log can produce after allowing for slabs, saw kerf, taper, and waste. That is why several different log rules exist, including the Doyle, Scribner, and International 1/4-inch rules. Each one estimates lumber yield differently, and each is still used in different regions and markets.
Key point: A log’s true cubic volume and its scaled board foot volume are not the same thing. Board foot log rules are yield estimates, not exact physical measurements.
What Inputs Matter Most?
To estimate board feet accurately, you need a few essential measurements and assumptions:
- Small-end diameter inside bark: This is the most common scaling diameter because it reflects the limiting size of the log.
- Log length: Usually measured in feet, often rounded according to regional scaling practice.
- Log rule: Doyle, Scribner, or International 1/4-inch are the most common in the United States.
- Number of logs: Useful when scaling a truckload, deck, or harvest total.
- Log quality: Sweep, crook, rot, knots, and defect can reduce merchantable board feet.
For best results, you should always know which rule your local mill, buyer, state forestry agency, or timber contract uses. The same log can show meaningfully different board foot estimates depending on the rule selected.
Board Foot Formula Versus Log Rule Formula
If you are calculating lumber after boards have already been sawn, the board foot formula is simple:
Board feet = (Thickness in inches × Width in inches × Length in feet) ÷ 12
For example, a 2 × 10 board that is 12 feet long contains:
(2 × 10 × 12) ÷ 12 = 20 board feet
But a standing tree or a round log is different. Since the wood is still in log form, mills and foresters use log rules to estimate sawn yield. These rules are based on assumptions about saw kerf, slab loss, taper, and recovery. That is why calculators like the one above use scaling formulas rather than just cylinder geometry.
Common Log Rules Used to Calculate Board Feet in a Log
1. Doyle Rule
The Doyle rule is widely used in parts of the Midwest and South. It tends to underestimate yield from smaller logs because it assumes relatively large slab and saw kerf losses. A common simplified formula is:
Doyle BF = ((D – 4)2 × L) ÷ 16
Where D is the small-end diameter in inches and L is the log length in feet. This rule becomes more reasonable on larger logs, but for small diameters it can be quite conservative.
2. Scribner Rule
The Scribner rule estimates volume by modeling the number of boards that can be sawn from the log cross-section. It is generally considered more balanced than Doyle for moderate diameters, though it still has limitations. A common calculator approximation is:
Scribner BF = (0.79 × D2 – 2 × D – 4) × (L ÷ 16)
3. International 1/4-inch Rule
The International 1/4-inch rule is often considered the most technically refined of the three major traditional rules because it incorporates more realistic allowances for taper and saw kerf. A common practical approximation is:
International BF = (0.22 × D2 – 0.71 × D) × (L ÷ 4)
In many situations, this rule gives higher values than Doyle and often somewhat higher than Scribner, especially where log size and length support better recovery.
Worked Example
Suppose you have a log that is 20 inches in small-end diameter inside bark and 16 feet long. Here is how the three rules compare using the calculator formulas:
| Log Rule | Estimated Board Feet for 20 in × 16 ft Log | General Behavior |
|---|---|---|
| Doyle | 256 BF | Often conservative, especially on smaller logs |
| Scribner | 272 BF | Moderate estimate, common in many log markets |
| International 1/4-inch | 295 BF | Often closer to modern sawing assumptions |
This example shows why it is essential to specify the rule. The same physical log can vary by nearly 40 board feet depending on the method used. If you are buying or selling many logs, those differences add up quickly.
How to Measure a Log Correctly
- Measure small-end diameter inside bark. Use a log rule stick, diameter tape, or calipers. If bark is included in the measurement, deduct bark thickness according to local practice.
- Measure merchantable length. Most scaling systems use feet and sometimes allow trim. Confirm whether your buyer measures to the nearest foot, half foot, or standard log length.
- Check for defects. Rot, sweep, crook, checks, and large knots can reduce usable scale.
- Choose the correct log rule. Use the rule specified in your timber sale agreement, mill purchase terms, or regional custom.
- Multiply by quantity. If all logs are similar, multiplying by the number of logs gives a quick batch estimate.
Why Different Regions Use Different Rules
Log scaling practices developed historically, and many rules remain in use because of market tradition rather than because one rule is universally superior. Some buyers quote prices in Doyle scale. Others use Scribner. Some regions, consulting foresters, and educational programs may prefer the International 1/4-inch rule because it better approximates actual lumber recovery in many modern contexts.
The important lesson is consistency. If you compare stumpage prices, mill bids, or truckload values, make sure the quoted price and the log scale use the same rule. A higher price per thousand board feet under one rule is not automatically a better offer than a lower price under another rule.
Comparison Table: How Rule Choice Changes Value
Below is a simple pricing illustration using a hypothetical log price of $550 per thousand board feet and the same 20 inch by 16 foot log from the earlier example.
| Log Rule | Estimated Scale | Value at $550/MBF | Difference from Doyle |
|---|---|---|---|
| Doyle | 256 BF | $140.80 | Baseline |
| Scribner | 272 BF | $149.60 | +$8.80 |
| International 1/4-inch | 295 BF | $162.25 | +$21.45 |
Even on one log, value differences can be noticeable. On a trailer load or a tract sale, they can become substantial. That is why foresters always clarify the rule being used before discussing price comparisons.
Real Forestry Context and Statistics
Forestry professionals often evaluate timber using large-scale inventory and product output data, not just a single log estimate. For example, the U.S. Forest Service reports nationwide forest inventory and timber product output trends that show how species mix, region, and end use affect wood markets. Likewise, the USDA Forest Products Laboratory publishes engineering and wood utilization references widely used in the forest sector. For field measurement methods, educational resources from land-grant institutions such as Penn State Extension help explain practical scaling and merchantability decisions.
Some broad industry facts provide helpful context:
- The United States contains hundreds of millions of acres of forest land, according to federal forest inventory programs, making consistent volume measurement essential for commerce and management.
- Board foot scaling remains especially important in sawlog transactions, while pulpwood and biomass are often traded by weight or cord volume instead.
- Modern sawmills may recover lumber more efficiently than the assumptions embedded in older log rules, which is one reason actual mill yield and scaled volume are not always identical.
Common Mistakes When Estimating Board Feet in a Log
Using outside-bark diameter without adjustment
Bark does not become lumber. If your market requires inside-bark diameter and you use outside-bark measurements, your estimate may be too high.
Ignoring length conventions
Some mills buy in fixed lengths such as 8, 10, 12, 14, and 16 feet, often with trim allowances. Measuring casually can create scale differences.
Comparing prices across different rules
A bid of $600 per thousand Scribner is not directly comparable to $600 per thousand Doyle. Always compare equivalent units.
Assuming all logs are defect-free
Rot pockets, excessive taper, sweep, and other defects reduce merchantable volume and may result in scaling deductions.
Expecting exact lumber tally from log scale
Log rules are estimates. Actual output depends on sawing pattern, kerf, equipment, species, defect, and target products.
When to Use a Board Foot Log Calculator
- Estimating sawlog yield before felling or hauling
- Comparing potential value between timber sale offers
- Planning custom milling jobs
- Teaching forestry, wood products, or sawmilling basics
- Creating rough project estimates for barn lumber, beams, or live-edge slabs
Tips for More Accurate Results
- Measure multiple diameters if the log is out of round and average them according to local practice.
- Use a scaling stick or diameter tape designed for forestry work.
- Separate logs by species and quality class before pricing.
- Ask your mill which rule they purchase on and whether they apply defect deductions.
- For high-value timber, consider consulting a professional forester for inventory and marketing assistance.
Final Takeaway
To calculate board feet in a log, you need more than just diameter and length. You also need to understand the log rule used to estimate sawable lumber output. Doyle, Scribner, and International 1/4-inch can all produce different answers for the same log, and those differences can materially affect value, planning, and negotiation. The calculator above makes the process faster by letting you enter your measurements once and compare the major rules instantly.
If you want the best practical result, measure the small-end diameter inside bark, confirm the merchantable length, select the rule used in your market, and treat the result as a well-informed estimate rather than a guaranteed lumber tally. That approach aligns with real-world forestry practice and gives you a solid basis for timber decisions.