Board Feet in a Log Calculator
Calculate Board Feet
Estimate the lumber yield (board feet) from a log using standard log scaling rules.
Comparison of Board Feet by Different Log Rules for the given inputs.
| Diameter (in) | Board Feet (Selected Rule) |
|---|---|
| – | – |
| – | – |
| – | – |
Board feet variation with diameter using the selected rule.
What is a Board Feet in a Log Calculator?
A board feet in a log calculator is a tool used in the forestry and lumber industries to estimate the amount of lumber (measured in board feet) that can be sawn from a log of a given diameter and length. One board foot is a unit of volume for lumber, equivalent to a piece of wood 12 inches long, 12 inches wide, and 1 inch thick (144 cubic inches).
This calculator utilizes standard log scaling rules—Doyle, Scribner, and International 1/4″—to provide these estimates. Log scaling is the process of measuring logs to determine their volume, typically in board feet, and these rules are different mathematical methods to achieve this, each with its own history and typical applications. Foresters, loggers, sawmill operators, and timber buyers use a board feet in a log calculator to assess the value and potential yield of logs before processing.
Common misconceptions are that all rules give the same result, or that the calculated board feet will be the exact amount of lumber produced. In reality, the actual yield can vary based on the sawyer’s skill, kerf (saw blade thickness), log defects, and the dimensions of lumber being cut.
Board Feet in a Log Calculator Formula and Mathematical Explanation
The board feet in a log calculator uses one of several formulas based on the selected log rule:
- Doyle Log Rule: Tends to underestimate small logs and overestimate large logs. The formula is:
Board Feet = ((D – 4) / 4)2 * L
Where D is the small-end diameter in inches (inside bark), and L is the log length in feet. - Scribner Log Rule (Approximate Formula): Based on diagrams of 1-inch boards within circles representing log ends, minus waste. A common approximation is:
Board Feet ≈ (0.79 * D2 – 2 * D – 4) * L / 16
This is an approximation of the more complex table-based Scribner rule. - International 1/4″ Log Rule: Considered the most accurate, it accounts for a 1/4-inch kerf and a 1/2-inch taper every 4 feet. It’s calculated by summing the board feet in 4-foot sections:
For each 4-foot section: BFsection = 0.905 * (0.22 * d2 – 0.71 * d), where d is the diameter at the small end of the 4-foot section. The diameter increases by 0.5 inches for each subsequent 4-foot section. The calculator sums these sections and adds the volume for any remaining partial section.
The formulas aim to estimate the volume of sawn lumber, considering deductions for saw kerf and slabbing.
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| D | Log Diameter (small end, inside bark) | inches | 6 – 40 |
| L | Log Length | feet | 8 – 20 |
| BF | Board Feet | board ft | Varies |
Practical Examples (Real-World Use Cases)
Example 1: Calculating Board Feet for a Pine Log (Doyle)
A logger has a pine log that measures 16 inches in diameter at the small end and is 16 feet long. They want to use the Doyle rule.
- D = 16 inches
- L = 16 feet
- Rule = Doyle
- Board Feet = ((16 – 4) / 4)2 * 16 = (12 / 4)2 * 16 = 32 * 16 = 9 * 16 = 144 board feet.
The board feet in a log calculator would show 144 board feet using the Doyle rule.
Example 2: Calculating Board Feet for an Oak Log (International 1/4″)
A sawmill operator receives an oak log 20 inches in diameter and 12 feet long. They use the International 1/4″ rule.
- D = 20 inches
- L = 12 feet (three 4-foot sections)
- Rule = International 1/4″
- Section 1 (D=20): 0.905 * (0.22*202 – 0.71*20) = 0.905 * (88 – 14.2) = 66.819 BF
- Section 2 (D=20.5): 0.905 * (0.22*20.52 – 0.71*20.5) = 0.905 * (92.455 – 14.555) = 70.504 BF
- Section 3 (D=21): 0.905 * (0.22*212 – 0.71*21) = 0.905 * (97.02 – 14.91) = 74.304 BF
- Total Board Feet ≈ 66.819 + 70.504 + 74.304 = 211.6 board feet.
The board feet in a log calculator automates this sectional calculation for the International 1/4″ rule.
How to Use This Board Feet in a Log Calculator
- Enter Log Diameter: Input the diameter of the log at its smallest end, measured inside the bark, in inches.
- Enter Log Length: Input the length of the log in feet.
- Select Log Scale Rule: Choose the log scaling rule (Doyle, Scribner Approx., or International 1/4″) you wish to use from the dropdown menu.
- Calculate: The calculator will automatically update the estimated board feet as you input or change values, or you can click “Calculate”.
- Read Results: The primary result is the estimated board feet. Intermediate values like the rule used, inputs, and approximate cubic foot volume are also shown. The chart and table provide further comparisons.
The results help estimate the lumber yield, which is crucial for valuing logs and planning sawmill operations. Comparing results from different rules can also be informative.
Key Factors That Affect Board Feet in a Log Calculator Results
- Log Diameter: The most significant factor. Board feet increase exponentially with diameter.
- Log Length: Board feet increase linearly with length for Doyle and Scribner, and slightly more with International due to taper allowance.
- Log Rule Used: Different rules yield different results, especially for small or very large diameters. Doyle undervalues small logs, International is generally most accurate.
- Taper: The rate at which the log’s diameter decreases from butt to top. The International 1/4″ rule explicitly accounts for a standard taper (1/2″ per 4ft), others less so. High taper reduces yield relative to small-end diameter.
- Defects: The calculator assumes a sound, straight log. Defects like rot, knots, sweep (curve), or crook will reduce the actual lumber yield compared to the calculated board feet.
- Saw Kerf: The thickness of the saw blade. The International 1/4″ rule assumes 1/4″, but if a different kerf is used, the yield will vary.
- Sawyer Efficiency: The skill of the person sawing the log significantly impacts how much usable lumber is recovered.
Understanding these factors helps interpret the results from the board feet in a log calculator more accurately.
Frequently Asked Questions (FAQ)
- What is the most accurate log rule?
- The International 1/4″ log rule is generally considered the most accurate as it accounts for taper and a specific kerf, closely estimating the actual lumber output from sound logs.
- Why do different log rules give different board feet values?
- The rules were developed at different times, with different assumptions about milling practices, saw kerf, and the smallest board size to be tallied. Doyle was based on early milling, Scribner on diagrams, and International on a more mathematical approach with defined kerf and taper.
- Does this calculator account for log defects?
- No, the board feet in a log calculator provides an estimate for a straight, sound log. Deductions for defects (rot, knots, sweep, etc.) must be made separately by an experienced scaler.
- What if my log is longer than 20 feet?
- While the calculator can accept longer lengths, log rules are often applied to logs in segments (e.g., 16 or 20 feet maximum scaling length), and very long logs might be scaled as two or more shorter logs.
- Can I use this calculator for hardwood and softwood?
- Yes, the log scaling rules are applied to both hardwood and softwood logs. The species doesn’t change the board foot calculation itself, though it affects the value and use of the lumber.
- What does ‘inside bark’ mean for diameter?
- It means the diameter measurement should be taken after excluding the bark thickness, measuring the wood cylinder itself at the small end.
- How is board footage different from cubic footage?
- Board footage measures the volume of lumber that can be sawn (1 board foot = 144 cubic inches of sawn lumber), while cubic footage measures the total wood volume of the log cylinder (including waste like sawdust and slabs). The calculator gives an approximate cubic foot volume for reference.
- Is the Scribner rule used here the table or formula version?
- This board feet in a log calculator uses a common mathematical approximation of the Scribner rule for ease of calculation. Official Scribner scaling is often done using tables or more complex formulas derived from them.
Related Tools and Internal Resources
- Doyle Log Rule Explained: A detailed look at the Doyle log rule, its history, and application.
- Understanding the Scribner Log Rule: Learn more about the Scribner rule and how it’s used.
- International 1/4″ Log Rule Details: In-depth information on the International 1/4″ rule.
- Timber Measurement Guide: A guide to various methods of measuring timber and logs.
- Lumber Yield From Logs: Factors affecting how much lumber you can get from logs.
- Log Value Estimation: How to estimate the monetary value of standing timber or logs.