Board Foot in a Log Calculator
An expert tool to help you learn **how to calculate board feet in a log** using the industry-standard Doyle Log Scale.
Formula: Board Feet = ((Diameter – 4)² * Length) / 16
Board Feet vs. Diameter (for current log length)
Doyle Log Scale Reference Table
| Diameter (in) | 8 ft Length | 10 ft Length | 12 ft Length | 14 ft Length | 16 ft Length |
|---|---|---|---|---|---|
| 10 | 18 | 22 | 27 | 31 | 36 |
| 12 | 32 | 40 | 48 | 56 | 64 |
| 14 | 50 | 62 | 75 | 87 | 100 |
| 16 | 72 | 90 | 108 | 126 | 144 |
| 18 | 98 | 122 | 147 | 171 | 196 |
| 20 | 128 | 160 | 192 | 224 | 256 |
| 24 | 200 | 250 | 300 | 350 | 400 |
What is a Board Foot?
A “board foot” is the standard unit of volume measurement for lumber in the United States and Canada. It represents a piece of wood that is one foot long, one foot wide, and one inch thick (1′ x 1′ x 1″), or its volumetric equivalent of 144 cubic inches. When you need to **how to calculate board feet in a log**, you are estimating how many of these 144-cubic-inch blocks of usable lumber can be sawn from a cylindrical log. This calculation is fundamental for anyone in the timber industry, from foresters valuing a stand of trees to sawmill operators determining production and pricing. Common misconceptions are that it’s a measure of length or that it’s the same as a square foot; in reality, it is a measure of volume.
Board Foot Formula and Mathematical Explanation
There are several methods, or “log rules,” to estimate the board feet in a log. Each rule is a formula that accounts for the unusable wood that is lost to slabs, edgings, and sawdust (kerf). The Doyle Log Scale is one of the oldest and most widely used, especially for hardwood logs. Its persistence is due to its simplicity. The primary formula for those learning **how to calculate board feet in a log** using the Doyle rule is:
Board Feet = ((Diameter – 4)² * Length) / 16
The logic is straightforward: it subtracts 4 inches from the diameter to account for slabbing (the initial cuts to square the log), squares the result, multiplies by the length, and divides by 16. This rule is known to underestimate the yield of small logs and overestimate the yield of large logs. For more information on different log scaling methods, you can consult a guide on log scaling methods.
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Diameter (D) | The diameter of the log’s small end, measured inside the bark. | Inches | 8 – 40+ |
| Length (L) | The length of the log. | Feet | 8 – 20 |
| Board Feet (BF) | The estimated volume of usable lumber. | Board Feet | Varies widely |
Practical Examples
Example 1: A Standard Pine Log
You have a pine log that is 16 feet long with a small-end diameter of 14 inches. Using the Doyle rule to figure out **how to calculate board feet in a log**:
Inputs: Diameter = 14 inches, Length = 16 feet
Calculation: BF = ((14 – 4)² * 16) / 16 = (10² * 16) / 16 = (100 * 16) / 16 = 100 Board Feet.
Interpretation: You can expect to mill approximately 100 board feet of lumber from this log.
Example 2: A Large Oak Log
You are evaluating a large oak log for purchase. It is 12 feet long with a small-end diameter of 24 inches.
Inputs: Diameter = 24 inches, Length = 12 feet
Calculation: BF = ((24 – 4)² * 12) / 16 = (20² * 12) / 16 = (400 * 12) / 16 = 300 Board Feet.
Interpretation: This high-value log is estimated to yield 300 board feet. A detailed explanation of the Doyle Log Rule is explained more here.
How to Use This Board Foot Calculator
This calculator makes it simple to understand **how to calculate board feet in a log**. Follow these steps for an accurate estimation:
- Measure Log Diameter: Using a tape measure, find the diameter of the small end of the log. Be sure to measure *inside* the bark on both sides of the center point and average the measurement if the log isn’t perfectly round. Enter this value in the “Log Diameter” field in inches.
- Measure Log Length: Measure the entire length of the log from one end to the other. Enter this value in the “Log Length” field in feet.
- Read the Results: The calculator will instantly update, showing the “Estimated Total Board Feet” based on the Doyle Log Scale. The intermediate values and chart will also adjust to reflect your inputs.
- Decision Making: Use this estimate to value logs for buying or selling, or to plan your milling projects. If you are looking to buy standing timber, this calculation is a critical first step.
Key Factors That Affect Board Foot Results
The result of any board foot calculation is an estimate. The actual lumber yield can be influenced by several factors. Understanding these factors is key to truly mastering **how to calculate board feet in a log**.
- Log Rule Used: The Doyle scale is just one of many. The Scribner log scale and International 1/4-inch rule will give different results for the same log. The International rule is often considered the most accurate.
- Log Diameter: This is the most significant factor. As diameter increases, the potential board foot volume increases exponentially.
- Log Taper: Logs are wider at the base than at the top. Since log rules only use the small-end diameter, a log with significant taper will yield more lumber than the rule predicts.
- Saw Kerf: This is the thickness of the saw blade. A thinner blade creates less sawdust and therefore increases the lumber yield. Old log rules were based on thicker blades than modern bandsaw mills use.
- Log Defects: The presence of rot, cracks, knots, or curves will reduce the amount of usable lumber that can be sawn from a log. A scaler will make deductions from the gross scale to account for these defects.
- Sawyer’s Skill: An experienced sawyer can make cutting decisions that maximize the yield from a log, producing more high-quality lumber and less waste.
Frequently Asked Questions (FAQ)
The International 1/4-Inch Log Rule is generally considered the most accurate because its formula more closely accounts for log taper and actual lumber yield. However, the most *common* rule used in a specific region is often the standard for business, regardless of accuracy.
No. Standard practice for **how to calculate board feet in a log** requires measuring the diameter *inside* the bark (DIB). You must subtract the bark thickness from your measurement before entering it into the calculator.
The flat 4-inch deduction for slabbing is proportionally very large for a small-diameter log (e.g., an 8-inch log), effectively removing a huge percentage of its volume in the calculation. This same 4-inch deduction is less significant on a 30-inch log.
For logs that are not perfectly round, take two measurements of the small-end diameter at 90 degrees to each other and average them. Use this average diameter in the calculator.
Overrun is the difference between the actual amount of lumber sawn from a log and the amount predicted by the log scale. With modern, thin-kerf saws, sawmills almost always have an overrun compared to the Doyle scale, especially on smaller logs.
Yes, but it requires additional steps. You must estimate the diameter at breast height (DBH), the merchantable height of the tree (how many logs can be cut), and then estimate the top diameter of each potential log to apply the log rule. This is a more advanced skill.
Kerf refers to the width of the cut made by a saw blade. This wood is turned into sawdust and is a primary source of loss when milling lumber. Modern bandsaws have a much smaller kerf than older circular saws, which is why they can yield more lumber from the same log.
This calculator estimates the potential yield from a *round log*. A lumber volume calculator, on the other hand, calculates the board feet of already-milled, *rectangular boards* of lumber. The process of learning how to calculate board feet in a log is an estimation of future yield.