Board Feet in a Log Calculator

Estimate the board feet volume of a log using standard log scaling rules. Enter the log’s dimensions and select a scaling rule with our board feet in a log calculator.

Board Feet Comparison Table

Estimated board feet for various diameters at 16 ft length using the Doyle rule.

Diameter (in)	Board Feet (Doyle, 16ft)

Board Feet Comparison Chart (16 ft Log)

Comparison of Doyle, Scribner (approx.), and International 1/4″ (approx.) rules for a 16 ft log across different diameters.

What is a Board Feet in a Log Calculator?

A board feet in a log calculator is a tool used to estimate the volume of lumber, measured in board feet, that can be sawn from a log of a given size. One board foot is a unit of volume equivalent to a piece of wood 12 inches long, 12 inches wide, and 1 inch thick (144 cubic inches). Log scalers and foresters use these calculators and log scaling rules to determine the potential yield of logs before they are milled.

These calculators typically employ one of several standard log scaling rules: Doyle, Scribner, or International 1/4″. Each rule uses a different mathematical formula or table to estimate the board feet, and the results can vary significantly, especially for smaller or larger diameter logs. The choice of rule often depends on regional practices and the type of timber being scaled.

Who Should Use a Board Feet in a Log Calculator?

• Timber sellers and buyers
• Foresters and forest managers
• Sawmill operators
• Loggers
• Landowners managing timber resources

Common Misconceptions

A common misconception is that the calculated board feet represent the exact amount of lumber that will be produced. In reality, the actual yield can be affected by factors like saw kerf (width of the saw cut), sawing methods, log taper, and defects within the log (rot, knots, sweep). The board feet in a log calculator provides an estimate based on ideal conditions and the chosen rule.

Board Feet in a Log Calculator Formulas and Mathematical Explanation

Different log scaling rules use different formulas to estimate board feet. Here are the common ones used by a board feet in a log calculator:

1. Doyle Log Rule

The Doyle rule is a formula-based rule that tends to underscale small logs and overscale large logs compared to the actual lumber yield. It’s simple to apply.

Formula: `BF = ((D – 4) / 4)^2 * L`

• BF = Board Feet
• D = Diameter of the small end of the log (inside bark, inches)
• L = Length of the log (feet)

The rule deducts 4 inches for slabbing and saw kerf, then squares one-quarter of the remaining diameter and multiplies by the length.

2. Scribner Log Rule

The Scribner rule was originally created by drawing diagrams of 1-inch boards within circles representing log ends of various diameters and summing the board feet. It is often used from tables, but approximations exist.

Approximation Formula: `BF = (0.0494 * D^2 – 0.124 * D – 0.269) * L` (This is one approximation, others exist and tables are more accurate).

Scribner generally gives a more reasonable estimate than Doyle, especially for medium-sized logs, but doesn’t account for taper well.

3. International 1/4″ Log Rule

The International 1/4″ rule is a formula-based rule designed to be more accurate, considering a 1/4-inch saw kerf and a 1/2-inch taper for every 4 feet of log length (though simplified formulas often use the small-end diameter for the whole length for ease of use in a basic board feet in a log calculator).

Simplified Formula (based on small end, derived from 16ft base): `BF = (0.04975*D^2 – 0.0859375*D – 0.076875)*L`

More accurately, it considers 4-foot sections with taper. The formula for a 4-foot section is `BF(4ft) = 0.905 * (0.22*D^2 – 0.71*D)`, where D is the diameter for that section. Our board feet in a log calculator uses a simplified approximation based on the small end for ease of input.

Variables Table

Variable	Meaning	Unit	Typical Range
D	Log Diameter (small end, inside bark)	Inches	6 – 40+
L	Log Length	Feet	8 – 40+
BF	Board Feet	BF	Varies greatly

Variables used in board feet calculations.

Practical Examples (Real-World Use Cases)

Example 1: Scaling a Pine Log with Doyle

A logger has a pine log that measures 14 inches in diameter at the small end and is 16 feet long. They use the Doyle rule.

• D = 14 inches
• L = 16 feet
• Rule = Doyle

Using the board feet in a log calculator (or formula `BF = ((14 – 4) / 4)^2 * 16`):

BF = (10 / 4)^2 * 16 = (2.5)^2 * 16 = 6.25 * 16 = 100 BF (Doyle)

The estimated volume is 100 board feet using the Doyle rule.

Example 2: Scaling an Oak Log with International 1/4″

A sawmill receives an oak log measuring 20 inches in diameter (small end) and 12 feet long. They prefer the International 1/4″ rule for hardwoods.

• D = 20 inches
• L = 12 feet
• Rule = International 1/4″

Using the simplified International 1/4″ formula in the board feet in a log calculator (`BF = (0.04975*20^2 – 0.0859375*20 – 0.076875)*12`):

BF = (0.04975 * 400 – 1.71875 – 0.076875) * 12 = (19.9 – 1.71875 – 0.076875) * 12 = 18.104375 * 12 ≈ 217 BF (Int 1/4″)

The estimated volume is around 217 board feet using the International 1/4″ rule approximation.

How to Use This Board Feet in a Log Calculator

1. Enter Log Diameter: Input the average diameter of the small end of the log, measured inside the bark, in inches.
2. Enter Log Length: Input the length of the log in feet.
3. Select Log Scaling Rule: Choose the desired log scaling rule (Doyle, Scribner, or International 1/4″) from the dropdown menu.
4. View Results: The board feet in a log calculator will instantly display the estimated board feet based on the selected rule, as well as estimates from the other two rules for comparison. The formula used for the primary result is also shown.
5. Interpret Table and Chart: The table and chart below the main results provide further context, showing board feet for different diameters and comparing the rules visually.
6. Reset or Copy: Use the “Reset” button to return to default values or “Copy Results” to copy the main outputs.

The results help in estimating the potential lumber yield before milling. Be aware that the chosen rule significantly impacts the result, especially for different log sizes.

Key Factors That Affect Board Feet in a Log Calculator Results

1. Log Diameter: This is the most significant factor. Board feet increase rapidly with diameter.
2. Log Length: Longer logs generally yield more board feet, proportionally.
3. Log Scaling Rule Used: As seen, Doyle, Scribner, and International 1/4″ give different estimates. The choice of rule is crucial. A {related_keywords}[0] method depends on the rule.
4. Taper: The natural decrease in diameter from the butt end to the small end. Some rules (like International more accurately) account for taper, while others using only the small-end diameter may underestimate volume in highly tapered logs. Our board feet in a log calculator uses simplified formulas based on small-end diameter.
5. Defects: Rot, knots, cracks, sweep (curve), or crook (abrupt bend) reduce the amount of usable lumber, and scalers often make deductions for these, which are not automatically included in basic board feet in a log calculator formulas.
6. Saw Kerf: The width of wood removed by the saw blade during milling. The International 1/4″ rule explicitly accounts for a 1/4″ kerf, while others imply different allowances.
7. Shrinkage: Wood shrinks as it dries, which can slightly reduce the final tallied board footage of dried lumber compared to the green log scale.
8. Sawyer’s Efficiency: How the sawyer cuts the log to maximize usable lumber also affects the actual yield versus the scaled volume.

Frequently Asked Questions (FAQ)

What is the most accurate log scaling rule?

The International 1/4″ rule is generally considered the most accurate as it mathematically accounts for taper and saw kerf. However, its accuracy depends on the log being relatively straight and cylindrical. Local practices often dictate which rule is used for buying and selling timber.

Why do Doyle, Scribner, and International rules give different results?

They were developed at different times using different methods. Doyle is a simple formula that heavily penalizes small diameters. Scribner was based on diagrams and is more empirical. International 1/4″ is a formula designed to be more mathematically precise about lumber recovery with a specific kerf.

Does this board feet in a log calculator account for log taper?

Our calculator uses simplified formulas based on the small-end diameter, as is common for basic field estimations with these rules. The International 1/4″ rule inherently accounts for taper better when applied section by section, but our simplified version gives an estimate based on the small end for the full length.

What if my log is not perfectly round?

You should take two measurements at right angles at the small end (inside bark) and average them to get the diameter for the board feet in a log calculator.

How do I account for defects?

This calculator does not automatically deduct for defects. A trained log scaler would visually assess the log and make manual deductions from the gross scale based on the type, size, and location of defects according to specific scaling guidelines.

Can I use this calculator for firewood volume?

No, this board feet in a log calculator is for estimating lumber volume (board feet), not firewood volume, which is usually measured in cords or cubic feet.

What is “overrun” or “underrun”?

Overrun is when the actual lumber sawn from a log is more than the estimated board feet by the log rule. Underrun is when it’s less. Doyle often results in overrun for small logs, while Scribner can have less variance.

Is there a difference between board feet and linear feet?

Yes. Board feet is a measure of volume (1 ft x 1 ft x 1 in). Linear feet is just a measure of length.

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