How To Calculate The Board Feet In A Log

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Estimate log yield fast with Doyle, Scribner, or International 1/4-inch rules. Enter diameter, length, and quantity to get board foot totals, a method comparison, and a visual chart.

Board Foot Calculator

Expert Guide: How to Calculate the Board Feet in a Log

Calculating the board feet in a log is one of the most practical skills in forestry, sawmilling, timber buying, and land management. Whether you are estimating the value of a few walnut logs, scaling mixed hardwood logs at a landing, or comparing bids from a mill, the goal is the same: convert a round log into a useful estimate of how many board feet of lumber it can 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 means one board foot contains 144 cubic inches of wood. Logs are not sawn lumber, though, so foresters and mill buyers do not usually calculate log board feet by simply converting the raw cylinder volume into lumber volume. Instead, they use log rules, which are formulas or scale tables designed to estimate how much sawn lumber can reasonably be recovered from a log.

The three most common log rules in the United States are Doyle, Scribner, and International 1/4-inch. Each rule makes different assumptions about slab loss, saw kerf, and taper. That is why the exact same log can produce different board foot estimates depending on the rule used. Understanding these differences is essential if you want to compare timber prices fairly or estimate yield with confidence.

What You Need to Measure

To calculate board feet in a log, you generally need only two core measurements and one rule selection:

• Small-end diameter inside bark in inches. This is often abbreviated as DIB.
• Merchantable log length in feet.
• Log rule such as Doyle, Scribner, or International 1/4-inch.

The small end matters because lumber yield is constrained by the narrowest usable cross section of the log. If you measure the large end instead, your estimate will usually be too high. Most professional scaling practices also deduct obvious defects, crook, rot, or sweep before assigning a final scale.

The Basic Concept Behind Board Foot Scaling

If logs were perfect cylinders and mills had zero waste, you could calculate the rough wood volume in cubic feet and convert that into board feet. But real milling does not work that way. A round log must first be slabbed into a cant, then edged into boards, and every saw cut removes some material as kerf. Bark, taper, knots, rot, and handling losses further reduce recovery. Log rules try to estimate this practical recovery in a repeatable way.

Board foot in sawn lumber = thickness (inches) x width (inches) x length (feet) / 12

For raw logs, however, you usually apply a log rule formula rather than the simple lumber formula above.

Common Log Rule Formulas

Many landowners hear log buyers quote board feet without realizing that the number depends on the scaling system. Here are the formulas used by this calculator:

• Doyle Rule: BF = ((D – 4) x (D – 4) x L) / 16
• Scribner Rule: BF = ((0.79 x D x D) – (2 x D) – 4) x L / 16
• International 1/4-inch Rule: BF = ((0.22 x D x D) – (0.71 x D)) x (L / 4)

In these formulas, D is the small-end diameter inside bark in inches and L is the log length in feet. Because these are estimates, they are best used for comparison, timber sale planning, and communication with mills rather than as a guarantee of exact lumber output.

Step-by-Step: How to Calculate Board Feet in a Log

1. Measure the small-end diameter inside bark. Use a log scale stick or tape. If bark is included, your estimate can be inflated.
2. Measure the merchantable length. Use the usable straight section of the log, not the total stem length if defects or flare limit recovery.
3. Select the correct log rule. Ask the mill, timber buyer, or local forestry office which rule is standard in your region.
4. Apply the formula. Plug the diameter and length into the chosen rule.
5. Multiply by the number of logs. If you are scaling a load or a stand, total the per-log estimate across all logs.
6. Adjust expectations for defects. Rot, taper, sweep, shake, and crook can reduce actual recoverable lumber.

Worked Example

Suppose you have a 16-foot log with a 16-inch small-end diameter inside bark. Here is how the three common rules compare:

• Doyle: ((16 – 4) x (16 – 4) x 16) / 16 = 144 board feet
• Scribner: ((0.79 x 16 x 16) – (2 x 16) – 4) x 16 / 16 = 166.24 board feet
• International 1/4-inch: ((0.22 x 16 x 16) – (0.71 x 16)) x (16 / 4) = 179.84 board feet

This example shows why the selected rule matters. On the same log, the estimate ranges from about 144 to almost 180 board feet. If you are negotiating a stumpage contract or comparing delivered log prices, you must verify which rule is being used or the financial difference can be significant.

Rule Comparison Table for a 16-Foot Log

The table below compares approximate board foot estimates for common diameters using the formulas above. These are practical scaling estimates, not theoretical cylinder volumes.

Small-End Diameter (in)	Doyle Rule (BF)	Scribner Rule (BF)	International 1/4-inch (BF)
12	64.00	85.76	92.64
16	144.00	166.24	179.84
20	256.00	272.00	295.20
24	400.00	403.04	438.72

Theoretical Maximum Volume Versus Scaled Board Feet

Another useful perspective is to compare a log rule estimate against the geometric volume of a perfect cylinder. This is not what a mill will recover, but it shows why scaled board feet are always lower than the wood physically present in the round log.

Diameter (in)	Length (ft)	Cylinder Volume (cubic feet)	Theoretical Maximum (board feet)
12	16	12.57	150.80
16	16	22.34	268.08
20	16	34.91	418.88
24	16	50.27	603.19

Notice how even a perfect 16-inch by 16-foot cylinder contains about 268 theoretical board feet of wood volume, yet practical scale estimates range far lower. The difference reflects real sawmill constraints and why log rules remain essential in commerce.

When to Use Doyle, Scribner, or International 1/4-inch

Doyle is common in some hardwood markets and is easy to compute, but it tends to under-scale small logs. Buyers and sellers should be cautious when comparing Doyle numbers across mixed diameter classes because the rule penalizes smaller logs more heavily.

Scribner is another traditional rule used in many regions. It is based on diagrammed boards cut from circles and often falls between Doyle and International for the same log.

International 1/4-inch is often considered one of the more consistent rules because it better accounts for taper and a realistic saw kerf assumption. Many foresters prefer it when accuracy across a wider range of diameters is important.

Common Mistakes That Lead to Bad Estimates

• Measuring over bark instead of inside bark. Bark thickness can meaningfully affect scale.
• Using the wrong end of the log. The small end is usually the correct reference point.
• Mixing log rules. A price quoted per thousand board feet under one rule is not directly comparable to another rule without adjustment.
• Ignoring defect deductions. Hollow sections, rot pockets, and sweep can reduce actual lumber recovery dramatically.
• Assuming board foot scale equals mill output. Different sawing patterns, product targets, and machinery can alter final lumber tally.

How Mills and Foresters Use Board Foot Calculations

Foresters use log scale estimates for timber cruises, sale preparation, and stand valuation. Log buyers use them to build delivered cost models and set bids. Sawmills use them for procurement planning, inventory, and production forecasting. Landowners use board foot estimates to compare offers, especially in selective harvests where a few premium logs can account for a large share of total value.

If you are selling logs, ask four questions before relying on a quote:

1. Which log rule is being used?
2. Are measurements inside bark or over bark?
3. How are defects deducted?
4. Is payment based on scale, weight, or actual mill tally?

Those questions often matter more than the raw board foot number itself.

Board Feet in Logs Versus Board Feet in Lumber

It is also important to separate log scale from finished lumber tally. A board foot in lumber is exact and based on product dimensions. A board foot in a log is an estimate based on a scaling rule. Because a mill may optimize for grade, width, thickness, or specialty cuts, the actual lumber package produced from a log can differ from the original scale estimate. In addition, kiln drying and planing reduce finished dimensions even though lumber is still marketed using nominal sizes.

Practical Tips for Better Accuracy

• Use a scale stick or diameter tape designed for forestry work.
• Measure each log individually if value matters. Average diameter methods are quick but less accurate.
• Sort logs by species and grade before estimating value.
• Keep a field sheet with diameter, length, defects, and final rule used.
• Confirm local standards because regional practices differ by species, market, and mill technology.

Authoritative Forestry and Measurement Resources

If you want deeper technical guidance on timber measurement, mensuration, and scaling standards, review these authoritative sources:

• USDA Forest Service – federal forestry guidance, timber measurement references, and management publications.
• Penn State Extension – forest management and woodland measurement education.
• University of Missouri Extension – practical forestry resources for log valuation and woodland owners.

Final Takeaway

To calculate the board feet in a log, measure the small-end diameter inside bark, measure the merchantable length, choose the correct scaling rule, and apply the appropriate formula. For quick field use, the calculator above lets you compare Doyle, Scribner, and International 1/4-inch results instantly. The most important thing to remember is that a log’s board foot estimate depends heavily on the rule used. If you are buying, selling, or managing timber, always compare numbers on the same basis.