How to Calculate the Board Feet in a Log
Use this premium log scale calculator to estimate board feet from log diameter and log length using the Doyle, Scribner, or International 1/4-inch rules.
Expert Guide: How to Calculate the Board Feet in a Log
Knowing how to calculate the board feet in a log is one of the most practical skills in forestry, sawmilling, timber buying, and woodlot management. Whether you are selling sawlogs, buying timber, estimating lumber recovery, or simply trying to understand how much usable wood a tree contains, board-foot scaling gives you a consistent way to estimate value and yield. The key point is that board feet measure potential lumber output, not just the raw solid volume of the log. That is why the same log can produce different board-foot figures under different log rules.
A board foot is a piece of wood measuring 12 inches long, 12 inches wide, and 1 inch thick. Mathematically, that equals 144 cubic inches, or one-twelfth of a cubic foot. When you are working with logs, however, you usually do not convert the cylinder volume directly into board feet. Instead, most log buyers and foresters use standardized log scaling rules that estimate how much sawn lumber can be recovered after accounting for slabs, taper, edging, trim, and saw kerf. The most common rules in North America are the Doyle Rule, Scribner Rule, and International 1/4-inch Rule.
Step 1: Measure the small-end diameter inside bark
To estimate board feet accurately, measure the small end of the log, not the large butt end. In many scaling systems, the diameter should be taken inside bark, because bark thickness does not become lumber. Use a log scale stick, diameter tape, or calipers. Measure across the shortest axis if the log is slightly oval, or average two measurements if local practice calls for it. Small errors matter. A difference of just 1 inch in diameter can change the board-foot tally significantly, especially on medium-sized logs.
Step 2: Measure the log length
Measure the merchantable length in feet. In some operations, logs are cut to standard lengths such as 8, 10, 12, 14, or 16 feet, often with trim allowance added. If you are using a scaling rule table from a mill or extension guide, make sure your length matches the rule format they expect. Some formulas are easiest to use in 4-foot increments, while many field tables are already prepared for common sawlog lengths. This calculator accepts any practical length value and applies the formulas directly.
Step 3: Choose the right log rule
The reason there is no single universal answer to “how many board feet are in this log?” is that different log rules estimate recoverable lumber differently. Here is what each rule generally does:
- Doyle Rule: very common in some hardwood regions. It tends to undervalue small logs because the formula subtracts 4 inches from diameter before squaring.
- Scribner Rule: based on diagrammed boards sawn from a round log. It is often more moderate than Doyle on smaller diameters.
- International 1/4-inch Rule: designed to better reflect actual sawing losses and usually gives more consistent estimates across a wider range of diameters and lengths.
Common formulas used to estimate board feet
For practical field estimation, these formulas are commonly used:
- Doyle Rule: Board Feet = ((D – 4) × (D – 4) × L) ÷ 16
- Scribner Rule: Board Feet = ((0.79 × D × D) – (2 × D) – 4) × L ÷ 16
- International 1/4-inch Rule: Board Feet = ((0.199 × D × D) – (0.642 × D) – 1) × (L ÷ 4)
In these formulas, D is the small-end diameter inside bark in inches and L is the log length in feet. These equations are simplifications used for estimation and can vary slightly from printed scale tables. In trade, a local mill, forester, or timber buyer may round figures according to their own scaling standard, especially where trim and defect deductions are involved.
Worked example: a 16-inch by 16-foot log
Suppose a log measures 16 inches at the small end inside bark and 16 feet long. Using standard estimating formulas:
- Doyle: ((16 – 4)² × 16) ÷ 16 = 144 board feet
- Scribner: ((0.79 × 16²) – (2 × 16) – 4) × 16 ÷ 16 = about 166 board feet
- International 1/4-inch: ((0.199 × 16²) – (0.642 × 16) – 1) × (16 ÷ 4) = about 159 board feet
Notice how the same log can scale differently depending on the rule. That is why buyers and sellers always need to agree on the rule before discussing price per thousand board feet. A price quote without a stated log rule can be misleading because the total value changes when the estimated volume changes.
Comparison table: estimated board feet for 16-foot logs
| Small-End Diameter | Doyle Rule | Scribner Rule | International 1/4-inch Rule |
|---|---|---|---|
| 10 inches | 36 bf | 45 bf | 50 bf |
| 12 inches | 64 bf | 86 bf | 78 bf |
| 14 inches | 100 bf | 123 bf | 115 bf |
| 16 inches | 144 bf | 166 bf | 159 bf |
| 18 inches | 196 bf | 214 bf | 209 bf |
| 20 inches | 256 bf | 268 bf | 265 bf |
The table shows a common pattern seen in timber scaling. Doyle is notably lower on smaller diameters, then narrows the gap as log size increases. That is one reason small hardwood logs often appear to be “discounted” when scaled by Doyle compared with International 1/4-inch.
Why direct cubic volume is not the same as board-foot scale
People sometimes ask why they cannot simply calculate the volume of a log as a cylinder and convert that number to board feet. The answer is that a round log includes bark, taper, slab loss, edging loss, trim, and sawing waste. Board-foot scaling tries to estimate the recoverable lumber from that raw shape. For example, 12 board feet equals 1 cubic foot of finished lumber volume, but a raw log needs to contain more than that cubic amount to produce the same tally because part of the log is lost during processing.
| Board Feet | Cubic Inches of Lumber | Cubic Feet of Lumber | Example Interpretation |
|---|---|---|---|
| 1 bf | 144 | 0.0833 | One board 12 in × 12 in × 1 in |
| 50 bf | 7,200 | 4.17 | Small sawlog output range |
| 100 bf | 14,400 | 8.33 | Useful benchmark for pricing logs |
| 250 bf | 36,000 | 20.83 | Larger quality sawlog estimate |
Defects that reduce actual yield
Even the best log rule is still an estimate. Real-world lumber recovery depends heavily on log quality. Sweep, crook, rot pockets, splits, ring shake, butt flare, embedded metal, and excessive taper can reduce the amount of usable lumber. In professional scaling, a gross board-foot figure may be reduced by a defect deduction to produce a net scale. If you are buying timber, always ask whether the volume quoted is gross or net. If you are selling logs, understand whether defects will be determined in the woods, at roadside, or at the mill.
How foresters and mills use board-foot estimates
Board-foot estimates are used in several ways:
- Setting stumpage or roadside prices for sawtimber
- Estimating the value of standing timber before harvest
- Planning truck loads and mill intake volume
- Comparing stands by species, quality class, and diameter distribution
- Forecasting lumber production from a timber sale
In many regions, state extension services and university forestry programs teach woodland owners how to estimate volume before requesting bids. That is valuable because a landowner who knows approximate volume is in a much stronger position to compare offers fairly.
Best practices for more accurate log scaling
- Measure diameter at the small end inside bark whenever the rule requires it.
- Use a consistent log rule across the entire job.
- Separate species and grade if value matters, because board feet alone do not determine price.
- Account for defects honestly rather than relying only on gross scale.
- Check whether your buyer rounds to whole inches, even lengths, or standard scale tables.
- When in doubt, confirm local scaling practice with a consulting forester or extension forestry specialist.
Which log rule should you use?
The best rule is often the one used consistently in your local market. If your hardwood buyer quotes Doyle, then your estimates should also be in Doyle so your numbers align with the sale basis. If you want a more technically balanced estimate of recoverable lumber, International 1/4-inch is often preferred by foresters and analysts because it better reflects actual sawing loss over a broader range of log sizes. Scribner remains important historically and is still used in some areas and species groups. The critical step is transparency: always state the rule along with the volume.
Authoritative references and further reading
For deeper guidance on log scaling, timber measurement, and woodland valuation, review these authoritative resources:
Final takeaway
To calculate the board feet in a log, you need the small-end diameter inside bark, the merchantable log length, and the appropriate scaling rule. Then apply the rule formula or use a scale table. Remember that board feet are an estimate of potential lumber output, not just raw log volume. For the most useful result, measure carefully, choose the correct rule for your local market, and note any defects that would affect net scale. The calculator above gives you a fast way to compare the major log rules and see how much the estimate can change before the log ever reaches the mill.