Board Foot Calculator for Standing Timber

A board foot calculator for standing timber estimates the volume of lumber you can expect to get from a tree before it is cut. You enter the tree’s diameter at breast height (DBH), the number of logs, and their average length, and the calculator returns the total board feet using the Doyle or International 1/4-inch log rule. This gives you a quick, practical estimate for planning a harvest or valuing timber on the stump.

Formula

The calculator uses two standard formulas for estimating board feet from standing timber. The Doyle rule is the most common in the eastern United States and is simple to apply:

Board feet (Doyle) = (number of logs) × ((DBH – 4) / 4)² × (log length)

Where:

• DBH = diameter at breast height, measured in inches at 4.5 feet above the ground
• Log length = length of each log in feet (usually 8, 12, or 16 feet)
• Number of logs = how many logs you expect to get from the tree

The International 1/4-inch rule is more accurate for smaller logs and is often used in the northern U.S. and Canada. Its formula is:

Board feet (Int. 1/4) = n × (0.0494 × DBH² × L – 0.124 × DBH × L + 0.008 × L²)

Where DBH and L are in inches and feet respectively, and n is the number of logs. The International rule accounts for saw kerf (the width of the saw cut) and shrinkage, so it gives a closer estimate to actual mill output.

Worked Example

Let’s use the default values from the calculator: a tree with a DBH of 20 inches, three logs each 16 feet long, using the Doyle rule.

Step 1: Subtract 4 from the DBH: 20 – 4 = 16

Step 2: Divide by 4: 16 / 4 = 4

Step 3: Square the result: 4² = 16

Step 4: Multiply by the log length: 16 × 16 = 256

Step 5: Multiply by the number of logs: 256 × 3 = 768

The Doyle rule gives 768 board feet. The International rule would give a different number (in this case, about 1,014 board feet) because it assumes less waste and thinner saw kerf. The calculator shows both so you can compare.

How to Measure a Standing Tree

Getting an accurate DBH is the most important step. Use a diameter tape (which measures circumference and converts to diameter) or a regular tape measure and divide the circumference by 3.1416. Measure at 4.5 feet above the ground on the uphill side of the tree. If the tree is on a slope, measure from the high side. For trees with buttresses or swell at the base, measure above the abnormal area.

To estimate the number of logs, look at the merchantable height—the point where the trunk narrows to about 6-8 inches inside the bark. A standard log is 16 feet long, so divide the merchantable height by 16 and round down. For example, if the tree has 40 feet of usable trunk, you get two 16-foot logs (32 feet) with some leftover that might make a short log.

Why the Doyle Rule Underestimates Small Trees

The Doyle rule was developed in the 1800s when sawmills wasted more wood. It subtracts 4 inches from the diameter to account for the saw kerf and slab, but that fixed deduction is proportionally larger for small trees. A 10-inch tree yields almost nothing under Doyle, while the International rule gives a more realistic estimate. If you are evaluating small-diameter timber, the International rule is usually closer to what a mill will actually produce. For large trees (24 inches and up), the two rules converge.

Common Mistakes When Estimating Board Feet

• Measuring diameter inside bark vs. outside bark: The formulas assume diameter outside bark. If you measure inside bark, you’ll overestimate.
• Using the wrong log length: Logs are usually sold in 2-foot increments (8, 10, 12, 16 feet). A 15-foot log is not standard; you’d get a 14-foot or 16-foot log.
• Forgetting to count only merchantable logs: The top of the tree and branches are not sawlogs. Use the 6-inch minimum diameter rule.
• Mixing units: The formulas require inches for DBH and feet for length. Converting to metric requires careful unit conversion (1 inch = 2.54 cm, 1 foot = 0.3048 m).
• Ignoring defects: Holes, rot, crooks, or forks reduce usable lumber. A professional cruiser will deduct for defects, sometimes up to 30%.

Limits of the Formula

These formulas estimate the volume of lumber that can be sawn from a log, but they do not predict the grade or quality of that lumber. Two trees with the same DBH and length can have vastly different values if one is straight and clear and the other has knots or sweep. Also, the formulas assume a perfectly cylindrical log; real trees taper, and the taper is not accounted for. For a more precise estimate, you would need to measure the diameter at both ends of each log and use a more complex formula like Smalian’s. The board foot estimate is a starting point, not a guarantee of mill output.

How to Use the Result

The board foot figure is useful for comparing trees or estimating a timber sale. To get a rough value, multiply the board feet by the current regional price per board foot for that species (you’ll need to look that up locally). Remember that stumpage prices vary widely by species, region, and market conditions. The estimate also helps you decide whether a tree is worth harvesting or better left for wildlife and aesthetics. For a formal timber sale, always hire a professional forester to do a timber cruise—they will measure every tree and use a more rigorous method.

Frequently Asked Questions

What is a board foot?

A board foot is a unit of lumber volume equal to 1 inch thick × 12 inches wide × 1 foot long. It’s the standard measure for selling lumber in North America. One board foot is 144 cubic inches of wood.

How many board feet are in a cord of wood?

A cord is a stack of wood 4 feet × 4 feet × 8 feet, which equals 128 cubic feet. However, a cord is a measure of volume including air spaces, so it doesn’t convert directly to board feet. A cord of sawlogs might yield 500-800 board feet depending on log size and rule used.

What is the difference between Doyle, Scribner, and International rules?

These are different log rules—tables or formulas that estimate how many board feet can be sawn from a log. Doyle is simple but underestimates small logs. Scribner is a diagram-based rule that is accurate for medium logs. International 1/4-inch is the most accurate for all sizes. Different regions and mills use different rules, so always ask which rule is being used.

Can I use this calculator for metric measurements?

No, the formulas require inches for diameter and feet for length. If you have metric measurements, convert first: 1 inch = 2.54 cm, 1 foot = 0.3048 m. For example, a 50 cm DBH is about 19.7 inches, and a 5 m log is about 16.4 feet.

How accurate is this estimate for a real tree?

For a healthy, straight tree with no major defects, the estimate is usually within 10-20% of actual mill output. However, defects, taper, and measurement error can cause bigger discrepancies. If you’re making a financial decision, get a professional timber cruise.

Why does the calculator show two different results?

It shows both Doyle and International estimates so you can see the range. The Doyle rule is conservative (lower) and the International rule is more optimistic (higher). The true volume is usually between the two. For small trees, use International; for large trees, Doyle is closer.

Related

• Board and Batten Wall Calculation: Materials and Spacing
• Board Foot Calculator for Foam: Measure Volume
• Blown-In Insulation Calculator: Estimate Bags and Coverage

in d | DBH (inches) | in | 20 | 0
in l | Log length (feet) | ft | 16 | 0
in n | Number of logs | - | 3 | 0
sel r | Log rule | Doyle=1, International=2 | 1
out bf | Board feet (Doyle) | bd ft | (n * ((d - 4) / 4)^2 * l)  | 0
out bf_int | Board feet (Int. 1/4) | bd ft | (n * (0.0494 * d^2 * l - 0.124 * d * l + 0.008 * l^2)) | 0