Tree CFT Calculator: Measure Wood Volume

This tree CFT calculator works out the volume of a standing tree or a log in cubic feet (CFT) from its girth (circumference) and usable height or length. Enter the girth and height (or length) in feet and inches, and you get the volume in cubic feet, plus an estimate in board feet for lumber. The calculation uses the standard formula for the volume of a cylinder, adjusted for the taper of a real tree trunk.

Formula

The volume of a tree trunk is approximated as a cylinder, but because trunks taper, the effective cross-sectional area is taken at about one-third of the height from the base (or at breast height for standing trees). The formula used here is:

Volume (cu ft) = (G² × H) / (4π)

• G = girth (circumference) in feet, measured at breast height (4.5 feet above ground) for standing trees, or at the small end for logs.
• H = usable height in feet (for a standing tree, the length from the base to the point where the trunk diameter falls below 4 inches, or to the first major branch; for a log, the length of the log).
• π ≈ 3.14159

This formula derives from the cylinder volume V = π × r² × h, where r = G / (2π), so r² = G² / (4π²), giving V = π × (G² / (4π²)) × H = (G² × H) / (4π). It assumes the tree is a perfect cylinder, but using girth at breast height and the full height approximates the actual volume reasonably well for many species.

Worked Example

Using the default values: girth = 5.0 ft, height = 20 ft.

1. Square the girth: 5.0² = 25.0
2. Multiply by height: 25.0 × 20 = 500
3. Divide by (4 × π): 500 / (4 × 3.14159) = 500 / 12.56636 = 39.7887

The volume is approximately 39.8 cubic feet. The board foot estimate: 39.8 × 5.5 = 218.8, so about 219 board feet. This matches the calculator output (rounded to 1 decimal for CFT and 0 for board feet).

When to Use This Calculator

Use this calculator when you need to estimate the volume of a standing tree for timber sale, firewood planning, or to compare trees. It is also handy for estimating the volume of a single log that you plan to mill. For a more precise measurement, foresters use specialized tools like a clinometer and a diameter tape, but this formula gives a quick, field-friendly estimate.

For firewood, a standard cord is 128 cubic feet of stacked wood (including air spaces), so you can divide the tree’s volume by 128 to get an approximate number of cords. For lumber, a board foot is 1 foot × 1 foot × 1 inch (144 cubic inches), and the conversion factor of 5.5 is a rough average for hardwood sawlogs; the actual yield depends on the log’s taper, defects, and sawing pattern.

How to Measure Girth and Height

Accurate measurement is key to a useful estimate.

• Girth: Use a tape measure to find the circumference at breast height (4.5 feet above ground). If the tree flares at the base, measure above the flare. For a log, measure the circumference at the small end (the top).
• Height: For a standing tree, measure from the ground (or stump height) to the point where the trunk is about 4 inches in diameter (or to the first major branch). A clinometer or a simple stick method can be used; if you cannot measure, you can estimate using a 45-degree angle from a known distance.
• For logs: Measure the length along the center of the log, excluding bark that will be removed.

Common Mistakes and Limitations

The most common mistake is mixing units—for example, measuring girth in inches and height in feet. Always convert to feet before using the formula (divide inches by 12). Another mistake is using the diameter instead of the girth; the formula is specifically for circumference. If you have the diameter (D), use the formula V = (π × D² × H) / 4, or convert: G = π × D.

This formula assumes a perfect cylinder, so it overestimates volume for trees with significant taper and underestimates for trees with a lot of butt swell. It also ignores the volume of branches and the fact that the base of the trunk is often wider. For a more accurate estimate, use a form factor (typically 0.4 to 0.6 for many species) to adjust the cylinder volume. The result is an estimate, not an exact measurement; actual volume can vary by ±20% depending on the tree’s shape.

Alternatives and Related Calculations

If you need more precision, consider these methods:

• Diameter tape: A tape that gives diameter directly from circumference, used by professional foresters.
• Log rule (Scribner, Doyle, International): These rules estimate board feet from log diameter and length, accounting for saw kerf and slab waste. The International rule is the most accurate for sawlogs.
• Weight-based estimate: For firewood, you can weigh a sample and extrapolate, but moisture content makes it variable.
• 3D scanning: For high-value trees, laser scanning can produce a precise volume, but it is rarely worth the cost for a single tree.

For firewood, remember that a cord is a volume of stacked wood, not solid wood; the solid wood volume in a cord is roughly 80-100 cubic feet depending on how tightly it is stacked.

Frequently Asked Questions

How do I convert my tree’s diameter to girth?

Multiply the diameter by π (3.14159). For example, a tree with a diameter of 2 feet has a girth of about 6.28 feet. If you have a diameter tape, it reads girth directly.

What is a board foot and how is it related to cubic feet?

A board foot is a volume of 1 foot × 1 foot × 1 inch (144 cubic inches). One cubic foot equals 12 board feet. The calculator’s board foot estimate uses a factor of 5.5 because sawing a log into lumber produces waste (sawdust, slabs), so you get fewer board feet than the solid volume would suggest. The actual yield depends on log quality and sawing method.

Can I use this for firewood planning?

Yes, but remember that a cord of firewood is 128 cubic feet of stacked wood, including air spaces. A typical tree with a 5-foot girth and 20 feet of usable height yields about 40 cubic feet of solid wood, which is roughly 0.3 cords. For a full cord, you would need about 3 such trees.

Why does my measurement differ from a professional forester’s estimate?

Professionals use more precise instruments and often apply species-specific form factors. They also measure to a smaller top diameter (often 4 inches) and account for defects. Your measurement may also differ if you measure girth at a different height or if you include the bark. The calculator gives a rough estimate; for legal or commercial purposes, rely on a certified forester.

What if my tree is not perfectly round?

Most tree trunks are not perfectly round. Measure the girth at the narrowest and widest points and average them, or measure at breast height in two perpendicular directions and average. The formula assumes a circular cross-section, so the average girth gives a reasonable estimate.

How do I measure the height of a very tall tree without special tools?

Use the stick method: hold a straight stick vertically at arm’s length, with the bottom of the stick at eye level. Walk backward until the top of the stick aligns with the top of the tree and the bottom with the base. The distance from you to the tree is approximately equal to the tree’s height. For a more accurate method, use a clinometer or a smartphone app with a built-in inclinometer.

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in g | Girth (circumference) at breast height | ft | 5.0 | 0
in h | Usable height (or log length) | ft | 20 | 0
out cft | Volume (cubic feet) | cu ft | (g^2 * h) / (4 * pi) | 1
out bdft | Lumber estimate (board feet) | bd ft | ((g^2 * h) / (4 * pi)) * 5.5 | 0