Timber Volume Calculators

0 calculators tagged with “Timber Volume”

Timber volume is the amount of wood in a tree, log, or stand of trees — the primary commercial metric in forestry. It is measured in cubic meters (m³) or board feet (BF) and estimated from tree diameter at breast height (DBH) and height using volume equations, taper functions, or log rules. Accurate volume estimation is the foundation of timber cruising, forest inventory, harvest planning, carbon accounting, and timber appraisal. Methods range from simple geometric approximations to sophisticated taper models integrated over the full stem.

All Calculators

No calculators found for this topic.

Tree Volume Estimation

Cylinder Approximation

Volume ≈ π × (DBH/2)² × height × form factor (f)
Form factor f ≈ 0.45–0.55 for most conifers (accounts for taper).
Example: DBH = 30 cm (r = 0.15 m), height = 20 m, f = 0.50:
V = π × 0.15² × 20 × 0.50 = 0.707 m³

Smalian's Formula (Logs)

V = L × (A_butt + A_tip) / 2
L = log length; A = π × (d/2)² at each end.

Huber's Formula

V = L × A_midpoint
More accurate than Smalian's for tapered logs — uses midpoint cross-section area.

Volume Tables

Pre-computed tables give tree volume from DBH and height. Local volume tables are calibrated from felled-tree measurements. Tariff tables use only DBH (assuming a fixed height-diameter relationship) for quicker field use.

Log Rules (Lumber Volume)

  • Doyle rule: V (BF) = L × (D − 4)² / 16 — simplest; understates small logs
  • Scribner rule: Based on log diagrams; more accurate for small logs than Doyle
  • International 1/4-inch rule: Most accurate; uses saw kerf and board thickness assumptions

Units

  • 1 m³ ≈ 424 board feet
  • 1 board foot = 1 in × 12 in × 12 in = 2.36 × 10⁻³ m³
  • Cord: 128 ft³ stacked ≈ 2.55 m³ solid wood

Glossary

Timber Volume
The amount of wood in a tree, log, or stand, measured in cubic meters or board feet. Estimated from DBH and height using volume equations, taper functions, or log rules. The primary commercial metric in forestry.
Form Factor
A coefficient (0.45–0.55 for conifers) accounting for stem taper in volume estimation. Ratio of actual stem volume to the volume of a cylinder with the same DBH and height. Varies by species, site, and tree age.
Board Foot (BF)
Volume of lumber 1 inch × 12 inches × 12 inches ≈ 2.36 × 10⁻³ m³. Standard lumber measurement in North American timber trade. 1 m³ ≈ 424 board feet.

Frequently Asked Questions

Standard approach: Volume ≈ π × r² × H × f, where r = DBH/2, H = tree height, and f = form factor (~0.45–0.55 for conifers, accounting for taper). More accurate results use local volume tables that give volume directly from DBH and height — calibrated by felling and measuring sample trees. Taper functions (e.g., Kozak's variable-form model) describe how diameter changes with height and can be integrated to give precise stem volume.

V = L × (A_butt + A_tip) / 2, where L = log length and A = cross-sectional area at each end (π × (d/2)²). It averages the two end areas and multiplies by length. Example: 4 m log, butt diameter 30 cm, tip 20 cm → A_butt = 0.0707 m²; A_tip = 0.0314 m² → V = 4 × (0.0707 + 0.0314)/2 = 0.204 m³. Huber's formula (midpoint area) is more accurate for strongly tapered logs.

A board foot is the volume of lumber 1 inch thick × 12 inches wide × 12 inches long = 144 cubic inches = 2.36 × 10⁻³ m³. It is the standard lumber measurement in North American timber trade. Approximately 1 m³ ≈ 424 board feet. Board feet measure merchantable lumber yield from logs, not total wood volume — which includes bark, slabs, and saw kerf losses.

Doyle rule: BF = L × (D−4)²/16 — easy to calculate but seriously underestimates volume in small logs (< 20 cm). International 1/4-inch rule: more complex formula accounting for saw kerf and board thickness; gives more accurate lumber yield estimates across all log sizes. Doyle can undervalue small-diameter timber by 30–40% compared to International rule. Always specify which rule is used in timber sale contracts.