Article — Lumber Board Feet Calculator
A board foot of lumber is 144 cubic inches — a piece 12 inches wide, 12 inches long, and 1 inch thick, or any combination with the same volume. To get the board feet of any board, multiply thickness in inches by width in inches by length in feet, then divide by 12. A standard 2x4×8 (planed) is (1.5 × 3.5 × 8) ÷ 12 = 3.5 board feet. That single equation drives every lumber order from a backyard fence to a sawmill’s daily tally.
This article covers the formula, the gap between nominal sizes (the “2x4” on the sticker) and actual planed dimensions (1.5 in × 3.5 in), the difference between board feet and linear feet, how yards build their per-BF prices, and the log rules sawyers use to estimate board feet from a standing tree.
What a board foot of lumber actually is
The board foot is a U.S. and Canadian unit for lumber volume. One board foot equals 144 cubic inches: think of a piece a foot square and an inch thick, or a 1 in × 6 in board two feet long. It is a volume unit, not a length, which is exactly why it does not match linear feet.
The unit dates to the 19th century, when American lumber merchants needed a standard for boards of irregular dimensions. The National Hardwood Lumber Association formalised board-foot tallying for hardwood lumber, and the convention spread to softwood construction lumber too. Today every U.S. lumber yard, sawmill, and forest-products statistic uses BF for hardwood and most rough-sawn softwood; dimensional softwood (2x4s and friends) is more often sold by the piece.
The United States produces roughly 30–40 billion board feet of softwood lumber in a typical year and another 10–12 billion of hardwood lumber. That is enough wood to wrap a 1 in × 12 in board around the equator more than 1,500 times.
The board feet formula in plain math
The standard formula is BF = (T × W × L) ÷ 12, where T and W are in inches and L is in feet. The divide-by-12 looks arbitrary until you remember the unit definition: 1 BF = 144 cubic inches. T (in) × W (in) × L (ft × 12) gives cubic inches, and 144 = 12 × 12 lets you cancel one of those twelves.
If you measure length in inches instead of feet, the formula becomes BF = (T × W × L) ÷ 144. Same answer, different denominator. Stick with the feet version for boards and the inches version for short cutoffs or hardwood blanks under a foot long.
- 2x4×8 ft — 3.50 BF (1.5 × 3.5 × 8 ÷ 12)
- 2x6×12 ft — 8.25 BF
- 2x10×16 ft — 18.50 BF
- 4x4×8 ft post — 8.17 BF (planed 3.5 × 3.5)
- 1x6×10 ft hardwood plank — 3.44 BF (using planed 0.75 × 5.5)
Nominal vs actual lumber dimensions
The single largest source of board-foot mistakes is forgetting that a 2x4 is not 2 inches by 4 inches. After kiln drying and planing, a softwood 2x4 measures 1.5 in × 3.5 in. Every nominal softwood size shrinks similarly: 2x6 becomes 1.5 × 5.5, 2x10 becomes 1.5 × 9.25, 4x4 becomes 3.5 × 3.5.
For softwood construction lumber, U.S. and Canadian yards historically tally board feet using the nominal dimensions, since that is how the trade was set up and how customers expect to be billed. For hardwood lumber, the National Hardwood Lumber Association rules call for actual dimensions, tallied to the nearest BF after the lumber is dressed. This calculator uses actual planed dimensions in both modes, because that is the physically correct math — it is up to you to match your supplier’s convention when you compare quotes.
If you ever see a board-foot calculator return 5.33 for a 2x4×8, it is using the nominal 2 × 4 inches instead of the actual 1.5 × 3.5. The honest answer is 3.5 BF. The 5.33 figure shows up in older softwood tally books that use nominal sizing — legitimate in that context, but it should never be confused with the physical wood volume.
Board feet vs linear feet — not the same thing
Linear feet (or running feet) measures only length. Board feet measures volume. A 10-foot 2x4 is 10 linear feet but only 4.38 board feet. A 10-foot 1x12 is also 10 linear feet but 7.50 board feet. The cross-section matters; that is the entire point of the board-foot unit.
Flooring, trim, and siding are usually quoted in linear feet because their cross-section is fixed and the buyer wants to know how long a run they cover. Rough lumber, hardwood blanks, and any project where the wood will be ripped or planed to size are quoted in board feet because the buyer cares about total volume of material.
The cubic-foot conversion is exact: 1 cubic foot of solid wood = 12 board feet. A pickup-truck-bed load of stacked lumber (call it 40 cubic feet, give or take) is roughly 480 board feet — before subtracting the air gaps between boards, which can knock 15–20 percent off the solid-wood total.
How yards price lumber by board foot
Hardwood and rough-sawn lumber are priced per board foot at the yard. Softwood dimensional lumber is usually priced per piece, but a per-BF figure is easy to back out: divide the piece price by the BF tally. A 2x4×8 at $5.50 works out to $1.57 per BF using actual dimensions, or $1.03 per BF using the nominal-tally convention.
Typical 2024–2025 yard prices: softwood (pine, spruce, fir) runs $2–$6 per BF depending on grade and length. Domestic hardwoods sit at $6–$20 per BF: red oak around $7, hard maple around $9, walnut around $14, cherry around $10. Exotics start at $20 and run past $100 (genuine teak, ziricote, ebony). Grade, moisture content (kiln-dried vs air-dried vs green), and whether the wood is surfaced (S4S = surfaced four sides) all shift the price.
- SPF 2x4 dimensional — ~$2–$4 per BF
- Red oak 4/4 S2S — ~$6–$8 per BF
- Hard maple 4/4 S2S — ~$8–$10 per BF
- Black walnut 4/4 S2S — ~$12–$16 per BF
- Genuine mahogany 4/4 S2S — ~$14–$20 per BF
- Volume discount — expect 10–25% off list above 100–500 BF
Hardwood thickness is quoted in quarters of an inch before planing: 4/4 = 1 in rough, planed to ~13/16. 5/4 = 1.25 in rough, planed to ~1.0625. 8/4 = 2 in rough, planed to ~1.75. Board-foot math uses the planed (actual) thickness, not the 4/4 label.
Log rules: board feet before the lumber exists
Sawmills and timber buyers need to estimate how many board feet of lumber a standing tree or felled log will yield, before any cuts are made. The standard tools are log rules: empirical formulas that take small-end diameter and length and return a BF estimate.
The three U.S. rules in common use are Doyle, Scribner, and International ¼-inch. Doyle (1825) is the most conservative — it under-estimates yield for small logs because it assumes a wide sawkerf. Scribner (1846) uses a diagram-based table and gives moderate yields. International ¼″ is the most accurate against modern mill output. The University of Tennessee and Virginia Tech extension services publish full conversion tables. For the same 12-inch, 16-foot log: Doyle = 64 BF, Scribner = 79 BF, International = 95 BF. The 50-percent spread is real and matters — always ask which rule a timber buyer is quoting.
A log rule predicts sawn lumber yield from a log, not the volume of the round log itself. The unsawn log contains more wood than any log rule gives credit for — the rest becomes sawdust, edgings, and slabs. Do not feed log-rule BF into a board-foot lumber calculator; the units are nominally the same but the meaning differs.