What a board foot measures and why lumber is sold this way
A board foot is a unit of volume: 144 cubic inches, or one twelfth of a cubic foot. The reference piece is one inch thick, twelve inches wide and twelve inches long, but any combination that multiplies to 144 cubic inches is one board foot — a 2 × 6 × 6 inch block is one, and so is a 1 × 4 × 36 inch strip.
Volume is the right unit for hardwood because hardwood does not come in standard sizes. A sawyer cuts a log into whatever widths the log yields, so a stack of cherry contains boards from 4 to 14 inches wide, all different lengths, and there is no meaningful "per piece" price. Pricing the volume treats every board the same way and lets the yard price by species, grade and thickness rather than by shape.
Softwood construction lumber goes the other way. Because a 2 × 4 is always a 2 × 4, dimensional softwood is usually sold by the piece or by the linear foot, and its board-foot tally uses the nominal size rather than the actual one — a nominal 2 × 4 that measures 1.5 × 3.5 inches still counts as 0.667 board feet per foot of length in a lumber tally. That difference between nominal and actual is the single most common source of confusion when the two worlds meet.
The formula and the quarter notation
Multiply the three dimensions in inches and divide by 144. If the length is in feet, divide by 12 instead, because the length term is already twelve times larger. Both forms give the identical answer, and the second is the one to do in your head at the lumber rack: thickness in inches × width in inches × length in feet ÷ 12.
Hardwood thickness is quoted in quarters of an inch. 4/4 ("four quarter") is one inch, 5/4 is 1.25 inches, 6/4 is 1.5 inches, 8/4 is two inches, and 12/4 is three inches. Crucially, that is the rough sawn thickness. A 4/4 board surfaced on two faces arrives at about 13/16 inch thick, and the yard still charges you for a full inch, because you are buying the wood that was removed as much as the wood that remains. Enter the rough number.
Width and length work the other way: hardwood is measured and charged at its actual, surfaced size. Some yards round widths down to the nearest inch or half inch when tallying, and NHLA grading rules define how the width of a taper-sawn board is taken. If your tally and the yard's differ by a few percent on random-width stock, this is usually why.
The linear foot conversion answers a different question: how much length you have. Multiply the board count by the length in feet. Cost per linear foot then tells you what a foot of that specific board section costs, which is the number to compare when you are choosing between a wide board and two narrow ones for the same job.
Worked example: pricing a cherry order for a bookcase
You need six pieces of 4/4 cherry, 7.25 inches wide and 8 feet long, at $6.50 per board foot, and you want 20% extra for defects and cutting.
- Rough thickness. 4/4 means 1 inch, even though the surfaced boards will measure about 13/16.
- Board feet per board. 1 × 7.25 × 96 ÷ 144 = 696 ÷ 144 = 4.8333 BF. Using the feet form: 1 × 7.25 × 8 ÷ 12 = 58 ÷ 12 = 4.8333 BF — the same number.
- Total tally. 4.8333 × 6 = 29.0 BF.
- Cost. 29.0 × 6.50 = $188.50.
- Linear feet. 8 ft × 6 boards = 48 linear feet, so $188.50 ÷ 48 = $3.93 per linear foot of 7¼-inch board.
- With 20% waste. 29.0 × 1.20 = 34.8 BF to order, which is a little over seven boards of this size.
- Volume check. 1 × 7.25 × 96 × 6 ÷ 1728 = 2.4167 cubic feet, or 0.0684 m³ — useful when a supplier quotes in cubic metres.
Note what happens if you enter 0.8125 inches instead of 1: the tally drops to 23.6 BF and the price to $153, and you would arrive at the till $35 short. Always enter the rough thickness.
Reading the result: yield, waste and what you actually get
Board feet are not usable board feet. A rough board arrives with wane on an edge, a bow along its length and checks at the ends, and you lose material at every step: jointing one face, planing to thickness, ripping the edges straight, and docking the ends. On clear FAS-grade hardwood in wide boards, a 15% allowance is usually enough. On lower grades, narrow stock, or a project full of short parts cut from long boards, 30% is realistic. Anyone cutting curved parts should plan on more than that.
Grade drives yield, and yield drives real cost. NHLA grades describe the percentage of clear cuttings a board will produce: FAS boards yield at least 83⅓% clear, No. 1 Common at least 66⅔%, No. 2A Common at least 50%. A No. 1 Common board at 70% of the FAS price is cheaper per usable board foot than FAS if your parts are short, and more expensive if your parts are long and wide. Compare price ÷ expected yield, not price alone.
Thickness is bought in steps. If a finished part needs to be 7/8 inch thick, you cannot buy 4/4 and get there after surfacing — you need 5/4, and your board-foot count rises 25% for the same face area. Design part thicknesses around the quarter steps before you price anything.
For sheet goods and project layout, the deck board calculator and firewood cord calculator cover the other two volume units the timber trade uses, and if you are quoting a job rather than buying for yourself, put the material total through the markup vs margin calculator so your material markup is the one you intend.
Board feet per linear foot, by thickness and width
| Width | 4/4 (1 in) | 5/4 (1¼ in) | 6/4 (1½ in) | 8/4 (2 in) | 12/4 (3 in) |
|---|---|---|---|---|---|
| 3 in | 0.250 | 0.313 | 0.375 | 0.500 | 0.750 |
| 4 in | 0.333 | 0.417 | 0.500 | 0.667 | 1.000 |
| 5 in | 0.417 | 0.521 | 0.625 | 0.833 | 1.250 |
| 6 in | 0.500 | 0.625 | 0.750 | 1.000 | 1.500 |
| 8 in | 0.667 | 0.833 | 1.000 | 1.333 | 2.000 |
| 10 in | 0.833 | 1.042 | 1.250 | 1.667 | 2.500 |
| 12 in | 1.000 | 1.250 | 1.500 | 2.000 | 3.000 |
Each cell is thickness × width ÷ 12. The table is exact; the rounding is to three decimals.
Where the 144 comes from, and who defines the tally
The board foot has been the North American hardwood unit since the nineteenth century, and the modern rules for measuring and grading it are published by the National Hardwood Lumber Association in the Rules for the Measurement and Inspection of Hardwood and Cypress. Those rules define surface measure, how widths and lengths are taken, how thickness is assigned before and after surfacing, and the clear-cutting yields that separate FAS from the Common grades. If you are buying by the truckload, or disputing a tally, the NHLA rulebook is the document that settles it.
Log volume is a different problem again and uses log rules — Doyle, Scribner and International 1/4-inch — which estimate the board feet a log will yield after sawing. They disagree with one another significantly on small logs, so a sawmill quote always names the rule it used.
Mistakes that make a lumber order wrong
- Using the surfaced thickness. 4/4 stock measures about 13/16 after planing but is billed as a full inch. Entering 0.8125 understates the tally by 19%.
- Treating nominal softwood sizes as actual. A 2 × 4 measures 1.5 × 3.5 inches. Softwood tallies use the nominal size; hardwood tallies use the actual size. Do not mix conventions.
- Forgetting that the length term changes the divisor. Divide by 144 with the length in inches, by 12 with the length in feet. Halving that mistake produces a twelve-fold error.
- Buying the exact tally. Rough lumber has defects, and machining removes material. Order 15-30% extra or you will make a second trip.
- Comparing prices across grades. A cheaper board foot in a lower grade is only cheaper if your parts fit the clear cuttings that grade guarantees.
- Ignoring the thickness step. A part finishing at 7/8 inch must be cut from 5/4, not 4/4, which raises the volume you need by a quarter.
Board feet, linear feet and cubic metres
Three units describe the same pile of wood, and each answers a different question. Board feet measure volume and are what you pay for. Linear feet measure length only and are what you need when the part has a fixed cross-section — trim, edging, a run of face frame stock. Square feet measure face area and are what flooring, veneer and sheet goods are sold in.
Converting between them requires the cross-section. Board feet to linear feet is BF × 144 ÷ (thickness × width): a 20 BF pile of 4/4 × 6 inch stock is 20 × 144 ÷ 6 = 480 inches = 40 linear feet. That conversion is meaningless without knowing the thickness and width, which is why a quote in linear feet must always state the section it applies to.
Outside North America, lumber trades in cubic metres. One cubic metre is 423.776 board feet, so a price of $6.50 per board foot is about $2,755 per cubic metre. European suppliers quoting hardwood in cubic metres are usually quoting rough sawn and kiln dried, which corresponds to the same rough thickness convention this calculator uses.
One last practical note: board feet describe the wood, not the moisture in it. Kiln-dried lumber has already shrunk, typically by 3-8% across the grain from green to 6-8% moisture content, so a green tally and a kiln-dried tally of the same boards will not match. Buy on the dried dimensions if you are building furniture with it.