Wood Volume Calculator — Blocks, Logs, Boards & Shapes

How to calculate the volume of a wooden block

The volume of a wooden block is the amount of three-dimensional space the wood occupies, and for any rectangular block it follows the most basic formula in woodworking: volume = thickness × width × length. Measure all three dimensions in the same unit, multiply them, and the product is the volume in that unit cubed — cubic inches if you measured in inches, cubic centimeters if you measured in centimeters. There is no hidden factor, no species adjustment, and no nominal-versus-actual subtlety as long as you measure the real, physical piece in front of you.

The only step people get wrong is the unit conversion afterward. Cubic units convert by the cube of the linear factor, which is why the numbers grow so fast: there are 12 inches in a foot but 12 × 12 × 12 = 1,728 cubic inches in a cubic foot. Divide cubic inches by 1,728 to get cubic feet. In metric the same logic gives 100 × 100 × 100 = 1,000,000 cubic centimeters per cubic meter, so divide cm³ by a million. A shop block measuring 6 × 4 × 3 inches is 72 in³, which is 72 ÷ 1,728 = 0.0417 ft³ — about 1.18 liters, or 0.5 board feet. That tiny-looking number is real: half a board foot is a slab the size of a sheet of paper but an inch thick.

Boards are just long, thin blocks. A dressed 2×6 that is 10 feet long is 1.5 × 5.5 × 120 inches in actual dimensions, so its volume is 990 in³ = 0.573 ft³ = 6.875 board feet. Whenever you know a board's thickness and width in inches and its length in feet, the classic board foot formula — thickness × width × length ÷ 12 — produces exactly the same number, because the ÷ 12 is simply folding the 1,728 conversion and the 144 cubic inches per board foot together. If you would rather start from board feet and convert the other direction, the board foot converter handles square feet and linear feet alongside volume.

Volume of a wooden log — cylinder, frustum and log volume formulas

Round wood breaks the rectangle rule. A log's cross-section is a circle, so its volume starts with the cylinder formula: V = π × r² × length, where r is half the diameter. A perfectly straight 12-inch-diameter post 8 feet long has a radius of 6 inches = 0.5 feet, so V = π × 0.25 × 8 = 6.28 ft³ — exactly 75.4 board feet of solid wood. That is noticeably more wood than the same diameter suggests intuitively, because area scales with the square of the radius: doubling a log's diameter quadruples its volume per foot of length.

Real logs are almost never cylinders. A butt log tapers from its wide base to its narrow top, and the correct geometric shape is a frustum — a cone with the top sliced off parallel to the base. The log volume formula for a frustum is V = π × L ÷ 3 × (R² + R×r + r²), with R the large-end radius, r the small-end radius, and L the length. This is the exact volume of the tapered solid, and it is what the Log Frustum mode in the calculator above computes. For a 16-foot log with a 16-inch butt and a 12-inch top: R = 0.667 ft, r = 0.5 ft, and V = π × 16/3 × (0.444 + 0.333 + 0.25) = 17.2 ft³, or about 207 board feet.

Choosing between cylinder, frustum, and average end area

Which formula should you reach for? If the two end diameters are within about 10% of each other, the cylinder formula using the mid-point diameter is within a couple of percent of the frustum result and is faster to apply in the field. If the taper is obvious — and butt logs from natural stands often taper 1–2 inches per 8 feet — use the frustum formula or the forester's shortcut, the average end area method: compute the cross-sectional area at each end (π × radius² for each), average the two areas, and multiply by length. Average end area slightly overestimates strongly tapered logs because it treats the wood as bulging outward along the whole length, while the frustum formula accounts for the taper exactly. For quick estimates, the error is small; for buying and selling by volume, use the frustum.

Two field realities push every estimate upward. First, logs are rarely perfectly round — oval sections from growth stress or flattening mean the true cross-section area is closer to the average of the long and short diameters than to either alone, so measure the widest and narrowest span of the end face and average them. Second, bark adds roughly half an inch of diameter that you will not sell as lumber; scaling conventions usually deduct bark, but a physical volume estimate for weight or firewood should include it. And remember that log volume is not log scale: Doyle, Scribner and International rules estimate the lumber a log will yield after kerf and slabs, which is always less than the physical volume. This page gives you true volume; a log rule gives you the scale ticket.

From wood volume to board feet — and back

A board foot is defined as a piece of wood 12 inches × 12 inches × 1 inch, which is 144 cubic inches, or exactly one twelfth of a cubic foot. That makes the conversion between wood volume and board feet the simplest in the whole lumber toolbox: board feet = cubic feet × 12, and going the other way, cubic feet = board feet ÷ 12. One cubic meter of wood is 35.315 cubic feet, which is 423.8 board feet — a useful number when a European timber invoice arrives in m³ and your supplier thinks in BF.

Why does the lumber trade even use board feet instead of plain volume? History, mostly — the unit encodes thickness-adjusted pricing, so a 4/4 board and an 8/4 board of the same face area automatically cost proportionally different amounts. But when you already know raw volume — because you measured a log, a stack, or an odd-shaped blank — converting to board feet tells you what that wood would be "worth" in sawmill pricing terms. Just keep the sawmill recovery caveat in mind: a hardwood log yields roughly 50–65% of its round volume as graded lumber once kerf, slabs, and edging are removed, so 200 board feet inside a log typically scales and sells as 100–130 board feet of boards.

Timber volume in cubic feet, cubic meters, liters and gallons

Different corners of the wood trade measure the same timber volume differently, and it pays to speak all the dialects. North American framing and hardwood pricing live in board feet and cubic feet. The international timber trade, pulp and biomass reporting, and most of Europe use cubic meters — a logging truck load is often quoted around 30–40 m³ of roundwood. Firewood is sold by the cord in North America (128 ft³ of stacked wood) and by the stere — one cubic meter of stacked wood — in Europe. Small quantities such as turning blanks, pen blanks and carving blocks are measured in cubic inches, and the aquarium-style displacement method naturally produces milliliters, which map one-to-one onto cubic centimeters.

Gallons and liters deserve a special note because they feel out of place in woodworking — until you use the displacement method. If a carving blank pushes the water in a bucket up by 3 gallons, it is 3 × 0.1337 = 0.401 ft³ of wood, about 4.8 board feet; a rise of 11.4 liters is 0.402 ft³, the same piece measured in metric. The conversion table above collects all of these factors in one place so you never have to trust a forum answer at midnight. The table also includes the standard cord, the one entry where the conversion deliberately overstates the wood: a cord is a stack, not a solid.

Wood volume to weight — species density table

Weight is volume's twin question, and the bridge between them is density: weight = volume × density. Because species densities span a factor of more than twelve — from balsa at 7 lb/ft³ to ipe at 90 lb/ft³ — choosing the right density matters far more than refining the geometry. The values below are standard reference densities at 12% moisture content, the seasoned state of most lumber; the calculator's species list uses the same source data. Pick a species above and the weight appears in both pounds and kilograms, or work out detailed per-piece and per-foot weights in the lumber weight calculator.

Densities at 12% moisture content, adapted from the USDA Forest Products Laboratory Wood Handbook (Chapter 4). Balsa is shown for scale — it is not in the standard construction list.

Worked examples — blocks, boards and logs step by step

Example 1 — the volume of a small wooden block

A kid's science project asks for the mass and volume of a wooden block, and the block measures 6 in × 4 in × 3 in. Volume = 6 × 4 × 3 = 72 in³. Convert to cubic feet: 72 ÷ 1,728 = 0.0417 ft³. In liters: 0.0417 × 28.317 = 1.18 L. Now the mass: the block is SPF framing offcut, density 28 lb/ft³, so weight = 0.0417 × 28 = 1.17 lb — about 530 grams, which is exactly what a kitchen scale will read. If the block had been oak at 44 lb/ft³ the same geometry would weigh 1.83 lb, a 56% difference from species alone.

Example 2 — the volume of a wooden plank

You are pricing a hardwood plank quoted in actual dimensions: 1.5 inches thick, 5.5 inches wide, 10 feet long. Working in inches: 1.5 × 5.5 × 120 = 990 in³ = 0.573 ft³. Board feet = 0.573 × 12 = 6.875 BF — which you can double-check against the classic formula, 1.5 × 5.5 × 10 ÷ 12 = 6.875 BF. At Douglas Fir's 34 lb/ft³ the plank weighs 19.5 lb; in black walnut at 61 lb/ft³ it is 35 lb. Multiply by the quantity field when a whole lift of boards needs pricing — the calculator handles the batch in one pass.

Example 3 — the volume of a tapered log

A 16-foot pine log measures 16 inches across at the butt and 12 inches at the top. Radii: R = 8 in = 0.667 ft, r = 6 in = 0.5 ft. Frustum volume = π × 16 ÷ 3 × (0.667² + 0.667 × 0.5 + 0.5²) = 16.755 × 1.028 = 17.22 ft³. That is 206.7 board feet of solid wood, 0.488 m³, 487.6 liters, or 128.8 gallons of displaced water. Weight at 28 lb/ft³ (SPF): 482 lb; if it were red oak it would be 758 lb — a useful sanity check before you try to lever it alone. The mid-point cylinder estimate, π × 0.583² × 16 = 17.06 ft³, lands within 1% here because the taper is modest; on a butt log with 6 inches of taper it would miss by 5% or more.

Measuring irregular shapes — the displacement method

When a piece refuses to fit any formula — burls, forked branches, driftwood, a roughed-out bowl — stop doing geometry and do physics instead. Fill a straight-sided container with enough water to submerge the piece, note the starting level, push the wood fully under (it floats, so you will need to hold it down with a thin skewer), and read the new level. The rise in water volume equals the piece's volume, because the wood displaces its own volume of water. One milliliter of rise = 1 cm³ = 0.0000353 ft³, and one gallon of rise = 0.1337 ft³.

Three practical tips make the displacement method accurate. First, soak or briefly submerge the piece before measuring if it is dry — otherwise it drinks some of the water it displaces and understates its own volume by a few percent. Second, keep bubbles off the surface: trapped air adds phantom volume. Third, decide deliberately whether bark counts. For weight or firewood it does; for lumber yield it does not, so shave or deduct it. The same water rise also gives you density for free — weigh the piece, divide by the displaced volume, and you have measured that specific piece's density rather than trusting a species average.

Common mistakes when calculating wood volume

Using nominal dimensions instead of actual ones. A "2×6" is 1.5 × 5.5 inches dressed, not 2 × 6 — an error of about 35% in the volume of every board. Always measure the dressed piece or use an actual-dimension table when the piece is not in your hands.

Mixing units inside one multiplication. Thickness in inches × width in inches × length in feet is the classic trap: the result is neither cubic inches nor cubic feet. Either convert everything to inches (length × 12) and divide by 1,728, or use the board foot formula that expects exactly T and W in inches and L in feet. The calculator's unit toggle exists so you never have to hold these factors in your head.

Treating a tapered log as a cylinder. Using the butt diameter for the whole log can overstate volume by 10–20% on strongly tapered stock. Measure both ends and use the frustum formula — it is not harder, it just needs a second diameter.

Forgetting that stack volume is not wood volume. A cord, a lift of lumber, or a truckload of firewood contains air. Apply a solid-content fraction — roughly 65–80% for firewood stacks — before converting to weight or board feet, or your estimate will run heavy by a third.

Ignoring moisture. Volume shifts a few percent between green and dry, but weight shifts far more because water is heavy — green oak can weigh 20–30 lb/ft³ more than its seasoned reference density. Volume estimates transfer cleanly across moisture states; weight estimates do not.

This wood volume calculator is one tool in the LumberCalculator.net set — the flagship lumber calculator at LumberCalculator.net estimates board feet, framing and coverage, and you can browse every calculator on one page. Use it for any volume of a wooden block, log volume, or timber volume question, in any units, free and without sign-up.