Why does a wooden board always warp the same way?
— A carpenter can tell just by looking at the growth rings on the cut end
Cutting boards, shelves, floorboards — after a few years of use, they all warp a little. It's not random. They bow almost without fail in the direction that flattens the arc of the growth rings. That's because wood shrinks twice as much in one direction as it does in the other.
You leave a kitchen cutting board standing on its edge and forget about it for a while. When you finally lay it flat again, the middle lifts up, and it rattles when you press on it.
Flip it over, and suddenly it sits perfectly flat. The warp always dips the same way on the same side.
A carpenter glances at the cut end of the board and says, "this side goes up." How can they tell just by looking?
There are only two reasons
As wood dries and shrinks, it shrinks about twice as much along the growth rings as it does from the centre outward. Along its length, it barely shrinks at all.
A board cut from a log has growth rings running a different way on its two faces. The side that shrinks more is pulled harder, and the board bends into a bow.
Put these two facts together, and the direction of the warp is decided from the start. Let's go through it step by step.
How much does wood shrink, and in which direction?
Wood is built like a bundle of thin straws. Each straw is a cell that once carried water. The walls of these cells are soaked through with water.
When wood dries, the water inside the straws leaves first. During this stage, the wood barely changes size at all — only the contents are draining away.
But once that water is gone and drying continues, water starts leaving the cell walls themselves. The walls thin out, and the whole piece of wood begins to shrink. Woodworkers call this turning point the fibre saturation point. Below it, the wood shrinks.
Here's the key part: how much it shrinks depends heavily on direction. Look at the left side of Figure 1. On the cut end of a log, the growth rings form concentric circles.
The direction running around along the growth rings is called the tangential direction; the direction from the centre outward is the radial direction. In a given piece of wood, the tangential direction is known to shrink about twice as much as the radial direction.
What causes this difference is a set of cell rows that run radially outward from the centre of the tree, called ray tissue (or wood rays). They brace the wood like struts running in the outward direction.
So the direction of warp is decided from the start
When a board is cut from a log, the growth rings inside it run in an arc, as shown on the right of Figure 1. The side where the arc bulges outward is the face that faced the outside of the log. This is called the bark side; the opposite face, toward the tree's core, is called the pith side.
On the bark side, the growth rings run nearly parallel to the face of the board — that is, close to the tangential direction, which shrinks a lot. On the pith side, the rings run closer to the radial direction, so shrinkage is smaller.
When one face of a board shrinks much more than the other, the board curls with the shrinking side on the inside. This is why it bows in the direction that flattens the arc of the growth rings — with the bark-side face ending up as the dip.
This is exactly why a carpenter checks the cut end: to see which way that arc runs. When laying floorboards, they face the bark side up. If the top face dips ever so slightly, the edges of the board get pressed down rather than lifting — so it won't rattle.
If you cut a board straight through the centre of the log, the radial direction is the same everywhere across the face. There's no difference in shrinkage between the two sides, so it barely warps at all. This cutting method is called quarter-sawing. It costs more because only a few such boards can be cut from a single log.
This shrinkage isn't permanent damage. In humid seasons, wood soaks up water again and swells back. Sliding paper doors (fusuma and shoji) becoming heavier or lighter to slide between summer and winter comes from the same cause.
Summary
Wood shrinks by different amounts depending on direction, shrinking most along the growth rings. Because the two faces of a board differ in this way, it bows in the direction that flattens the arc of the rings. Since the direction is fixed, you can predict it just by looking at the cut end.
A board isn't bending at random.
It's simply following the blueprint laid down by its growth rings.
How growth rings themselves form, one per year, is covered in "Why does a tree grow exactly one ring a year?", and the wisdom of felling timber in winter to reduce its moisture content is covered in "Why is timber felled from autumn through winter?". Reading the grain also shows up in a stonemason's craft — see "How can a stonemason split huge boulders using nothing but wedges?".
- Look at the short cut end of a cutting board or shelf. You'll see the growth-ring lines forming an arc.
- Compare the side the arc bulges toward with the direction the board is warping. It should be bowing in the direction that flattens the arc.
- Soak a wooden chopstick in water for 30 minutes, then let it dry flat for a day. What was straight will end up slightly curved.
Engineered wood and plywood cancel out this movement by layering pieces with alternating grain directions. To see real warping, pick a solid, single piece of wood.
Want to know more? — Terms, formulas, and how this connects to your textbooksWe label each section by level, from middle-school science to university specialist courses
- MSCovered in middle-school science
- HSCovered in high-school "Physics Basics / Chemistry Basics"
- HS+High-school advanced material, or textbook sidebar content
- Univ.Not covered in high school — university specialist courses (materials science, wood science)
- ResearchNot yet settled as textbook fact — what researchers are actively investigating
MSTerminology: this phenomenon has names
- Moisture content: the weight of water in wood divided by the weight of the wood fully dried out. In green (freshly cut) wood, this can exceed 100%.
- Fibre saturation point: the point where the water in the cell cavities is gone and water starts leaving the cell walls themselves. For many species this is around 30% moisture content. Below this point, wood shrinks.
- Bark side and pith side: the face where the arc of the growth rings on the cut end bulges outward is the bark side — the face that was on the outside of the log. The opposite face, facing the tree's core, is the pith side.
MSHSChecking with a formula: how much does a 15 cm-wide board warp?
When the two faces of a board shrink by different amounts, the board curls into a bow. We can calculate how much the middle lifts. It's the same idea as a bimetallic thermometer needle bending when two metal strips are bonded together.
| In symbols | δ ＝ (αt − αr) × ΔU × W² ÷ (8 × h) |
| In words | Warp height ＝ (difference between tangential and radial shrinkage rates) × (change in moisture content) × (board width squared) ÷ (8 × board thickness) |
| Where it comes from | When the two faces of a board differ in strain, the board forms a circular arc of constant curvature. That curvature is set by "the strain difference between the two faces ÷ thickness." The height at the middle of a circular arc is "curvature × width² ÷ 8." This formula links the two together. |
| Board width W | 150 mm |
| Board thickness h | 15 mm |
| Tangential shrinkage rate αt | 0.0025 per unit moisture content (typical for Japanese cedar/sugi) |
| Radial shrinkage rate αr | 0.0012 per unit moisture content (typical for sugi) |
| Change in moisture content ΔU | from 20 to 10, i.e. 10 |
On the symbols: everything is in millimetres. The shrinkage rate is a unitless number describing "what fraction the wood shrinks for each 1-point drop in moisture content."
| Difference in shrinkage rates | 0.0025 − 0.0012 ＝ 0.0013 |
| Strain difference between the two faces | 0.0013 × 10 ＝ 0.013 |
| Board width squared | 150 × 150 ＝ 22500 |
| Numerator combined | 0.013 × 22500 ＝ 292.5 |
| Denominator (8 × thickness) | 8 × 15 ＝ 120 |
| Warp height δ | 292.5 ÷ 120 ≒ 2.4 |
③ In real terms: the middle of a 15 cm-wide board lifts by about 2.4 mm — roughly the thickness of two stacked coins. That's plenty to make a cutting board rattle. The formula also shows that a thicker board warps less, while a wider board warps a lot more.
HSHS+Where does the shrinkage difference come from?
HSThe main component of cell walls is cellulose, whose long, thin molecules line up in bundles. Water barely penetrates along the direction of a bundle, but moves in and out across it. That's why wood barely shrinks along its length, but shrinks across its width.
HS+The ratio of tangential to radial shrinkage rate is called the T/R ratio in wood science, and it's roughly 2 for many species. This is thought to be explained by the ray tissue restraining the radial direction, and by the layered structure alternating between latewood and earlywood. Latewood, the denser, darker part of a growth ring, is thought to hold back the thinner, lighter part that would otherwise shrink more.
Univ.Wood is treated as an orthotropic material
Wood is treated as an orthotropic material, with three mutually perpendicular principal axes: longitudinal, radial, and tangential. Describing its elasticity requires nine independent constants, rather than the two constants used for isotropic materials. This framework is shared with composite-materials mechanics, and the same mathematics is used in designing fibre-reinforced plastics. Deformation from drying is solved with an equation of the same form used for thermal expansion, treating the shrinkage rate as a coefficient applied to moisture content.
📖 Background and further reading: Anisotropy (Japanese Wikipedia) ／ Wood (Japanese Wikipedia)
ResearchWhat's still not fully understood
- Why the ratio comes out to roughly 2. Species with more ray tissue tend to show a smaller ratio, but there are reported cases where ray-tissue volume alone doesn't explain it. Separating out the contribution of the layered structure is ongoing work.
- Internal stress left over from drying. When the surface dries and stiffens first, stress remains locked inside the board. Predicting this accurately with numerical simulation is still considered a hard problem.
- Deformation across repeated cycles. As wood repeatedly gets damp and dries out, some deformation fails to fully reverse and accumulates over time. The mechanism behind this isn't fully worked out yet.
In other words, everything in this article is "the best explanation we have right now." The numbers vary a great deal by species and by part of the tree, so treat them as rough guides only.
How this maps onto the curriculum, by level
| Level | Subject / unit | Where in this article |
|---|---|---|
| MS | Science / plant structure, states of matter | Cell walls and water, shrinking as wood dries |
| HS | Physics Basics / force and deformation, Chemistry Basics / polymers | Strain and bending, orientation of cellulose |
| HS+ | Physics / thermal expansion and beams | The idea of a bimetallic strip bending |
| Univ. | Materials science, wood science | Orthotropy, shrinkage-rate coefficients |
| Research | Wood physics | Origin of the ratio, residual stress, repeated-cycle deformation |
| — | Everyday connection | Which way to lay a cutting board, floorboard, or shelf |
- Wood (Japanese Wikipedia) ― overview of structure, moisture content, and cutting methods
- Forestry and Forest Products Research Institute (森林総合研究所), supervising ed., Handbook of the Wood Industry (木材工業ハンドブック), Maruzen Publishing ― species-specific shrinkage rates and fibre saturation points
- Japan Wood Research Society (日本木材学会), ed., Handbook of Wood Science (木質科学ハンドブック), Asakura Publishing ― anisotropy of wood and deformation from drying
- Fushitani Yoshimi (伏谷賢美) et al., Physics of Wood (木材の物理), Bun-eido Shuppan ― anisotropy of shrinkage and the role of ray tissue
- Anisotropy (Japanese Wikipedia) ― the concept of materials whose properties vary by direction
※This article is a general-audience science explainer. The figures given are approximations meant to illustrate the underlying mechanism. Shrinkage rates vary greatly by species, part of the tree, and drying method. For actual woodworking or construction, follow the material's specifications and expert advice.