The one line of arithmetic behind all of it
Wood shrinks and swells across the grain as it gives up or takes on moisture, and barely moves along the grain at all. The change is close enough to proportional that a single multiplication gets you there:
change in width = width × shrinkage coefficient × change in moisture content
The coefficient comes from the species. Published tables give total shrinkage from green to ovendry, split into tangential (across the growth rings, which is the face of a flatsawn board) and radial (along the rays, which is the face of a quartersawn board). Because essentially all of that shrinkage happens between the fibre saturation point at roughly 30 percent moisture content and bone dry, dividing the published percentage by 30 gives the change per single point of moisture content.
Work one by hand. A 30 inch wide flatsawn white oak tabletop, going from 6 percent moisture content in a heated winter house to 12 percent in a humid August:
- White oak tangential shrinkage: 10.5 percent green to ovendry
- Coefficient: 10.5 / 100 / 30 = 0.0035 per point of moisture content
- Moisture change: 12 − 6 = 6 points
- Change: 30 × 0.0035 × 6 = 0.63 inches, call it 5/8"
Five-eighths of an inch. That is the number that breaks tabletops, and it is why an apron-to-top attachment has to slide. The same top in quartersawn white oak uses the radial figure of 5.6 percent, a coefficient of 0.00187, and moves 0.336 inches — a bit over 5/16". Quartersawing does not stop movement. It roughly halves it.
Flatsawn, riftsawn, quartersawn
What matters is the angle of the growth rings to the face of the board, because that decides whether the width of the board is running tangentially or radially through the tree.
| Ring angle to the face | Called | Coefficient used | Relative movement |
|---|---|---|---|
| 0 to 30 degrees | Flatsawn / plainsawn | Tangential | The largest, roughly twice radial |
| 30 to 60 degrees | Riftsawn | Between the two | Mid-way, and hard to pin down |
| 60 to 90 degrees | Quartersawn | Radial | Roughly half of flatsawn |
Riftsawn is handled here as the midpoint of the two coefficients, which is a convenience rather than a measurement. A board at 35 degrees behaves much more like flatsawn than a board at 55 degrees does. If you are close to a limit and the stock is rift, use the flatsawn figure.
Most real boards are not uniform. A wide flatsawn plank has quartered grain at the edges and flat grain in the middle, which is exactly why it cups: the two zones want to change width by different amounts. That is a reason to expect the calculated figure to be a reasonable average across the board, not a promise about any one inch of it.
Moisture content, and getting it from humidity
If you have a moisture meter, use it and work in moisture content directly. If you do not, wood in a stable environment settles at an equilibrium moisture content set mostly by the relative humidity around it. At about 70°F the relationship runs roughly like this:
| Relative humidity | Equilibrium moisture content | Where that happens |
|---|---|---|
| 20% | 4.5% | Heated house in a hard northern winter |
| 30% | 6.2% | Typical heated indoor winter |
| 40% | 7.7% | Comfortable conditioned indoor year-round |
| 50% | 9.2% | Mild indoor summer |
| 60% | 11.0% | Humid indoor summer, unconditioned |
| 70% | 13.1% | Damp basement, unheated shop |
| 80% | 16.0% | Coastal summer, covered outdoor |
Temperature shifts these figures a little, and the values differ slightly depending on whether the wood is drying down to that humidity or wetting up to it. Neither effect is large enough to change what you build. The swing between your winter and summer numbers is what matters, and for most heated-and-air-conditioned houses that swing is four to six points of moisture content.
Turning movement into joinery
Once you have the number, the design question is only ever the same one: where is the wood held, and where is it free.
- Tabletop to base. Fix the top solidly at one point, usually the centre of each apron, and let everything else slide. A top held at its centre only has to move half the total at each edge, which halves the slot length you need. Buttons in a groove, figure-eight fasteners and Z-clips all do this; screws through round holes do not.
- Breadboard ends. Glue and pin the centre tenon. Everything outboard of it gets an elongated mortise and a pin through a slot. The outer pins need to travel about half the total movement, in the direction the top is going.
- Frame and panel. The panel floats. Groove depth has to be the tongue engagement you want plus room for the panel to grow on each side. If you build in winter at the dry extreme, all of the clearance goes to expansion; build in a humid August and the panel will shrink and can show an unfinished line at the edge, which is why panels get finished before assembly.
- Drawer bottoms, case backs. Same rule. Slot at the back, screw through the slot, never glue the panel into its groove.
The one case where the arithmetic does not save you is cross-grain glue. Gluing a solid apron across the grain of a solid top, or a solid batten across a panel, sets up a fight between two pieces that want different widths. The wood does not compromise. It splits, or the glue line fails, and which one happens is decided by whichever is weaker.
How wrong this can be, and in which direction
The coefficients here are species averages from published shrinkage data. Real boards vary by a surprising amount around them: density, growth rate, position in the log, reaction wood and whether the board was kiln dried or air dried all shift the number. Treat the result as accurate to maybe plus or minus 20 percent for a given board, and better than that for a wide top glued up from several boards, where the variation averages out.
What matters more than the magnitude is the direction of the error. Allowing too much movement costs you a slightly longer slot that nobody will ever see. Allowing too little costs you the piece. Every time you are rounding, round the way that gives the wood more room.
Questions people ask
Does finish stop wood from moving?
No. Finish slows the exchange of moisture, it does not prevent it. A film finish like polyurethane or lacquer will slow the movement enough that a piece rides through short humidity spikes without responding, which is genuinely useful, but over a full season the wood reaches equilibrium anyway. Oil finishes slow it hardly at all. The practical rules that follow are: finish all surfaces including the underside of a top, so both faces exchange moisture at the same rate and the board does not cup, and design the joinery as though the finish were not there.
Why does my quartersawn board still move?
Because quartersawing changes which coefficient applies, not whether wood moves. Radial shrinkage is typically about half of tangential, so a quartersawn board moves roughly half as much across its width as a flatsawn one of the same species and size. On a 30 inch white oak top over a six point moisture swing that is the difference between about 5/8 inch and about 5/16 inch. Both need accommodating. What quartersawn stock does buy you is stability of shape as well as size: it is far less prone to cupping, because the grain angle is consistent right across the board.
How long should lumber sit in the shop before I build with it?
Until it stops changing, which you can only know by measuring. A rough guide is a couple of weeks for surfaced boards under an inch thick that came from a similar environment, and a month or more for thick stock or anything that came out of an unheated barn. Sticker it with spacers so air reaches every face, keep it off a concrete floor, and weigh a sample board or meter it every few days. When two readings a week apart agree, it has settled. Building with wood that is still moving is the second most common cause of failed panels, after not allowing for the movement at all.
Does the thickness or length of the board move too?
Thickness moves by the same coefficients, but on a 3/4 inch board even a large moisture swing is a couple of thousandths of an inch and nothing cares. Length moves along the grain by roughly a tenth to two tenths of a percent from green to ovendry, which over a six point moisture change on a six foot rail is well under a hundredth of an inch. Ignore both. The only dimension that ever needs designing around is width across the grain, and that is what this calculator gives you.