The formula
Change in width = width × coefficient × (ending moisture − starting moisture)
A positive change is swelling. A negative change is shrinkage. The coefficient is the fractional change per 1% of moisture, based on the size of the wood near 10% moisture content. CutCalc takes the numbers from the Wood Handbook of the U.S. Forest Products Laboratory, a public-domain reference, and only claims them inside 6% to 14%. The wood movement calculator uses that formula and flags a moisture content outside the band.
The dimension you type is the one that is moving. For a panel, that is the width across the grain. Movement along the grain is left out. It is small next to the cross-grain term at furniture lengths.
Tangential and radial
Tangential movement follows the growth rings, the long way around the log. Radial movement goes from the bark toward the centre, across the rings. Flat-sawn stock shows the rings as arches on the face, and its width is tangential. Quarter-sawn stock shows the rings as short stripes, and its width is radial. For the species on the calculator, tangential is the larger number. Sugar maple is 0.00353 tangential and 0.00165 radial, a bit more than twice as much. Commercial red oak is 0.00369 tangential and 0.00158 radial.
Thickness of a flat-sawn board is the radial direction, so a ¾ inch top moves much less through its thickness than across its width. The gap you leave is almost always about the width.
If the rings run on a diagonal and you cannot call the board flat-sawn or quarter-sawn, mixed grain uses the average of the two coefficients. It is a middle guess for a planning gap, not a measurement of that particular board.
Worked examples
The handbook’s own check is white fir, tangential, 9.15 inches wide, from 8% to 11% moisture. The coefficient is 0.00245. The change is 9.15 × 0.00245 × 3, about 0.067 inch. The width becomes about 9.217 inches. The same board in the radial direction, coefficient 0.00112, moves about 0.031 inch. Three points of moisture is a modest swing. The flat-sawn face still moves about twice the quarter-sawn one.
A 12 inch flat-sawn red oak panel, from 12% in a humid shop down to 6%. That is six points, still inside the band. The change is 12 × 0.00369 × (6 − 12) = −0.266 inch, a bit over ¼ inch of shrinkage across the width. The same width quarter-sawn shrinks 0.114 inch.
A 16 inch sugar maple panel over the same six points. Flat-sawn, it shrinks 0.339 inch. Quarter-sawn, it shrinks 0.158 inch. A frame that captures the flat-sawn panel with no gap is asking the panel to get 0.339 inch narrower without anywhere to go, or to swell by that much if the season runs the other way. Leave at least that movement, and a little more if the shop may leave the 6% to 14% band. The extra is judgment. The coefficient is not.
| Board | Grain | Moisture | Change |
|---|---|---|---|
| White fir, 9.15 in | Tangential | 8% to 11% | +0.067 in |
| White fir, 9.15 in | Radial | 8% to 11% | +0.031 in |
| Red oak, 12 in | Tangential | 12% to 6% | −0.266 in |
| Red oak, 12 in | Radial | 12% to 6% | −0.114 in |
| Sugar maple, 16 in | Tangential | 12% to 6% | −0.339 in |
| Sugar maple, 16 in | Radial | 12% to 6% | −0.158 in |
A practical allowance
Size the gap from the width, the species, the grain, and the moisture swing you actually expect. A 6 point swing inside the handbook band is a reasonable planning range for an indoor piece. Flat-sawn stock of these species wants roughly twice the clearance of quarter-sawn stock. Buttons, slotted screw holes, and a frame groove that is deeper than the panel tongue are ways to give the panel that room. The number does not choose the hardware.
Do not apply the cross-grain coefficient to plywood as if it were solid stock. A veneered sheet is constrained by its plies and is a different problem. The dressed size of the solid board you started with is on the lumber sizes page. Movement then acts on the width you have after dressing, not on the nominal name.
What the estimate will not decide
- It does not predict cup, twist, or bow.
- It is not a kiln schedule, and it is not a moisture meter.
- Outside 6% to 14% it is still arithmetic with a coefficient that was not built for that band.
Questions
Does a board move along its length?
A little, and much less than it moves across the grain. Furniture lengths do not need that along-the-grain term for a gap at a panel end. This estimate is the cross-grain change only. It will not tell you the board will stay flat. Cup and twist depend on how the rings sit, not only on the average width.
Which way is tangential, and which is radial?
Tangential is around the growth rings. That is the width of a flat-sawn board, the one whose face shows the cathedral grain. Radial is across the rings, from bark toward pith. That is the width of a quarter-sawn board. On a flat-sawn board the thickness is the radial direction, and it is the smaller movement. Mixed grain, rings on a diagonal, uses the average of the two coefficients. It is a middle guess, and it is labeled as one.
What if the shop goes outside 6% to 14% moisture?
The coefficients were built for that band, around a size measured near 10% moisture content. The calculator still runs outside it and says so. Five percent in a heated shop in January is just outside. Treat the result as a planning size for a gap, and leave a little more than the number if a panel is trapped in a frame.
Is the gap a structural rating?
No. It is how far the width wants to go when the moisture content changes. It is not a shelf span, not a finish rating, and not a promise the board was dried to the percentage you typed. Measure the moisture if the gap is the difference between a panel that floats and a panel that splits the frame.