How wood shrinkage is calculated
Wood is hygroscopic: below the fiber saturation point (about 30% moisture content for most species), it shrinks as it dries and swells as it takes on moisture. This calculator uses the method published by the USDA Forest Products Laboratory in theWood Handbook (FPL-GTR-190), Chapter 4, Equation 4-7:
Sx = S0 × (30 − x) / 30
where S0 is the species’ total shrinkage from green to ovendry (a measured value from Wood Handbook Table 4-3), 30 is the assumed fiber saturation point in percent, and x is the moisture content of interest. Between two moisture contents MC1 and MC2 (both ≤ 30%), the shrinkage isS = S0 × (MC1 − MC2) / 30, and the change in board width is simply ΔD = width × S / 100. If the target moisture content is higher than the current one, the same equation predicts swelling instead of shrinkage.
Why grain orientation matters
Wood does not shrink equally in all directions. Tangential shrinkage (around the growth rings) is typically about twice the radial shrinkage (across the rings), while longitudinal shrinkage along the grain is negligible for most work. In aplainsawn board, the width lies in the tangential direction; in aquartersawn board, the width lies in the radial direction. If you are not sure how a board was sawn, the Wood Handbook approach of assuming the larger tangential value is the safer planning choice — this calculator defaults to plainsawn for that reason.
Shrinkage values used by this calculator
All coefficients below are green-to-ovendry total shrinkage percentages fromWood Handbook Table 4-3 (USDA Forest Products Laboratory, FPL-GTR-190):
| Species | Radial S0 (%) | Tangential S0 (%) |
|---|---|---|
| Red alder | 4.4 | 7.3 |
| White ash | 4.9 | 7.8 |
| Quaking aspen | 3.5 | 6.7 |
| Basswood | 6.6 | 9.3 |
| American beech | 5.5 | 11.9 |
| Yellow birch | 7.3 | 9.5 |
| Black cherry | 3.7 | 7.1 |
| Douglas-fir (coast) | 4.8 | 7.6 |
| Hickory (pecan) | 4.9 | 8.9 |
| Sugar maple | 4.8 | 9.9 |
| Northern red oak | 4.0 | 8.6 |
| White oak | 5.6 | 10.5 |
| Eastern white pine | 2.1 | 6.1 |
| Ponderosa pine | 3.9 | 6.2 |
| Redwood (old-growth) | 2.6 | 4.4 |
| Sitka spruce | 4.3 | 7.5 |
| Sweetgum | 5.3 | 10.2 |
| Black walnut | 5.5 | 7.8 |
| Western redcedar | 2.4 | 5.0 |
| Yellow-poplar | 4.6 | 8.2 |
Worked example
An 8-inch-wide plainsawn white oak board dries from 15% MC (air-dried) to 7% MC (indoor equilibrium). White oak’s tangential S0 is 10.5%, so S = 10.5 × (15 − 7) / 30 = 2.8%. The width change is 8 × 0.028 = 0.224 in, or about 7/32″. That is a lot of movement — enough to crack a glued-down panel, which is why cross-grain construction always needs room to move.
Practical notes
Real boards vary: density, ring orientation within the board, and drying history all shift the result, and the Wood Handbook reports a coefficient of variation around 15% for shrinkage values. Use this calculator to size expansion gaps, panel allowances, and drying targets, and always verify moisture content with a meter before final milling. Above 30% MC, no dimensional change occurs — the calculator clamps inputs to the 0–30% range accordingly.
Frequently Asked Questions
What formula does this wood shrinkage calculator use?
It uses Equation 4-7 from the USDA Forest Products Laboratory Wood Handbook (FPL-GTR-190, Chapter 4): Sx = S0 × (30 − x) / 30, where S0 is the total green-to-ovendry shrinkage percentage for the species and direction, 30% is the assumed fiber saturation point, and x is the moisture content. Shrinkage between two moisture contents is S = S0 × (MC1 − MC2) / 30.
What is the fiber saturation point and why does 30% matter?
Wood only shrinks or swells when its moisture content falls below the fiber saturation point — the point where cell walls start losing bound water, roughly 30% moisture content for most species. Above 30% MC, dimensional change is essentially zero, which is why this calculator caps both moisture inputs at 30%.
What is the difference between plainsawn and quartersawn shrinkage?
In a plainsawn (flatsawn) board, the width follows the tangential direction, which shrinks roughly twice as much as the radial direction. In a quartersawn board, the width follows the radial direction, so it moves much less. That is why quartersawn lumber is prized for stability in tabletops, flooring, and instrument making.
How accurate are these shrinkage predictions?
The Wood Handbook notes shrinkage of individual boards varies with density, growth-ring orientation, and drying conditions, with a coefficient of variation of roughly 15%. Treat the result as a solid planning estimate — leave extra allowance for critical joinery, panels, and breadboard ends.
How do I know the moisture content of my lumber?
Use a pin or pinless moisture meter. As reference points: freshly sawn (green) lumber is at or above 30% MC, air-dried lumber typically reaches 12–15% MC, kiln-dried lumber is usually 6–8% MC, and wood in a heated home equilibrates to roughly 6–9% MC depending on season and climate.
Does this calculator handle wood movement after the project is built?
Yes — the same math applies. Enter the moisture content the wood was built at as the current MC, and the seasonal extreme (e.g. 6% in winter heating season, 12% in a humid summer) as the target MC. The dimensional change is how much a panel of that width will move across the grain.