How to use it
Estimating seasonal movement
Choose the species and ring orientation
Flatsawn (rings across the width) uses the tangential coefficient; quartersawn (rings through the thickness) the radial one, about half as large. If you cannot tell, choose mixed or unknown and the tangential value is used, as the Handbook suggests.
Enter the width now
In inches or millimetres. Movement along the length is small for normal wood and is not calculated.
Enter the moisture content now and later
For example, the stock as it comes from the shop and the moisture it will reach in a humid summer or a heated winter. Use the helpers: equilibrium moisture content from the air's temperature and humidity, or moisture content from an ovendry sample.
Read the change
A positive change is swelling, a negative one shrinkage. Leave at least that much room in grooves, slots and gaps for a panel or top.
The method
Dimensional change between two moisture contents
C = S ÷ (100 × FSP − S × (FSP − 10))
ΔW = W × C × (MF − MI), both between 6% and 14%
ΔW = W × (MF − MI) ÷ (FSP × 100 ÷ S − FSP + MI), otherwise
- S
- shrinkage, green to ovendry: tangential or radial (Table 4–3) (%)
- FSP
- moisture content where shrinkage starts: 30, or 22 for western redcedar and redwood (%)
- C
- dimensional change coefficient, per 1% moisture, on the width at 10%
- W, ΔW
- width now, and its change (in or mm)
- MI, MF
- moisture content now and later, each limited to FSP (%)
Wood Handbook Eqs. 13–2, 13–3 and 13–4; the last is written with the species' FSP, as in Eq. 4–9. Above fiber saturation the width does not change.
| Board | Moisture | Change in width |
|---|---|---|
| White fir, flatsawn, 232 mm (9.15 in) | 8% → 11% | +1.70 mm (+0.067 in) — the Handbook's own example |
| White oak, flatsawn, 10 in | 6% → 12% | +0.226 in |
| White oak, quartersawn, 10 in | 6% → 12% | +0.116 in |
| Black cherry, flatsawn, 12 in | 6% → 12% | +0.179 in |
| White oak, flatsawn, 10 in | 20% → 8% | −0.435 in (outside 6–14%: Eq. 13–4) |
Worked by hand from the formulas and Table 4–3; the calculator gives the same to the figures shown.
Where the moisture contents come from
- Equilibrium moisture content (EMC). The moisture wood settles at in air of a given temperature and humidity: about 9.2% at 70 °F and 50% relative humidity, 6.2% at 30%, 16% at 80% (Table 4–2). The helper uses the Handbook's Eq. 4–5, which reproduces that table, for 30–120 °F and 5–95% humidity.
- Measured moisture content. Weigh a sample, dry it in an oven until its mass stops falling, and weigh it again; the helper applies MC = (mass − ovendry mass) ÷ ovendry mass × 100.
- Targets. For interior woodwork and furniture the Handbook recommends about 8% at installation in most of the United States (6–10% for individual pieces), 6% in the dry Southwest and 11% in damp, warm coastal areas.
How far to trust the answer
- Piece to piece. Shrinkage varies with a coefficient of variation of about 15% even for true flatsawn or quartersawn wood, and more in commercial lumber whose rings are rarely aligned perfectly. Treat the result as an average.
- Mixed orientation. For commercial lumber the Handbook expects this method to overestimate width change and underestimate thickness change.
- Linear assumption. The coefficient assumes shrinkage is proportional to moisture between 6% and 14%; the Handbook puts the error at about 5% of the change, on the low side.
- Slow response. Thick wood and finished wood take up and give off moisture slowly; a coating retards but does not prevent the change.
- Length. Normal wood barely shrinks along the grain, but reaction wood and juvenile wood near the pith can shrink up to about 2% lengthwise.
- Not listed. Baldcypress is left out of this calculator because the Handbook's shrinkage table gives no values for it.
Before fitting a panel or a top
- Species and ring orientation identified
- Moisture content now measured or estimated from the air
- The wettest and driest seasons' moisture estimated
- Room left in grooves and slots for the full swing
- Fasteners that let the width move
- About 15% more allowed for board-to-board variation
Flatsawn and quartersawn boards are explained in wood grain, moisture targets for buying in choosing lumber, and dryness grades in the lumber guide. A board's weight at a given moisture content is on the wood weight calculator.
Sources
Coefficients are computed from Table 4–3 by the Handbook's Eq. 13–2. They agree with its Table 13–5 for the species checked, but several pine rows of Table 13–5 (longleaf, pitch, pond, lodgepole) do not match Table 4–3, so the calculator does not copy that table.
- 1.
Chapter 13: Drying and Control of Moisture Content and Dimensional Changes. USDA Forest Service, Forest Products Laboratory — Wood Handbook, FPL-GTR-282, 2021.
Used for: The dimensional change coefficient C = S ÷ (100·FSP − S·(FSP − 10)) (Eq. 13–2) and ΔD = DI·C·(MF − MI) within 6–14% moisture content (Eq. 13–3), with Table 13–5 and the white-fir example (232 mm at 8% to 11%, 1.705 mm); ΔD = DI·(MF − MI) ÷ (30·100/S − 30 + MI) outside that range (Eq. 13–4), neither MC above about 30%; shrinkage taken to start at 22% for western redcedar and redwood; the linear method underestimating by about 5%; plainsawn width tending to be overestimated and thickness underestimated for commercial lumber; recommended moisture content at installation (Table 13–2).
- 2.
Chapter 4: Moisture Relations and Physical Properties of Wood. USDA Forest Service, Forest Products Laboratory — Wood Handbook, FPL-GTR-282, 2021.
Used for: Moisture content MC = (mwet − mdry) ÷ mdry × 100 (Eq. 4–2); equilibrium moisture content from temperature and relative humidity (Eq. 4–5, Table 4–2); shrinkage from green to ovendry by species (Table 4–3) and its linear approximation (Eq. 4–9), tangential values for plainsawn width, radial for quartersawn, tangential for mixed or unknown orientation; a coefficient of variation of about 15% for shrinkage; no dimensional change above fiber saturation; longitudinal shrinkage small but larger in reaction and juvenile wood.
- 3.
Chapter 3: Structure and Function of Wood. USDA Forest Service, Forest Products Laboratory — Wood Handbook, FPL-GTR-282, 2021.
Used for: Plainsawn (rings 0–45° to the face) and quartersawn (45–90°) lumber.
About this calculator
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