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Woodworking Math

Wood species

Northern white cedar wood

Northern white cedar is a softwood (Thuja occidentalis). At 12% moisture content it has a Janka hardness of 320 lbf (1,423 N) and it weighs about 22 lb/ft³ (347 kg/m³), 1.8 lb (0.82 kg) per board foot.

Also called: northern white-cedar, eastern white cedar, arborvitae.

Key numbers

Janka hardness, 12% MC
320 lbf (1,423 N)
Green: 230 lbf (1,023 N)
Weight at 12% MC
22 lb/ft³ (347 kg/m³)
1.8 lb per board foot
Specific gravity (oven-dry weight)
0.31 at 12% MC volume
0.29 on green volume
Shrinkage, green to oven-dry
4.9% tangential
Radial 2.2%, volumetric 7.2%

One source: USDA Forest Products Laboratory, the authority for species properties it measured

Why: Measured by the USDA Forest Products Laboratory; northern white cedar's density is worked from its specific gravity with the Handbook's own equation.

Work out what your boards weigh

How much northern white cedar moves

A 12 in wide flatsawn board of northern white-cedar that goes from 6% to 12% moisture content swells about 0.16 in (about 5/32 in, 4.2 mm). Quartersawn, the same board moves about 0.07 in (about 1/16 in, 1.8 mm). Flatsawn faces move 2.2 times as much as quartersawn ones, because the wood shrinks 4.9% around the growth rings but only 2.2% across them.

Worked with the Wood Handbook's dimensional change coefficients for northern white-cedar (Table 13-5: 0.00229 tangential, 0.00101 radial per 1% change in moisture content), which hold between 6% and 14%. For this species the Handbook assumes shrinkage starts at 22% moisture content instead of 30%. Individual boards vary: the Handbook gives shrinkage a coefficient of variation of about 15% (p. 4-11).

Work out how much your board will move

Color, grain and working

Color
Light brown heartwood and narrow, nearly white sapwood.
Working and character
Light, rather soft, low in strength and shock resistance, with low shrinkage. Easy to work, and the heartwood is very decay resistant.
Uses
Posts, poles, outdoor furniture, shingles, cabin logs, boats and wooden ware.

Adapted in our own words from the Wood Handbook, Chapter 2, p. 2-19.

Strength

Bending strength is the modulus of rupture (MOR); stiffness is the modulus of elasticity (MOE). Clear, straight-grained samples of northern white-cedar tested by the Forest Products Laboratory (Wood Handbook Table 5-3b). Knots and cross grain make lumber weaker than these clear samples (Handbook Chapter 5).

PropertyGreen12% MC
Bending strength (MOR)4,200 psi (29 MPa)6,500 psi (45 MPa)
Stiffness (MOE)640,000 psi (4.4 GPa)800,000 psi (5.5 GPa)
Crushing strength (compression parallel to grain)1,990 psi (14 MPa)3,960 psi (27 MPa)
Compression perpendicular to grain230 psi (2 MPa)310 psi (2 MPa)
Shear parallel to grain620 psi (4 MPa)850 psi (6 MPa)
Tension perpendicular to grain240 psi (2 MPa)240 psi (2 MPa)

A dash means the Handbook prints no value; none is filled in.

Dust and health

This is what the named authorities publish, not medical advice.

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Why these numbers

Why these numbers?
  1. The situation

    The USDA Forest Products Laboratory measured northern white-cedar at 320 lbf of side hardness at 12% moisture content, on clear, straight-grained samples (Wood Handbook Table 5-3b).

    One source: USDA Forest Products Laboratory, the authority for species properties it measured , sources [1]

  2. What that means

    Side hardness (Janka) is the load needed to press a 0.444 in (11.28 mm) steel ball halfway into the wood across the grain; a higher number dents less (Handbook p. 5-5).

    One source: USDA Forest Products Laboratory, the authority for species properties it measured , sources [1]

  3. So

    Density at 12% is water's density × specific gravity × (1 + 0.12) (Handbook Eq. 4-14): 62.43 × 0.31 × 1.12.

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 22 lb/ft³, or 1.8 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers