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Woodworking Math

Wood species

Spruce wood

Spruce is a softwood; this page covers the eastern spruces and engelmann spruce, led by red spruce (Picea rubens). At 12% moisture content it has a Janka hardness of 530 lbf (2,358 N) and it weighs about 28 lb/ft³ (448 kg/m³), 2.3 lb (1.06 kg) per board foot.

Names and species on this page: eastern spruce, red spruce, white spruce, black spruce, Engelmann spruce, mountain spruce.

Key numbers

Janka hardness, 12% MC
530 lbf (2,358 N)
Green: 340 lbf (1,512 N)
Weight at 12% MC
28 lb/ft³ (448 kg/m³)
2.3 lb per board foot
Specific gravity (oven-dry weight)
0.40 at 12% MC volume
0.37 on green volume
Shrinkage, green to oven-dry
7.8% tangential
Radial 3.8%, volumetric 11.8%

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

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

Work out what your boards weigh

How much spruce moves

A 12 in wide flatsawn board of red spruce that goes from 6% to 12% moisture content swells about 0.2 in (about 3/16 in, 5 mm). Quartersawn, the same board moves about 0.09 in (about 3/32 in, 2.4 mm). Flatsawn faces move 2.1 times as much as quartersawn ones, because the wood shrinks 7.8% around the growth rings but only 3.8% across them.

Worked with the Wood Handbook's dimensional change coefficients for red spruce (Table 13-5: 0.00274 tangential, 0.0013 radial per 1% change in moisture content), which hold between 6% and 14%. 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 colored, with little difference between heartwood and sapwood; Engelmann spruce is nearly white with a slight red tinge.
Grain and texture
Medium to fine texture; Engelmann spruce lumber usually carries many small knots.
Working and character
The eastern spruces are moderately light, easily worked, moderately strong and stiff, with moderate shrinkage, and dry easily. Engelmann spruce is lighter, softer and weaker.
Uses
Framing lumber, millwork, boxes and crates, and piano soundboards; much of it goes to pulp.

Adapted in our own words from the Wood Handbook, Chapter 2, p. 2-17 to 2-18.

Strength

Bending strength is the modulus of rupture (MOR); stiffness is the modulus of elasticity (MOE). Clear, straight-grained samples of red spruce 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)6,000 psi (41 MPa)10,800 psi (74 MPa)
Stiffness (MOE)1,330,000 psi (9.2 GPa)1,660,000 psi (11.4 GPa)
Crushing strength (compression parallel to grain)2,720 psi (19 MPa)5,540 psi (38 MPa)
Compression perpendicular to grain260 psi (2 MPa)550 psi (4 MPa)
Shear parallel to grain750 psi (5 MPa)1,290 psi (9 MPa)
Tension perpendicular to grain220 psi (2 MPa)350 psi (2 MPa)

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

The eastern spruces and engelmann spruce

The Handbook tests each species separately; they are sold together as spruce. Across the 4 species measured, Janka hardness at 12% runs from 390 to 530 lbf.

SpeciesJanka, 12% MCWeight, 12% MCTangential shrinkage
Red sprucePicea rubens530 lbf28 lb/ft³7.8%
White sprucePicea glauca410 lbf25 lb/ft³—
Black sprucePicea mariana530 lbf29 lb/ft³6.8%
Engelmann sprucePicea engelmannii390 lbf24 lb/ft³7.1%

Dust and health

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

Compare with

Why these numbers

Why these numbers?
  1. The situation

    The USDA Forest Products Laboratory measured red spruce at 530 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 × 0.40 × 1.12.

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 28 lb/ft³, or 2.3 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers