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Woodworking Math

Wood species

Birch wood

Birch is a hardwood; this page covers the birch, led by yellow birch (Betula alleghaniensis). At 12% moisture content it has a Janka hardness of 1,260 lbf (5,605 N) and it weighs about 43 lb/ft³ (694 kg/m³), 3.6 lb (1.64 kg) per board foot.

Names and species on this page: yellow birch, sweet birch, paper birch.

Key numbers

Janka hardness, 12% MC
1,260 lbf (5,605 N)
Green: 780 lbf (3,470 N)
Weight at 12% MC
43 lb/ft³ (694 kg/m³)
3.6 lb per board foot
Specific gravity (oven-dry weight)
0.62 at 12% MC volume
0.55 on green volume
Shrinkage, green to oven-dry
9.5% tangential
Radial 7.3%, volumetric 16.8%

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

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

Work out what your boards weigh

How much birch moves

A 12 in wide flatsawn board of yellow birch that goes from 6% to 12% moisture content swells about 0.24 in (about 1/4 in, 6.2 mm). Quartersawn, the same board moves about 0.18 in (about 3/16 in, 4.7 mm). Flatsawn faces move 1.3 times as much as quartersawn ones, because the wood shrinks 9.5% around the growth rings but only 7.3% across them.

Worked with the Wood Handbook's dimensional change coefficients for yellow birch (Table 13-5: 0.00338 tangential, 0.00256 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
Yellow birch has white sapwood and light reddish-brown heartwood; sweet birch has dark brown heartwood tinged with red.
Grain and texture
Fine and uniform.
Working and character
Yellow and sweet birch are heavy, hard, strong and tough. Paper birch is lighter, softer and weaker. All birch shrinks considerably while drying.
Uses
Furniture, interior woodwork, doors, cabinets and wooden ware; birch veneer plywood for doors, paneling and cabinets. Paper birch goes into turned goods, toys and small handles.

Adapted in our own words from the Wood Handbook, Chapter 2, p. 2-5.

Strength

Bending strength is the modulus of rupture (MOR); stiffness is the modulus of elasticity (MOE). Clear, straight-grained samples of yellow birch 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)8,300 psi (57 MPa)16,600 psi (114 MPa)
Stiffness (MOE)1,500,000 psi (10.3 GPa)2,010,000 psi (13.9 GPa)
Crushing strength (compression parallel to grain)3,380 psi (23 MPa)8,170 psi (56 MPa)
Compression perpendicular to grain430 psi (3 MPa)970 psi (7 MPa)
Shear parallel to grain1,110 psi (8 MPa)1,880 psi (13 MPa)
Tension perpendicular to grain430 psi (3 MPa)920 psi (6 MPa)

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

The birch

The Handbook tests each species separately; they are sold together as birch. Across the 3 species measured, Janka hardness at 12% runs from 910 to 1,470 lbf.

SpeciesJanka, 12% MCWeight, 12% MCTangential shrinkage
Yellow birchBetula alleghaniensis1,260 lbf43 lb/ft³9.5%
Sweet birchBetula lenta1,470 lbf45 lb/ft³9.0%
Paper birchBetula papyrifera910 lbf38 lb/ft³8.6%

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 yellow birch at 1,260 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 × 0.62 × 1.12.

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 43 lb/ft³, or 3.6 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers