Poisson's Ratio
When a material is stretched in one direction it tends to get thinner in the other two directions.
When a sample of material is stretched in one direction it tends to get thinner in the lateral direction  and if a sample is compressed in one direction it tends to get thicker in the lateral direction.
Poisson's ratio is
 the ratio of the relative contraction strain (transverse, lateral or radial strain) normal to the applied load  to the relative extension strain (or axial strain) in the direction of the applied load
Poisson's Ratio can be expressed as
μ =  ε _{ t } / ε _{ l } (1)
where
μ = Poisson's ratio
ε _{ t } = transverse strain (m/m, ft/ft)
ε _{ l } = longitudinal or axial strain (m/m, ft/ft)
Strain is defined as "deformation of a solid due to stress".
Longitudinal (or axial) strain can be expressed as
ε _{ l } = dl / L (2)
where
ε _{ l } = longitudinal or axial strain (dimensionless  or m/m, ft/ft)
dl = change in length (m, ft)
L = initial length (m, ft)
Contraction (or transverse, lateral or radial) strain can be expressed as
ε _{ t } = dr / r (3)
where
ε _{ t } = transverse, lateral or radial strain (dimensionless  or m/m, ft/ft)
dr = change in radius (m, ft)
r = initial radius (m, ft)
Eq. 1, 2 and 3 can be combined to
μ =  ( dr / r ) / ( dl / L ) (4)
Example  Stretching Aluminum
An aluminum bar with length 10 m and radius 100 mm (100 10^{3} m) is stretched 5 mm (5 10^{3} m) . The radial contraction in lateral direction can be rearranged to
dr =  μ r dl / L (5)
With Poisson's ratio for aluminum 0.334  the contraction can be calculated as
dr =  0.334 ( 100 10^{3} m ) ( 5 10^{3} m) / (10 m)
= 1.7 10 ^{ 5 } m
= 0.017 mm
Poisson's Ratios for Common Materials
For most common materials the Poisson's ratio is in the range 0  0.5 . Typical Poisson's Ratios for some common materials are indicated below.
Material  Poisson's Ratio  μ  

Upper limit  0.5 
Aluminum  0.334 
Aluminum, 6061T6  0.35 
Aluminum, 2024T4  0.32 
Beryllium Copper  0.285 
Brass, 7030  0.331 
Brass, cast  0.357 
Bronze  0.34 
Clay  0.41 
Concrete  0.1  0.2 
Copper  0.355 
Cork  0 
Glass, Soda  0.22 
Glass, Float  0.2  0.27 
Granite  0.2  0.3 
Ice  0.33 
Inconel  0.27  0.38 
Iron, Cast  gray  0.211 
Iron, Cast  0.22  0.30 
Iron, Ductile  0.26  0.31 
Iron, Malleable  0.271 
Lead  0.431 
Limestone  0.2  0.3 
Magnesium  0.35 
Magnesium Alloy  0.281 
Marble  0.2  0.3 
Molybdenum  0.307 
Monel metal  0.315 
Nickel Silver  0.322 
Nickel Steel  0.291 
Polystyrene  0.34 
Phosphor Bronze  0.359 
Rubber  0.48  ~0.5 
Sand  0.29 
Sandy loam  0.31 
Sandy clay  0.37 
Stainless Steel 188  0.305 
Steel, cast  0.265 
Steel, Coldrolled  0.287 
Steel, high carbon  0.295 
Steel, mild  0.303 
Titanium (99.0 Ti)  0.32 
Wrought iron  0.278 
Znickel  0.36 
Zinc  0.331 
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