0.3
76.9231
GPa
166.6667
GPa
0.3
0.0004
0.3
76.9231
GPa
166.6667
GPa
0.3
0.0004
Poisson's Ratio is a fundamental material property that describes the lateral contraction (or expansion) of a material when it is stretched (or compressed) in one direction. When you pull a rubber band, it gets thinner in the middle — Poisson's Ratio quantifies this effect. This calculator determines Poisson's Ratio from measured lateral and axial strains, and also computes the derived shear modulus and bulk modulus when Young's Modulus is provided.
Poisson's Ratio is defined as the negative ratio of lateral strain to axial strain under uniaxial loading:
$$\nu = -\frac{\varepsilon_{\text{lateral}}}{\varepsilon_{\text{axial}}}$$
where:
The negative sign is included because lateral strain is typically opposite in sign to axial strain (a material stretched axially contracts laterally). In this calculator, you enter the magnitudes of both strains as positive numbers, and ν is computed as their ratio.
Poisson's Ratio has theoretical bounds for stable, isotropic materials:
$$-1 \leq \nu \leq 0.5$$
Most materials fall between 0.2 and 0.5. A value of 0.5 means the material is perfectly incompressible (volume is preserved during deformation) — rubber and liquids approach this limit. A value of 0 means no lateral deformation occurs (cork behaves this way, which is why it seals bottles so well). Negative Poisson's ratio (auxetic materials) means the material expands laterally when stretched — certain engineered foams and metamaterials exhibit this unusual behavior.
When Poisson's Ratio is known along with Young's Modulus, all other isotropic elastic constants can be derived:
$$G = \frac{E}{2(1 + \nu)}$$
$$K = \frac{E}{3(1 - 2\nu)}$$
where G is the shear modulus and K is the bulk modulus. These relationships are cornerstones of linear elasticity theory and are essential for finite element analysis, structural engineering, and material characterization.
The volumetric strain under uniaxial loading is:
$$\varepsilon_V = (1 - 2\nu) \cdot \varepsilon_{\text{axial}}$$
This shows that when ν = 0.5, volume is exactly preserved during deformation — a hallmark of incompressible materials.
Poisson's Ratio near 0.5 indicates a nearly incompressible material (rubber, gold). Values around 0.3 are typical for metals (steel, aluminum). Values near 0 (cork, some foams) indicate minimal lateral response. If your calculated value exceeds 0.5 or is negative, verify your strain measurements — unless you are testing a known auxetic material. The derived G and K values require a valid Young's Modulus input in the advanced section.
Inputs
Results
Steel specimen with 0.001 axial strain and 0.0003 lateral contraction: ν = 0.0003/0.001 = 0.3. With E = 200 GPa: G = 200/2(1.3) = 76.9 GPa, K = 200/3(0.4) = 166.7 GPa.
Inputs
Results
Rubber with 10% axial strain and 4.8% lateral contraction: ν = 0.048/0.1 = 0.48 (nearly incompressible). The very high K/E ratio confirms rubber strongly resists volume change.
Poisson's Ratio (ν) describes how much a material contracts sideways when stretched lengthwise (or expands sideways when compressed). A value of 0.3 means the lateral contraction is 30% of the axial extension. It reflects the internal rearrangement of atoms under stress and is a fundamental property used in all stress-strain analyses.
Cork ≈ 0, Concrete ≈ 0.1–0.2, Glass ≈ 0.18–0.3, Steel ≈ 0.27–0.30, Aluminum ≈ 0.33, Copper ≈ 0.34, Titanium ≈ 0.34, Gold ≈ 0.42, Rubber ≈ 0.48–0.50. Most engineering metals cluster around 0.25–0.35.
For a stable isotropic material, the bulk modulus K = E/[3(1−2ν)] must be positive. If ν > 0.5, K becomes negative, meaning the material would expand under compression — a thermodynamically unstable condition. At ν = 0.5 exactly, K is infinite (perfectly incompressible). Anisotropic materials can have directional ratios exceeding 0.5.
Auxetic materials expand laterally when stretched, giving a negative Poisson's Ratio. Examples include certain re-entrant foams, origami-folded structures, and engineered metamaterials. They offer enhanced energy absorption, fracture resistance, and synclastic curvature (forming dome shapes). Values down to ν ≈ −0.7 have been achieved in designed structures.
Common methods: (1) Tensile test with biaxial extensometer or strain gauges measuring both axial and lateral strains simultaneously; (2) Ultrasonic method — measuring longitudinal and shear wave velocities, then computing ν = (v_L² − 2v_S²) / [2(v_L² − v_S²)]; (3) Digital Image Correlation (DIC) for full-field strain measurement during loading.
If you know both Poisson's Ratio (ν) and Young's Modulus (E), use: Shear Modulus G = E/[2(1+ν)] and Bulk Modulus K = E/[3(1−2ν)]. Enter Young's Modulus in the advanced inputs section of this calculator to see these derived values. Only two independent elastic constants are needed to fully characterize an isotropic material.
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