Calculate Poisson's ratio from strain, moduli pairs, or direct input. Derives shear and bulk modulus with 14-material comparison table.
Poisson's ratio (ν) describes how a material deforms laterally when stretched or compressed axially: ν = −ε_lateral / ε_axial. For most materials, stretching lengthwise causes a narrowing in the cross-section (ν > 0). Values range from −1 (exotic auxetics) to 0.5 (incompressible like rubber).
This calculator computes ν from three different input modes: strain measurements, Young's modulus + shear modulus (E, G), or Young's modulus + bulk modulus (E, K). It then derives the related elastic constants—shear modulus, bulk modulus, and Lamé's first parameter—completing the full set of isotropic elastic constants.
The 14-material reference table spans from auxetic foam (ν < 0) through cork (ν ≈ 0), metals (0.25–0.34), to rubber (ν ≈ 0.50). Understanding where a material falls on this scale is essential for structural analysis, materials selection, and FEA modeling. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Poisson's ratio is one of the two independent elastic constants for isotropic materials—you cannot do structural analysis without it. This calculator makes it easy to convert between different representations (strain data, moduli pairs) and to verify material properties.
The derived-moduli feature is especially useful: enter E and ν, and get G, K, and λ instantly—no need to remember the interconversion formulas.
ν = −ε_lateral/ε_axial. From moduli: ν = E/(2G) − 1, or ν = (3K − E)/(6K). Derived: G = E/(2(1+ν)), K = E/(3(1−2ν)), λ = Eν/((1+ν)(1−2ν)). Bounds: −1 ≤ ν ≤ 0.5 for isotropic materials.
Result: ν = 0.300 (Steel-like)
ν = −(−0.0003)/0.001 = 0.300. Closest match: Steel (ν = 0.30). With E = 200 GPa: G = 77.0 GPa, K = 167 GPa.
For isotropic materials, two constants define everything. Here is the full interconversion table:
| From → To | Formula | |---|---| | E, ν → G | G = E / (2(1+ν)) | | E, ν → K | K = E / (3(1−2ν)) | | E, ν → λ | λ = Eν / ((1+ν)(1−2ν)) | | E, G → ν | ν = E/(2G) − 1 | | E, K → ν | ν = (3K−E) / (6K) | | K, G → E | E = 9KG / (3K+G) | | K, G → ν | ν = (3K−2G) / (2(3K+G)) |
Materials with negative Poisson's ratio are called auxetics. When stretched, they get thicker in the direction perpendicular to the applied force. Applications include:
- **Impact protection**: Auxetic foams densify on impact, increasing energy absorption - **Medical stents**: Expand radially when pulled longitudinally - **Smart textiles**: Better draping and conformability - **Fasteners**: Auxetic bolts that expand into the hole under tension
Yes—auxetic materials expand laterally when stretched. Examples include certain foams, metamaterials, and some crystalline structures. The theoretical lower bound for isotropic materials is −1.
ν = 0.5 means volume is conserved (incompressible). Above 0.5, the material would increase in volume when compressed, violating thermodynamic stability for isotropic materials.
No lateral deformation when stretched—cork is the classic example. This is why cork seals work: pushing a cork into a bottle doesn't make it wider.
Finite element analysis requires both E and ν (or equivalent pairs) to define the stiffness matrix for linear elastic analysis. Wrong ν causes incorrect stress distribution.
For isotropic materials, ν is the same in all directions. Anisotropic materials (wood, composites) have different ν values for different loading directions.
For isotropic materials, any two constants (E, G, K, ν, λ) determine all others. The calculator uses E and ν to derive the rest.