Calculate Poisson's ratio from lateral and axial strain, or from Young's modulus and shear modulus. See typical values for common materials on the Reference tab.
From Strains — ν = −εlateral / εaxial
Strain perpendicular to the applied load, as a unitless ratio (usually negative for a stretched specimen).
Strain along the direction of the applied load, as a unitless ratio.
From E & G — ν = E / (2G) − 1
Elastic (tensile) modulus in gigapascals.
Shear (rigidity) modulus in gigapascals.
Typical Poisson's Ratio Values
These are commonly cited reference values for real materials — actual values vary with alloy, temperature, and manufacturing process.
Poisson's ratio tells you how a material's cross-section responds when you pull or push on it lengthwise.
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Walk-through
How to Use This Calculator
3 steps▸
1
Pick a tab for what you know
Use the From Strains tab when you already have lateral and axial strain measurements from a tensile test. Use the From E & G tab when you know a material's Young's modulus and shear modulus instead. The Reference tab lists typical Poisson's ratio values for common materials with no inputs required.
2
Enter your known values
Strain values are unitless ratios (e.g. 0.001), not percentages — lateral strain is usually negative for a stretched specimen since the material narrows as it lengthens. Young's modulus and shear modulus are entered in gigapascals (GPa).
3
Read the ratio and the interpretation
The result card shows Poisson's ratio (ν) — a dimensionless number typically between 0 and 0.5 for common materials. The interpretation line explains whether the value falls in the typical range, is near the incompressible limit, or is negative (auxetic).
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Reference
Formula & Methodology
2 formulas▸
Poisson's Ratio from Strains
ν = −ε_lateral / ε_axial
ν (nu) is Poisson's ratio, ε_lateral is the strain perpendicular to the applied load (transverse strain), and ε_axial is the strain along the direction of the applied load. Both strains are dimensionless ratios. The negative sign exists because a material stretched along its axis (positive axial strain) typically contracts sideways (negative lateral strain), so the ratio without the sign would come out negative for ordinary materials. Example: ε_lateral = −0.0003, ε_axial = 0.001 → ν = −(−0.0003)/0.001 = 0.3.
Poisson's Ratio from Elastic Constants
ν = E / (2G) − 1
E is Young's modulus (the elastic/tensile modulus) and G is the shear modulus (modulus of rigidity), both typically in GPa. This formula relates three of the elastic constants for an isotropic material — Young's modulus, shear modulus, and Poisson's ratio are not independent; knowing any two determines the third. Example: E = 200 GPa, G = 76.9 GPa → ν = 200/(2×76.9) − 1 ≈ 0.3, matching structural steel.
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Glossary
Key Terms Explained
7 terms▸
Poisson's Ratio ↗A dimensionless measure of how much a material contracts perpendicular to an applied load as it stretches along the load's direction, defined as ν = −ε_lateral/ε_axial. Named after Siméon Poisson. Ranges from −1 to 0.5 for isotropic materials; most common materials fall between 0.2 and 0.35.
Lateral Strain ↗The strain (dimensionless change in dimension over original dimension) measured perpendicular to the direction of an applied axial load — for example, how much a rod's diameter shrinks as it's stretched lengthwise. Usually negative when axial strain is positive.
Axial Strain ↗The strain measured along the direction of an applied load — how much a specimen elongates or compresses in the same direction the force is applied.
Elastic Modulus ↗A general term for any ratio of stress to strain that measures a material's stiffness in the elastic region. Young's modulus, shear modulus, and bulk modulus are all elastic moduli, and Poisson's ratio links them together for isotropic materials.
Shear Modulus ↗A measure of a material's stiffness under shear loading (forces that slide adjacent layers past each other), denoted G. Related to Young's modulus and Poisson's ratio by G = E / (2(1+ν)).
Auxetic Material ↗A material with a negative Poisson's ratio — it gets thicker (not thinner) perpendicular to the stretch direction when pulled. Rare in nature but engineered in some foams, textiles, and re-entrant honeycomb structures.
Incompressible ↗A material that does not change volume under deformation. For isotropic materials this corresponds to the theoretical upper bound ν = 0.5 — rubber and other elastomers sit very close to this limit.
ν = −ε_lateral/ε_axial = −(−0.0003)/0.001 = 0.3. This matches the textbook Poisson's ratio for structural steel — a 0.1% stretch produces a 0.03% narrowing perpendicular to the load, well within the typical 0.2–0.35 range for metals.
ν = E/(2G) − 1 = 200/(2 × 76.9) − 1 ≈ 0.301 — the same result as the strain-based example, since both paths describe the same steel. This shows how Poisson's ratio, Young's modulus, and shear modulus are linked for any isotropic material.
ν = −(−0.05)/0.1 = 0.5 — the theoretical maximum for an isotropic material and typical of rubber-like elastomers, which barely change volume when stretched or compressed. This contrasts with steel's 0.3, showing why rubber bulges very little at the sides even under large deformation.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Poisson's ratio tells you how a material's cross-section responds when you pull or push on it lengthwise. It's one of the three fundamental elastic constants engineers use alongside Young's modulus and shear modulus to fully describe how an isotropic material deforms under load.
Why Materials Get Thinner When Stretched
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Pull on a rubber band and it visibly narrows as it stretches — that narrowing is exactly what Poisson's ratio quantifies. Most materials conserve something close to their original volume when deformed elastically, so if they elongate in one direction they must contract in the perpendicular directions to compensate. Poisson's ratio is the proportionality constant between those two strains: ν = −ε_lateral/ε_axial. A material with ν close to 0.5 (like rubber) is nearly incompressible and narrows a lot per unit of stretch relative to its volume change; a material with ν close to 0 (like cork) barely narrows at all, which is exactly why cork makes a good wine-bottle stopper — it can be compressed into the neck without bulging sideways.
One of Three Linked Elastic Constants
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For an isotropic material, Young's modulus (E), shear modulus (G), and Poisson's ratio (ν) are not independent — any two determine the third via ν = E/(2G) − 1, equivalently G = E/(2(1+ν)). This calculator's second tab lets you compute ν directly from E and G when you have those values from a materials datasheet but not raw strain measurements. It's the same underlying material property either way; the two tabs will always agree for consistent inputs.
The Valid Range, and Auxetic Materials
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For isotropic materials, thermodynamic stability limits Poisson's ratio to the range −1 to 0.5. Almost every everyday material falls between 0 and 0.5, with most metals clustering around 0.25–0.35. Values near 0.5 indicate near-incompressibility (rubber, biological soft tissue). A small number of engineered materials — certain foams, re-entrant honeycomb lattices, and some textiles — are auxetic: they have a negative Poisson's ratio and actually get thicker perpendicular to a stretch. This calculator accepts any input combination within the strain or modulus tabs; values outside the typical range are still computed and flagged by the interpretation text rather than rejected, since auxetic materials are a legitimate (if unusual) case.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for Poisson's ratio?+
ν = −ε_lateral/ε_axial, using the lateral (transverse) and axial strains directly. It can also be computed from the elastic constants as ν = E/(2G) − 1, where E is Young's modulus and G is the shear modulus.
What is Poisson's ratio for steel?+
Structural steel has a Poisson's ratio of approximately 0.3. Aluminum is around 0.33, copper around 0.34, and cast iron around 0.26 — most structural metals fall in the 0.25–0.35 range.
What is the range of Poisson's ratio?+
For isotropic materials, Poisson's ratio ranges from −1 to 0.5. Values from 0 to 0.5 cover essentially all common materials, with 0.5 being the theoretical incompressible limit (rubber-like materials sit close to this) and 0 meaning a material doesn't contract sideways at all when stretched (cork is close to zero).
What is Poisson's ratio for rubber?+
Rubber and other elastomers have a Poisson's ratio close to 0.5, the theoretical upper bound for isotropic materials, because they are nearly incompressible — they barely change volume when stretched or compressed.
What is an auxetic material?+
An auxetic material has a negative Poisson's ratio — it gets thicker, not thinner, perpendicular to the direction it's being stretched. This is unusual in nature but has been engineered into certain foams, textiles, and honeycomb lattice structures.
How do I find Poisson's ratio from Young's modulus and shear modulus?+
Use ν = E/(2G) − 1, entering both moduli in the same units (this calculator uses GPa for both). This relationship holds for any isotropic elastic material and is the formula used on the From E & G tab.
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