Elastic Constants Calculator — E, G, K, ν Conversions
For any isotropic linear-elastic material, knowing any two of the four elastic constants — Young's modulus E, shear modulus G, bulk modulus K, and Poisson's ratio ν — uniquely determines the other two. Select the pair you know, enter their values, and the remaining constants are calculated instantly.
Known pair
Pa
Dimensionless ratio of lateral to axial strain; range (−1, 0.5) for isotropic solids
Young's modulus
Shear modulus
Bulk modulus
Poisson's ratio
- 1
Shear modulus G = E ÷ (2 × (1 + ν))
200 GPa ÷ (2 × (1 + 0.3)) = 76.923 GPa - 2
Bulk modulus K = E ÷ (3 × (1 − 2ν))
200 GPa ÷ (3 × (1 − 2 × 0.3)) = 166.667 GPa - 3
Poisson's ratio ν (input)
0.30000
How does this calculator work?
For isotropic elastic materials, any two of {E, G, K, ν} uniquely determine the other two via E = 2G(1+ν) = 3K(1−2ν) = 9KG/(3K+G). Choose the pair you know, enter both values in Pascals (or dimensionless for ν), and get all four constants plus the Lamé parameter λ. Physical validity requires −1 < ν < 0.5 and all moduli positive.
Formula
How this is calculated
An isotropic linear-elastic solid — one that behaves the same in every direction — has only two independent elastic constants. All four commonly used constants (E, G, K, ν) are mutually related; any two fix the others through the standard isotropic-elasticity identities. Young's modulus E (also called the tensile or elastic modulus) measures resistance to axial (stretching/compressing) stress. Shear modulus G (or rigidity modulus) measures resistance to shear stress. Bulk modulus K measures resistance to uniform volumetric compression. Poisson's ratio ν is the negative ratio of lateral to axial strain when a material is stretched — it is dimensionless and lies strictly between −1 and 0.5 for stable isotropic materials (most structural materials are near 0.25–0.35).
The calculator applies whichever of the six closed-form relations matches the chosen pair. For example, from E and ν: G = E / (2(1+ν)) and K = E / (3(1−2ν)). If the derived Poisson's ratio falls outside (−1, 0.5), or any modulus is non-positive, the inputs are physically inconsistent and no result is shown. The Lamé first parameter λ = K − 2G/3 is also displayed; it appears in the constitutive tensor form of Hooke's law.
Frequently asked questions
Those bounds follow from thermodynamic stability: a material must store positive strain energy in all deformation modes. A ν ≥ 0.5 would imply incompressibility (rubber approaches 0.5). A ν < −1 violates positive definiteness of the strain-energy density. Most metals are 0.25–0.35; cork is nearly 0.
Enter moduli in Pascals (Pa). For steel (E ≈ 200 GPa), type 200e9. The output automatically labels results as Pa, MPa or GPa depending on magnitude. Poisson's ratio is dimensionless.
No — the calculator assumes isotropic symmetry, where properties are the same in all directions. Anisotropic materials (composites, crystals, timber) require multiple independent constants and a full stiffness tensor.
Also known as
TG we-Calculate Editorial Team. (2026). Elastic Constants Calculator — E, G, K, ν Conversions [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/elastic-constants-calculator
TG we-Calculate Editorial Team. "Elastic Constants Calculator — E, G, K, ν Conversions." TG we-Calculate. 2026. https://we-calculate.com/calculator/elastic-constants-calculator.
TG we-Calculate Editorial Team, "Elastic Constants Calculator — E, G, K, ν Conversions," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/elastic-constants-calculator
@misc{wecalculate_elastic_constants_calculator, title = {Elastic Constants Calculator — E, G, K, ν Conversions}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/elastic-constants-calculator}}, year = {2026}, note = {TG we-Calculate} }
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