Elastic Constants Calculator
Convert between elastic constants (Young's modulus, shear modulus, bulk modulus, Poisson's ratio, Lamé's constant, P-wave modulus) for isotropic materials.
Note: For isotropic, homogeneous materials, any two independent elastic constants determine all others. Poisson's ratio range: −1 < ν < 0.5. All moduli in GPa.
About This Calculator
The Elastic Constants Calculator helps you convert between the six elastic moduli that describe how isotropic, homogeneous materials respond to stress and strain. These constants — Young's modulus (E), shear modulus (G), bulk modulus (K), Poisson's ratio (ν), Lamé's constant (λ), and P-wave modulus (M) — are fundamental in mechanical engineering, materials science, geophysics, and structural analysis.
For isotropic materials (materials whose properties are identical in all directions, such as steel, aluminum, or glass), only two independent elastic constants are needed to determine all the others. This is possible because the elastic behavior of isotropic materials is governed by Hooke's law, which relates stress and strain through a stiffness tensor with just two independent parameters.
Common conversions: Young's modulus (E) and Poisson's ratio (ν) are the most commonly measured pair. From these, shear modulus is computed as G = E / (2(1 + ν)) and bulk modulus as K = E / (3(1 − 2ν)). The P-wave modulus M = E(1 − ν) / ((1 + ν)(1 − 2ν)) is important in seismology and soil mechanics. For typical structural steel (E ≈ 200 GPa, ν ≈ 0.3), the shear modulus is approximately 77 GPa and the bulk modulus is about 167 GPa.
Simply select any two known constants from the dropdown menus, enter their values, and click Calculate. The calculator instantly computes all six elastic moduli with interactive bar and pie charts for visual comparison.
Frequently Asked Questions
What are elastic constants?
Elastic constants describe how a material deforms under stress. For isotropic materials, six interrelated constants exist. Any two determine all the others through well-established relationships from linear elasticity theory.
How do I convert between Young's modulus and shear modulus?
For 3D isotropic materials, G = E / (2(1 + ν)). You need both Young's modulus (E) and Poisson's ratio (ν) to find shear modulus (G). Our calculator handles all 15 possible pairs of known constants.
What is the range of Poisson's ratio?
For physically realizable isotropic materials, Poisson's ratio ranges from −1 to 0.5. Most metals and ceramics have ν ≈ 0.2–0.35. Rubber approaches 0.5, while auxetic materials can have negative ν.
What is Lamé's constant used for?
Lamé's first parameter (λ) relates normal stress to lateral strain. While it lacks a direct physical interpretation, it simplifies many elasticity equations and pairs naturally with shear modulus G (Lamé's second parameter).
What is the P-wave modulus?
The P-wave modulus (M), also called the longitudinal or constrained modulus, describes uniaxial strain with no lateral deformation. It is important in seismology for computing seismic wave velocities in geological materials.
Is this calculator free?
Yes, the Elastic Constants Calculator is completely free to use with no registration required.
Can I share my results?
Yes! The URL automatically updates with your selected constants and values, so you can bookmark or share your exact calculation.