Elastic Constants Calculator

Enter any two elastic constants for an isotropic material — choose from Young's modulus (E), Bulk modulus (K), Shear modulus (G), Poisson's ratio (ν), or Lamé's first constant (λ) — and the Elastic Constants Calculator derives all remaining moduli. Select your preferred unit (Pa, kPa, MPa, GPa, or psi) and see the full set of interrelated elastic constants computed from established isotropic material relationships. Also try the Beam Load Calculator.

Select the first elastic constant you know.

Enter the numeric value for your first constant (use selected unit for moduli).

Select the second elastic constant you know (must differ from the first).

Enter the numeric value for your second constant.

Applies to E, K, G, and λ outputs. Poisson's ratio (ν) is dimensionless.

Results

Young's Modulus (E)

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Bulk Modulus (K)

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Shear Modulus (G)

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Poisson's Ratio (ν)

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Lamé's First Constant (λ)

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Status

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Results Table

Frequently Asked Questions

What does the modulus of elasticity tell us?

The modulus of elasticity quantifies how a material responds to stress. It is defined as the ratio of stress to strain, so a higher modulus means the material is stiffer and deforms less under a given load. Young's modulus specifically describes this behavior under uniaxial tension or compression. See also our find Carbon Equivalent CE (IIW) with Carbon Equivalent Calculator.

How do I calculate shear modulus from Young's modulus?

If you know Young's modulus (E) and Poisson's ratio (ν), the shear modulus is G = E / (2(1 + ν)). For example, with E = 200 GPa and ν = 0.3, G = 200 / (2 × 1.3) ≈ 76.92 GPa. You can use this calculator by selecting E and ν as your two known constants.

Are Young's modulus and elastic modulus the same?

Young's modulus is one specific type of elastic modulus — it measures stiffness under uniaxial stress. The term 'elastic modulus' can refer to any of the elastic constants, including Bulk modulus, Shear modulus, or Lamé's constants. In casual use, 'elastic modulus' often means Young's modulus.

When is Lamé's first constant equal to the shear modulus?

Lamé's first constant (λ) equals the shear modulus (G) when Poisson's ratio ν = 0.25. This condition, sometimes called the Cauchy relation, is approximately satisfied by many common rocks and minerals, making it a useful simplification in geophysics. You might also find our Shear Stress (τ) — Shear Stress useful.

What is the bulk modulus if Young's modulus is 39 GPa?

Without a second known constant, the bulk modulus cannot be determined uniquely. For example, if ν = 0.3, then K = E / (3(1 − 2ν)) = 39 / (3 × 0.4) = 32.5 GPa. Enter E and ν into this calculator to get the exact result.

Why does this calculator require exactly two elastic constants?

For isotropic, homogeneous materials, the entire stress-strain relationship is fully described by just two independent elastic constants. All other elastic constants can be derived algebraically from any valid pair, which is why you only need two inputs.

What are typical values for common engineering materials?

Steel typically has E ≈ 200 GPa and ν ≈ 0.29. Aluminium has E ≈ 70 GPa and ν ≈ 0.33. Rubber has E ≈ 0.01–0.1 GPa with ν close to 0.5. Concrete has E ≈ 30 GPa and ν ≈ 0.2. These values vary by grade and treatment.

What constraints apply to Poisson's ratio for stable materials?

The Second Law of Thermodynamics requires −1 < ν < 0.5 for isotropic materials. A Poisson's ratio approaching 0.5 indicates an incompressible material (like rubber), while negative values correspond to auxetic materials that expand laterally when stretched.