Relate Young's modulus, shear modulus, bulk modulus, and Poisson's ratio. Find any elastic constant from the others with material presets and conversion formulas.
For any isotropic linear elastic material, all elastic behavior can be described by just two independent constants. The four commonly used elastic constants — Young's modulus (E), shear modulus (G), bulk modulus (K), and Poisson's ratio (ν) — are all interrelated, so knowing any two allows you to calculate the other two.
Young's modulus measures stiffness in tension or compression. Shear modulus (also called the modulus of rigidity) measures resistance to shearing deformation. Bulk modulus measures resistance to uniform compression. Poisson's ratio describes how much a material contracts laterally when stretched axially — most materials have values between 0.2 and 0.45, with rubber approaching 0.5 (incompressible) and cork near 0 (no lateral expansion).
This calculator lets you solve for any one of the four elastic constants given two others. It includes material presets for common engineering materials, a visual Poisson's ratio indicator, and complete conversion formula references for all constant pairs.
Converting between elastic constants means keeping several coupled formulas straight, and that is where algebraic slips happen. This calculator handles all six two-variable combinations instantly, includes the Lamé parameters and P-wave modulus used in continuum mechanics and seismology, and gives you material presets so you can verify a result against a known material instead of trusting memory alone.
Relationships (isotropic materials): E = 2G(1 + ν) = 3K(1 − 2ν) = 9KG/(3K + G) G = E/(2(1 + ν)) = 3K(1 − 2ν)/(2(1 + ν)) K = E/(3(1 − 2ν)) = EG/(3(3G − E)) ν = E/(2G) − 1 = (3K − 2G)/(2(3K + G)) Lamé Parameters: λ = K − 2G/3 μ = G (second Lamé parameter) P-Wave Modulus: M = K + 4G/3
Result: 206.2 GPa
With G = 79.3 GPa and ν = 0.3 (typical steel), Young's modulus is E = 2 × 79.3 × (1 + 0.3) = 206.2 GPa, and bulk modulus is K = 206.2 / (3 × (1 − 0.6)) = 171.8 GPa.
Young's modulus (E) measures tensile stiffness, shear modulus (G) measures resistance to shape change, bulk modulus (K) measures resistance to uniform compression, and Poisson's ratio (ν) captures how much a material narrows when stretched. For isotropic linear materials, any two of those are enough to recover the others.
Structural engineers use E for deflection and buckling checks. Mechanical engineers use G for torsion and shaft design. Geophysicists use K and G to interpret seismic wave speeds. If the constants you measure do not agree with one another, that is usually a sign to recheck the test method or the specimen assumptions.
These relationships only apply cleanly to isotropic, linearly elastic materials. Wood, composites, and many crystals need a fuller directional stiffness model, so this calculator is best used as a quick isotropic check rather than a universal material law.
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For isotropic (direction-independent) linear elastic materials, the stress-strain relationship is fully described by two independent parameters. All other elastic constants can be derived from any pair.
Most metals are 0.25–0.35. Rubber is nearly 0.5 (incompressible). Cork is near 0. Auxetic materials have negative Poisson's ratio (they expand laterally when stretched).
Young's modulus (E) is the most commonly used elastic constant in structural engineering. It determines deflection under load, natural frequencies, and critical buckling loads.
Bulk modulus is important for hydrostatic loading (uniform pressure from all directions), such as deep-sea or geological applications. It equals the inverse of compressibility.
Only for isotropic, linearly elastic materials. Anisotropic materials (wood, composites, crystals) require up to 21 independent elastic constants.
Lamé's first parameter (λ) and second parameter (μ = G) appear in the generalized Hooke's law tensor form used in continuum mechanics and finite element analysis. They are useful when you need a compact material model rather than just E, G, K, and ν.