Quick Solve

Rock Type Comparison

Solve for Target K/G Ratio

Convert Between Elastic Moduli

E and Poisson’s Ratio

Shear and Bulk Modulus

E and Shear Modulus

Bulk Modulus and Poisson’s Ratio

Young’s Modulus, E

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Shear Modulus, G

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Bulk Modulus, K

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Poisson’s Ratio

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Lame’s Parameter, lambda

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Isotropic elasticity relations: E = 2G(1+v) = 3K(1-2v) = 9KG/(3K+G). Enter any two independent moduli in GPa (or v as a unitless ratio) to solve all five. All results update live as you type.

Elastic Moduli Across Rock Types

Rock Type	E (GPa)	Poisson’s Ratio	G (GPa)	K (GPa)

Sedimentary Rocks

Igneous and Metamorphic

Each row solves shear and bulk modulus from Young’s modulus and Poisson’s ratio, so the chart compares stiffness across rock types on a consistent basis.

Solve Poisson’s Ratio and Moduli for a Target K/G Ratio

Young’s Modulus, E (GPa)

Target Bulk-to-Shear Ratio, K/G

Required Poisson’s Ratio

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Resulting Shear Modulus

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Resulting Bulk Modulus

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Solved directly from K/G = 2(1+v) / (3(1-2v)) rearranged for v, then G and K follow from E and v in closed form. A K/G ratio of 1.333 corresponds to v = 0.2, and the ratio grows quickly as v approaches 0.5.

Convert between Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio for an isotropic material, compare typical values across common rock types, or solve the Poisson’s ratio and moduli that produce a target bulk-to-shear modulus ratio. Everything updates live.

Diagram showing that any two of Young's modulus, shear modulus, bulk modulus, and Poisson's ratio fix the other two for an isotropic material — The same relations used across rock physics, geomechanics, and materials engineering

Isotropic Elastic Moduli

A homogeneous, isotropic elastic material needs only two independent constants to fully describe how it deforms under stress. In practice, four different pairs show up depending on the discipline and the measurement available: Young’s modulus with Poisson’s ratio in structural engineering, shear modulus with bulk modulus in seismic rock physics, Young’s modulus with shear modulus when both come from sonic logs, and bulk modulus with Poisson’s ratio in some geomechanics workflows.

This tool converts between all four moduli from any one of those four input pairs, compares typical values across common rock types, and reverse solves the Poisson’s ratio needed to hit a target bulk-to-shear modulus ratio.

The Conversion Formulas

The core relation ties Young’s modulus E, shear modulus G, bulk modulus K, and Poisson’s ratio v together as E = 2G(1 + v) = 3K(1 – 2v) = 9KG / (3K + G). From any two of the four, the standard closed-form relations recover the rest, including Lame’s first parameter, lambda = K – 2G/3, which appears alongside G in the stress-strain equations for an isotropic solid.

Because the four moduli are just different combinations of the same two underlying constants, converting between them is purely algebraic, no new physical measurement is required, only a consistent pair of known inputs.

Bar chart comparing Young's modulus, shear modulus, and bulk modulus across shale, sandstone, limestone, and granite — Stiffness increases sharply from shale through sandstone and limestone to granite

Comparing Rock Types

Softer, more porous rocks like shale carry lower moduli and a higher Poisson’s ratio, while dense, well-cemented rocks like granite carry much higher moduli and a comparatively lower Poisson’s ratio. The comparison tab lets you build a table across any set of rock types, entering only Young’s modulus and Poisson’s ratio for each, with shear and bulk modulus solved automatically for the chart.

Solving for a Target Modulus Ratio

Sometimes the known quantity is not a modulus at all but a ratio, for example a bulk-to-shear modulus ratio implied by a particular Vp/Vs value in a rock physics model. Rearranging the standard relations gives a closed-form solution for Poisson’s ratio directly from that ratio, v = (3r – 2) / (2 + 6r), where r is the target K/G ratio. Once v is known, shear and bulk modulus follow directly from Young’s modulus.

Diagram showing a target bulk-to-shear modulus ratio solving for Poisson's ratio, then shear modulus and bulk modulus — A K/G ratio of 1.333 corresponds to a Poisson’s ratio of 0.2

Common Mistakes

Mixing static and dynamic moduli, since moduli computed from sonic and density logs are dynamic values and typically read higher than the static moduli measured in a lab core test, especially in weaker rocks.

Entering a Poisson’s ratio at or above 0.5, which is not physically possible for a normal isotropic solid and forces the bulk modulus toward infinity in the conversion formulas.

Confusing Lame’s first parameter, lambda, with the shear modulus, G, sometimes called Lame’s second parameter, they appear together in the same equations but are not interchangeable.

Assuming a single pair of moduli applies uniformly across an entire rock volume, when in practice moduli vary with mineralogy, porosity, and fluid content from one interval to the next.

Who Uses This

Rock physicists and geomechanics engineers converting between modulus pairs for stress and failure modeling.

Petrophysicists comparing dynamic elastic properties across lithologies from sonic and density log data.

Structural and materials engineers who need a quick check between Young’s modulus, shear modulus, and Poisson’s ratio.

Students and instructors learning the standard isotropic elasticity relations and how the four moduli relate to one another.

Try It Above

Use the quick solve tab to convert between any pair of moduli, move to the rock type comparison tab to see how stiffness varies across lithologies, or use the solve tab when you need the Poisson’s ratio and moduli consistent with a target bulk-to-shear modulus ratio.

Related Calculators and References

Continue building your workflow with the Mud Weight and Hydrostatic Pressure Gradient Calculator. For background on the formulas used above, see Wikipedia: Elastic Modulus.