Turn pressure measurements into shear modulus with smart, unit-safe calculations in minutes. Compare methods, check assumptions, and download clean outputs for documentation every time.
Bulk modulus from pressure–volume data
Convert bulk modulus to shear modulus (isotropic solid)
Shear modulus from shear-wave speed
| Method | P₁ (MPa) | P₂ (MPa) | V₁ (L) | V₂ (L) | ν | Estimated K (GPa) | Estimated G (GPa) |
|---|---|---|---|---|---|---|---|
| Pressure–volume (two-point) | 0.1 | 50 | 1.000 | 0.985 | 0.30 | 3.35 | 1.54 |
| Shear-wave | — | — | — | — | — | — | 5.63 (ρ=2500, Vs=1500) |
Shear modulus, G, quantifies how strongly a material resists shape change at nearly constant volume. It controls torsional stiffness, shear strain under lateral loads, and the propagation of shear waves. Accurate G values improve structural safety, vibration predictions, and laboratory material characterization.
Many experiments generate pressure information more easily than direct shear tests. Compression tests, confined fluid loading, and hydrostatic pressurization produce pressure–volume behavior that reveals a material’s volumetric response. When combined with an assumed or measured Poisson ratio, that volumetric stiffness can be translated into shear stiffness.
Bulk modulus, K, describes resistance to uniform compression. In the two-point approach, the calculator estimates K from the slope of pressure change versus relative volume change using an average volume to reduce numerical bias. In practice, select two points within the same phase, temperature, and loading regime.
For an isotropic, linear elastic solid, K and G are linked through Poisson ratio, ν. The conversion used here increases G for higher K and decreases G as ν approaches 0.5. Because ν affects the conversion strongly, document how ν was obtained and keep it consistent with the test conditions.
Real measurements include noise and minor hysteresis. Dataset mode fits pressure versus volumetric strain relative to the first data point, then estimates K from the fitted slope. This reduces sensitivity to a single outlier and provides a more stable stiffness estimate when multiple measurements are available.
Pressure data may be reported in Pa, MPa, bar, atm, or psi, while volumes may be recorded in liters or cubic units. The calculator converts to SI internally, then converts results back to your chosen output units. This approach prevents mixing scales and keeps CSV and PDF exports consistent.
Metals often fall in the tens of GPa for G, many rocks in the 10–40 GPa range, and polymers can be far lower depending on temperature. A negative or near-zero computed modulus usually indicates inconsistent pressure–volume trends, an unrealistic ν, or insufficient volume change between points.
Engineering decisions benefit from transparent assumptions. Record the method used, pressure and volume units, reference volume definition, ν source, and any data trimming. Exporting to CSV supports quick audits, while the PDF summary provides a portable record for reports, lab notes, and reviews.
1) What does this calculator actually compute?
It estimates shear modulus using pressure–volume stiffness with Poisson ratio, or directly from bulk modulus with Poisson ratio, or from shear-wave speed with density, then outputs the result in your chosen unit.
2) When should I use the pressure–volume method?
Use it when you have reliable pressure and volume measurements under near-hydrostatic conditions and you can justify a Poisson ratio for the same material state, temperature, and loading rate.
3) Why does Poisson ratio affect the result so much?
Poisson ratio controls how volumetric stiffness partitions into shear stiffness in isotropic elasticity. As ν approaches 0.5, the material behaves nearly incompressibly, and the conversion from bulk modulus to shear modulus changes rapidly.
4) What is dataset mode doing differently?
Dataset mode uses multiple pressure–volume points, computes volumetric strain relative to the first volume, and fits a line to reduce noise sensitivity. The bulk modulus is taken from the fitted slope instead of one pair of points.
5) My computed modulus is negative. What should I check?
Confirm that volume decreases as pressure increases, verify units, ensure volume values are positive, and review ν. A sign issue or inconsistent data trend can flip the slope and produce a non-physical modulus.
6) Are the shear-wave results comparable to static results?
Often they differ. Shear-wave methods measure a dynamic modulus at higher frequencies and small strains, while static tests reflect slower loading and larger strains. Use comparable conditions when calibrating models or specifications.
7) How should I choose two points for the two-point method?
Pick points in the same linear region of your curve, avoid startup transients, and ensure a measurable volume change. Larger, clean ΔV/V improves numerical stability without crossing phase changes or damage onset.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.