Bulk Modulus Calculator
Bulk modulus K, elastic-constant relations, and sound speed — for isotropic linear-elastic materials.
K = −V₀ × ΔP / ΔVK resists uniform compression. Compressibility β = 1/K. Isotropic relations: E = 9KG/(3K+G), ν = (3K−2G)/(2(3K+G)). Sound speed: fluid c = √(K/ρ), solid (longitudinal) c = √((K+4G/3)/ρ).
Mode 1 — Bulk modulus from compression data
For passive materials ΔP and ΔV must have opposite signs (pressure up → volume down). A negative K means inconsistent inputs.
Mode 2 — Isotropic elastic-constant solver
Pick any two of the four constants; the other two are solved. Valid only for isotropic linear-elastic solids (−1 < ν < 0.5). For fluids (G = 0) use Mode 1 / Mode 3 instead. For the full 14-pair converter including Lamé λ, P-wave modulus M and cubic-crystal C11/C12/C44, see the elastic constants calculator.
Shear-modulus presets and torsion background: angle-of-twist calculator.
Mode 3 — Sound speed from bulk modulus
Need ρ in other units? Convert it with the density converter.
Worked examples
| Case | Inputs | Result |
|---|---|---|
| Water compression | V₀=1 m³, ΔV=−500 cm³, ΔP=1.1 MPa | K = 2.2000 GPa |
| Steel elastic constants | K=160 GPa, G=79.3 GPa | E = 204.1695 GPa, ν = 0.2873 |
| Sound in water | K=2.2 GPa, ρ=1000 kg/m³ | c = 1483.24 m/s |
| Longitudinal sound in steel | K=160 GPa, G=79.3 GPa, ρ=7850 kg/m³ | c = 5818.19 m/s |
Methodology: all computation is 100% client-side in your browser. The elastic-constant relations assume an isotropic linear-elastic solid; they do not apply to anisotropic materials (e.g. wood, composites), past yielding, or large deformations. For a fluid, G = 0 and Poisson's ratio is undefined (incompressible limit ν → 0.5).
Frequently asked questions
What is bulk modulus?
Bulk modulus K measures a material's resistance to uniform compression: K = −V₀ × ΔP / ΔV, where V₀ is the initial volume, ΔP the pressure change and ΔV the volume change. Example: compressing 1 m³ of water by 500 cm³ with ΔP = 1.1 MPa gives K = 2.2000 GPa.
What is compressibility?
Compressibility β is the reciprocal of bulk modulus: β = 1/K. For water (K = 2.2000 GPa), β = 4.545×10⁻¹⁰ Pa⁻¹ — water is nearly incompressible, which is why deep-ocean pressure barely shrinks it.
How are K, E, G and Poisson's ratio related?
For an isotropic linear-elastic solid, any two of the four constants determine the other two. From bulk modulus K and shear modulus G: E = 9KG/(3K+G) and ν = (3K−2G)/(2(3K+G)). Example: steel with K = 160 GPa and G = 79.3 GPa gives E = 204.1695 GPa and ν = 0.2873. Use the "Elastic relations" tab to solve any pair.
What values does Poisson's ratio take?
For isotropic linear-elastic materials −1 < ν < 0.5. Most metals sit around 0.28–0.35 (steel ≈ 0.29, aluminium ≈ 0.35); ν = 0.5 is the incompressible limit (fluids), and negative ν means auxetic behaviour. The calculator rejects ν outside (−1, 0.5).
What are typical bulk modulus values?
Room-temperature typical values: diamond 443 GPa, steel 160 GPa, copper 140 GPa, aluminium 76 GPa, water 2.2 GPa, and air 0.142 MPa (adiabatic, = γ·p₀ at sea level). Pick a preset in the calculator — each preset's K, G and density are mutually consistent.
How fast does sound travel in water?
In a fluid c = √(K/ρ). With K = 2.2 GPa and ρ = 1000 kg/m³, c = 1483.24 m/s — the well-known ~1.5 km/s figure used in underwater acoustics.
How fast does sound travel in steel?
For the longitudinal wave in a solid c = √((K+4G/3)/ρ). With K = 160 GPa, G = 79.3 GPa and ρ = 7850 kg/m³, c = 5818.19 m/s, about 17 times faster than in air (340.47 m/s).
What is the difference between adiabatic and isothermal bulk modulus?
For gases the bulk modulus depends on how fast you compress: adiabatic (fast, no heat exchange) K = γ·p, isothermal (slow) K = p. This calculator's air preset uses the adiabatic value 142.0000 kPa, which is what a sound wave sees.
When are the elastic-constant relations valid?
Only for isotropic linear-elastic solids: same properties in every direction, small deformations, below yielding. They do not apply to anisotropic materials (wood, fibre composites), rubber at large strain, or anything past its yield point.
Can I use this calculator for fluids?
Yes for Modes 1 and 3. A fluid has shear modulus G = 0, so Poisson's ratio is undefined (the ν → 0.5 incompressible limit) and Mode 2 does not apply — the relations need a solid with −1 < ν < 0.5.
What is the difference between bulk modulus and Young's modulus?
Bulk modulus K resists uniform volumetric compression (pressure from all sides); Young's modulus E resists uniaxial stretch. They are linked for isotropic solids — e.g. aluminium with K = 76 GPa and G = 26 GPa has E = 70.0157 GPa.
What units can I enter?
Pressure: Pa, kPa, MPa, GPa, bar, psi. Volume: m³, L, cm³, mm³, ft³, in³. Density: kg/m³, g/cm³, lb/ft³. Everything is converted to SI internally; results auto-scale (GPa/MPa/kPa) for readability.
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