Bulk Modulus Calculator
Bulk modulus (K) is a fundamental mechanical property that measures a material's resistance to uniform volumetric compression. It is defined as the ratio of applied volumetric stress (change in pressure) to the resulting volumetric strain (fractional volume change). Engineers and materials scientists use bulk modulus when designing pressure vessels, hydraulic systems, and any application where materials experience hydrostatic stress. Enter the pressure change (delta P) and the fractional volume change (delta V / V, as a decimal) to compute K. For example, steel under 1,000 MPa hydrostatic pressure typically contracts by about 0.00625 of its original volume, giving K = 160 GPa.
Bulk modulus formula
K = delta P / (delta V / V)
Where delta P is the applied pressure change (Pa or MPa), and delta V / V is the resulting fractional volume change (dimensionless, taken as a positive magnitude for compression). The result K has units of pressure.
Understanding bulk modulus in practice
Materials with high bulk modulus, such as ceramics and metals, require enormous pressures to produce measurable volume changes. Materials with low bulk modulus, such as polymers and fluids, are much more compressible. Bulk modulus is an essential parameter in geophysical seismic analysis, oil and gas exploration, and the design of deep-sea equipment. It is related to Young's modulus E and Poisson's ratio v by K = E / (3(1 - 2v)). For nearly incompressible materials like rubber (v near 0.5), K is very large relative to E.
Bulk modulus: frequently asked questions
What is bulk modulus?
Bulk modulus K is a material property that quantifies resistance to uniform compression. It equals the ratio of volumetric stress (applied pressure change) to volumetric strain (fractional change in volume). A higher K means the material is less compressible.
What are typical bulk modulus values for common materials?
Steel has a bulk modulus of about 160 GPa, aluminum around 76 GPa, water approximately 2.2 GPa, and rubber less than 2 GPa. Diamond, one of the stiffest materials, reaches about 440 GPa.
How is bulk modulus related to Young's modulus and Poisson's ratio?
The relationship is K = E / (3(1 - 2v)), where E is Young's modulus and v is Poisson's ratio. For an incompressible material (v = 0.5), K approaches infinity.
What units does bulk modulus use?
Bulk modulus has the same units as pressure: pascals (Pa), megapascals (MPa), or gigapascals (GPa). In US customary units, psi or ksi are also used.
Why does volumetric strain use a negative sign in the full formula?
A positive applied pressure causes a decrease in volume, so the volumetric strain (delta V / V) is negative. The negative sign in K = -V (dP/dV) ensures K is a positive quantity describing stiffness.
Official sources
- NIST, "Elastic Constants of Selected Materials": nist.gov.
- ASM International, "ASM Handbook Vol. 8: Mechanical Testing and Evaluation": asminternational.org.
- ASTM International, Standard Test Method for Hydrostatic Compressibility: astm.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.