Bulk Modulus Calculator — Material Compressibility
Enter the applied pressure change and the resulting volumetric strain to calculate the bulk modulus K (in GPa) — the material property that quantifies how much it resists uniform compression.
MPa
%
m³
Resistance of the material to uniform compression
20 GPa
KVolumetric strain (fraction)
Bulk modulus (MPa)
Bulk modulus (GPa)
- 1
Volumetric strain (fraction)
0.5 % ÷ 100 = 0.005Convert the percentage strain to a dimensionless fraction before dividing into ΔP. - 2
Bulk modulus (MPa)
100 MPa ÷ 0.005 = 20,000 - 3
Bulk modulus K (GPa)
20,000 MPa ÷ 1 000 = 20
How does this calculator work?
Bulk modulus K = ΔP ÷ (|ΔV|/V₀). Enter the pressure increment (MPa) and the percentage volume reduction to get K in GPa and the compressibility β = 1/K. Reference values: steel ~160 GPa, water ~2.2 GPa, rubber ~1.5 GPa.
Formula
How this is calculated
The bulk modulus K is defined as the ratio of the applied hydrostatic stress (pressure increment ΔP) to the resulting volumetric strain (the fractional change in volume |ΔV/V₀|). Because compression decreases volume when pressure increases, the ratio is made positive by convention: K = ΔP / (|ΔV| / V₀). A high K indicates a stiff material that compresses very little under large pressure; a low K indicates a compliant or highly compressible one.
Typical values (2025 reference): diamond, ~440 GPa; steel, ~160 GPa; granite, ~50 GPa; concrete, ~30 GPa; water, ~2.2 GPa; rubber, ~1.5–2 GPa. Enter any ΔP and volumetric strain from an experiment — or look up published values and back-calculate the expected strain for a given pressure. The compressibility β = 1/K is the reciprocal of K; it is the fractional volume change per unit pressure.
This calculator uses isothermal (constant-temperature) conditions and assumes linear elastic behaviour, i.e. the material returns to its original volume when the pressure is removed and the relationship between stress and strain is proportional. Fluids behave this way at moderate pressures; for solids, the linear assumption holds at small strains (typically below 1%). At large strains, K is pressure-dependent and a nonlinear equation of state is needed.
Frequently asked questions
Young's modulus E describes resistance to uniaxial (one-direction) compression or extension. Bulk modulus K describes resistance to uniform hydrostatic compression from all directions simultaneously. For isotropic materials they are related by K = E / [3(1−2ν)], where ν is Poisson's ratio. Incompressible materials have ν = 0.5 and infinite K.
Water has a bulk modulus of approximately 2.2 GPa at 20 °C and atmospheric pressure, which is why it is often treated as incompressible in engineering calculations — a 1 MPa pressure increase causes only a 0.045% volume reduction. The value increases modestly with depth (pressure) in the ocean.
Yes. The most common method is to apply a known hydrostatic pressure to a sample immersed in a pressure vessel and measure the volume change with a piston gauge or by weighing displaced fluid. Ultrasonic methods (measuring the speed of longitudinal sound waves) are also widely used: K_isentropic = ρ × v_L² − (4/3)G, where ρ is density and G is shear modulus.
TG we-Calculate Editorial Team. (2026). Bulk Modulus Calculator — Material Compressibility [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/bulk-modulus-calculator
TG we-Calculate Editorial Team. "Bulk Modulus Calculator — Material Compressibility." TG we-Calculate. 2026. https://we-calculate.com/calculator/bulk-modulus-calculator.
TG we-Calculate Editorial Team, "Bulk Modulus Calculator — Material Compressibility," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/bulk-modulus-calculator
@misc{wecalculate_bulk_modulus_calculator, title = {Bulk Modulus Calculator — Material Compressibility}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/bulk-modulus-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?