Bulk Modulus Calculator (K = −Δp ÷ ΔV/V₀, compressibility)

Understanding the bulk modulus calculator — concept and principle

The bulk modulus K measures how strongly a material resists being squeezed uniformly from all sides. This calculator finds K from a pressure change and the resulting volume change, and also gives the volumetric strain, the volume change and the compressibility.

Two hundred atmospheres squeeze water by less than 1%, which is why its bulk modulus is as high as 2.2 GPa.

How it is calculated

K = −Δp ÷ (ΔV ÷ V₀), where Δp is the pressure change and ΔV ÷ V₀ the fractional change in volume.
The minus sign makes K positive, because volume decreases when pressure rises.
Compressibility = 1 ÷ K.
With Δp in MPa, K is shown in MPa and GPa.

The principle

K is the three-dimensional counterpart of Young's modulus: stress divided by strain, where the stress is a uniform pressure and the strain is the fractional volume change. A high K means a tiny volume change for a large pressure. Solids and liquids have large bulk moduli because their atoms are already close together; gases are easily compressed. Reference values (OpenStax): steel about 160 GPa, copper 140 GPa, aluminium 75 GPa, crown glass 50 GPa, water 2.2 GPa. The relation assumes small, elastic changes at constant temperature.

Worked example

Default inputs: Δp = 20 MPa, V₀ = 1.000 L, volume after = 0.99091 L.

ΔV = 0.99091 − 1.000 = −0.00909 L = −9.09 mL.
Volumetric strain = −0.00909 ÷ 1.000 = −0.909%.
K = −20 MPa ÷ (−0.00909) ≈ 2,200 MPa = 2.2 GPa.
Compressibility = 1 ÷ 2.2 GPa ≈ 0.4545 per GPa.

This matches the textbook bulk modulus of water.

Each point is the calculator re-run with only “Pressure change Δp (MPa)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Pressure change Δp (MPa)	Bulk modulus K (GPa)
5	0.5501
10	1.1
15	1.65
20	2.2
25	2.75
30	3.3
40	4.4

How to read the result

Even water, which we think of as incompressible, shrinks by almost 1% under 20 MPa, the pressure about 2 km under the sea. Steel's K is about 70 times larger. In hydraulics, the fluid's bulk modulus sets how stiff the system feels; trapped air bubbles lower the effective K dramatically.

Common mistakes

Forgetting the minus sign and getting a negative K.
Using percentages as fractions (0.909 instead of 0.00909).
Mixing MPa and GPa.
Applying the formula to large compressions where K itself changes.

Keep in mind: Assumes small, elastic and isothermal changes. Engineering design needs measured material data and a qualified engineer.

Frequently asked questions

What is the bulk modulus of water?

About 2.2 GPa at room temperature.

What is the difference between bulk modulus and Young's modulus?

Bulk modulus describes uniform volume compression; Young's modulus describes stretching or compressing along one direction.

What is compressibility?

The reciprocal of the bulk modulus: the fractional volume change per unit pressure.

Sources: OpenStax, University Physics Volume 1, Chapter 12 Static Equilibrium and Elasticity (Table 12.1) · Callister, W. D. & Rethwisch, D. G., Materials Science and Engineering: An Introduction. Wiley

Checked 9 Nov 2026. OpenStax, University Physics Volume 1 (2016), §12.3 “Stress, Strain, and Elastic Modulus”: bulk modulus B = −Δp/(ΔV/V₀), compressibility k = 1/B, Table 12.1 elastic moduli.

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