What is bulk modulus?

Bulk modulus (K) is the ratio of applied hydrostatic pressure to the resulting fractional decrease in volume. A higher value means the material is stiffer and harder to compress. It is expressed in pascals (Pa) or gigapascals (GPa).

How is bulk modulus related to compressibility?

Compressibility (β) is simply the reciprocal of bulk modulus: β = 1/K. A material with a high bulk modulus has low compressibility, meaning it barely changes volume under pressure.

What is the formula for bulk modulus?

K = −ΔP / (ΔV / V₀), where ΔP is the applied pressure change, ΔV is the change in volume, and V₀ is the original volume. The negative sign ensures K is positive because volume decreases when pressure increases.

How is bulk modulus related to Young's modulus?

For an isotropic material: K = E / (3(1 − 2ν)), where E is Young's modulus and ν is Poisson's ratio. You can use our Young's Modulus Calculator for that conversion.

What units does this calculator use?

Pressure inputs accept MPa or GPa; volumetric strain is dimensionless (ΔV/V₀ as a fraction or percentage). The result is returned in the same pressure unit as the input.

Bulk Modulus Calculator

Name: Bulk Modulus Calculator
Availability: InStock
Author: Nham Vu

Compute bulk modulus K = ΔP / (−ΔV/V₀) from pressure and volume change, or solve for any missing variable.

Inputs

Solve for

Pressure Change (ΔP)

Volumetric Strain (ΔV/V₀)

Enter as a positive number (compression assumed).

Bulk Modulus (K)

Result

Enter values and click Calculate

Material Reference

Material	K (GPa)	β (GPa⁻¹)

Values are approximate and vary with temperature, purity, and processing.

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Summary

Compute bulk modulus K = ΔP / (−ΔV/V₀) from pressure and volume change, or solve for any missing variable.

How it works

Select which variable you want to solve for: bulk modulus, pressure change, or volumetric strain.
Enter the two known values with their units.
Click Calculate to get the result with unit conversion options.
Use the material reference table to look up typical bulk modulus values.
Compare your result against the reference to assess material behavior.

Use cases

Determine how much a fluid or solid compresses under hydrostatic pressure.
Verify material data sheets against measured pressure and volume change.
Select hydraulic fluid with adequate stiffness for a given system pressure.
Estimate compressibility of rock or soil layers in geotechnical analysis.
Check whether a polymer or elastomer is suitable for high-pressure sealing.
Convert between bulk modulus, Young's modulus, and Poisson's ratio in material design.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu