Compressibility Calculator — κ and Bulk Modulus
Compressibility κ tells you how much a material's volume shrinks per unit of applied pressure. Enter the initial volume, final volume, and pressure change to get κ (MPa⁻¹ and Pa⁻¹) and the bulk modulus K = 1/κ.
mL
mL
MPa
Fractional volume decrease per MPa of applied pressure (MPa⁻¹)
- 1
Volume decrease (ΔV)
100 − 99.5 mL = 0.5 mL - 2
Volumetric strain
0.5 ÷ 100 × 100 = 0.5 % - 3
Compressibility (κ)
0.5 ÷ (100 × 10) = 0.000500 MPa⁻¹
How does this calculator work?
Compressibility κ = (V₀ − V_f) / (V₀ × ΔP) measures how much a material's volume shrinks per unit of applied pressure; its reciprocal K = 1/κ is the bulk modulus. Enter initial volume (mL), final volume (mL), and pressure change (MPa) to get κ in MPa⁻¹ and Pa⁻¹, plus bulk modulus and volumetric strain.
Formula
How this is calculated
Compressibility κ (kappa) is defined as the fractional volume decrease per unit pressure increase: κ = −(1/V)(dV/dP). For finite measured changes this becomes κ = (V₀ − V_f) / (V₀ × ΔP), where V₀ is the initial volume, V_f is the volume under pressure, and ΔP is the applied pressure. The result has units of inverse pressure (MPa⁻¹ or Pa⁻¹ depending on the pressure unit used).
The reciprocal K = 1/κ is the bulk modulus (also called bulk incompressibility), expressed in the same pressure units. A high bulk modulus means the material is stiff and resists compression. For reference at room temperature: water K ≈ 2.2 GPa (κ ≈ 4.5 × 10⁻¹⁰ Pa⁻¹); structural steel K ≈ 160 GPa (κ ≈ 6 × 10⁻¹² Pa⁻¹); air at 1 atm (isothermal) K ≈ 0.1 MPa (κ ≈ 10⁻⁵ Pa⁻¹). Gases are many orders of magnitude more compressible than liquids, which are more compressible than solids.
This calculator assumes isothermal (constant-temperature) compression and linear elastic behaviour — valid only for small strains well below the material's yield or phase-transition pressure. For large pressure changes or near phase transitions, κ varies with pressure and a single-value approximation is less accurate.
Frequently asked questions
They are exact mathematical reciprocals: κ = 1/K and K = 1/κ. Compressibility quantifies ease of compression (large κ = easily compressed). Bulk modulus quantifies resistance to compression (large K = hard to compress, stiff material).
Compressibility describes volume reduction under increasing pressure. If V_f ≥ V₀ the sample expanded rather than contracted, which cannot be described by a positive compressibility — check your measurements or consider thermal expansion instead.
Water ≈ 4.5 × 10⁻¹⁰ Pa⁻¹, steel ≈ 6 × 10⁻¹² Pa⁻¹, rubber ≈ 1–2 × 10⁻⁹ Pa⁻¹, dry air ≈ 10⁻⁵ Pa⁻¹. Gases are 4–5 orders of magnitude more compressible than liquids, which are far more compressible than most engineering solids.
Also known as
TG we-Calculate Editorial Team. (2026). Compressibility Calculator — κ and Bulk Modulus [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/compressibility-calculator
TG we-Calculate Editorial Team. "Compressibility Calculator — κ and Bulk Modulus." TG we-Calculate. 2026. https://we-calculate.com/calculator/compressibility-calculator.
TG we-Calculate Editorial Team, "Compressibility Calculator — κ and Bulk Modulus," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/compressibility-calculator
@misc{wecalculate_compressibility_calculator, title = {Compressibility Calculator — κ and Bulk Modulus}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/compressibility-calculator}}, year = {2026}, note = {TG we-Calculate} }
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