Compressibility Calculator

What Are Bulk Modulus and Compressibility?

Bulk modulus measures how strongly a fluid or solid resists uniform compression. Compressibility is its reciprocal—how much relative volume change occurs per unit pressure increase.

Bulk Modulus and Compressibility Formulas

$$K = -\frac{V \,\Delta P}{\Delta V}$$ $$\beta = \frac{1}{K}$$

A negative $\Delta V$ means the volume shrinks when pressure rises, giving positive $K$. Water at room temperature has bulk modulus near 2.2 GPa and compressibility near 4.5 × 10⁻¹⁰ Pa⁻¹.

Example: 1 L (0.001 m³) compressed by 1 MPa with volume decrease 0.1 cm³ (1 × 10⁻⁷ m³) yields $K \approx 2.2$ GPa.

Frequently Asked Questions

What sign should ΔV have?

Compression produces negative ΔV (volume decreases). The formula includes a minus sign so bulk modulus stays positive for normal materials.

What is the difference between K and β?

Bulk modulus K is stiffness under pressure (Pa). Compressibility β = 1/K is the fractional volume change per pascal (Pa⁻¹). Large K means small β.

Does bulk modulus apply to gases?

Gases are highly compressible and K depends on thermodynamic conditions. This formula is most useful for liquids and solids over small strain.

Why use GPa for results?

Engineering tables list water near 2.2 GPa and steel near 160 GPa. GPa keeps numbers readable compared to pascals alone.

Can I solve for pressure or volume change?

Yes. Rearrange K = -VΔP/ΔV to isolate ΔP, ΔV, or V when the other quantities and K are known.

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What Are Bulk Modulus and Compressibility?

Bulk Modulus and Compressibility Formulas

Frequently Asked Questions

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