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Bulk modulus measures resistance to volume change: K = −Δp/(ΔV/V) for a small pressure increment. The minus sign makes K positive when compression reduces volume.
By Matan · Updated
Local compressibility
More precisely, K = −V dp/dV with the thermodynamic conditions specified. Compressibility is its reciprocal. A larger modulus means a smaller fractional volume change under the same pressure increment. It is not a fixed universal value independent of state. [1]
Worked volume change
For assumed K = 2.0 GPa and pressure increase 1.0 MPa, ΔV/V = −0.00050. A starting volume of 2.0 L decreases by approximately 0.0010 L, or 1.0 mL, in this small-change model.
Easy to reshape can mean hard to compress
A material can have low shear stiffness and comparatively high resistance to volume change. Rubber’s easy shape change does not make ordinary solid rubber highly volumetrically compressible. Foam and solid rubber are different cases.
Density also matters
For a fluid, sound speed involves the appropriate adiabatic bulk modulus and density, c = √(K/ρ). Modulus alone does not determine sound speed or density. Solids can also involve shear stiffness. [2]
Specify the process
Gas compression can be isothermal or adiabatic, giving different effective moduli. Large changes require the actual pressure–volume relationship rather than one linear increment.
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How this article was checked
Sources checked; calculations checked where shown. The definitions, model assumptions and main explanatory claims were cross-checked against the sources below. Worked-example arithmetic and units were checked separately. These examples are illustrative calculations, not experimental measurements.
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Sources and further reading
- OpenStax: Bulk modulus and compression — Bulk modulus and compression.
- OpenStax: Speed of sound in fluids — Speed of sound in fluids.
Cite this article
Matan. “Bulk modulus.” Your Physicist. Originally published 2023-03-17; updated 2026-09-10. https://your-physicist.com/bulk-modulus/
Revision history
: Added the missing sign and corrected rubber compressibility and modulus-only sound-speed claims. Added linked sources and a transparent verification record.
