Bulk Modulus & Compressibility

Calculate bulk modulus K = ΔP / |ΔV/V₀|, compressibility β = 1/K, and speed of sound c = √(K/ρ) in a fluid.

Fluid Properties & Statics

Common fluids — click to auto-fill K and ρ

Inputs

Bulk modulus K (GPa)

Fluid density (optional) ρ (kg/m³)

Required for speed of sound c = √(K/ρ).

Test pressure (optional) ΔP (MPa)

Enter a ΔP to compute the resulting volume strain |ΔV/V₀| = ΔP/K.

Reference — Bulk Modulus of Common Fluids

Fluid	K (GPa)	ρ (kg/m³)	c (m/s)
Water 20°C	2.18	998	1481
Water 4°C	2.06	1000	1435
Seawater	2.34	1025	1510
Mercury 20°C	28.5	13600	1450
Engine oil SAE30	1.5	880	1306
Ethanol 20°C	0.9	789	1068
Glycerin 25°C	4.35	1261	1857
Air 20°C (isoth.)	1.0132e-4	1.204	294
Air 20°C (isen.)	1.4186e-4	1.204	343

Air values: isothermal K_T = P ≈ 101.3 kPa; isentropic K_s = γP ≈ 141.9 kPa (γ = 1.4). Speed of sound in air uses c = √(γRT) = 343 m/s at 20°C.

Theory

Bulk modulus K:

K = −V (dP/dV) = ΔP / |ΔV/V₀| [Pa]

β = 1/K [Pa⁻¹] (compressibility)

c = √(K/ρ) [m/s] (speed of sound)

K measures how much pressure is needed to produce a given fractional volume decrease. A higher K means a stiffer, less compressible fluid.

Isothermal vs isentropic bulk modulus:

Type	Formula	Use when
K_T (isothermal)	K_T = −V (∂P/∂V)_T	Slow compression, heat can escape
K_s (isentropic)	K_s = γ K_T (ideal gas)	Fast / acoustic processes, no heat transfer

For liquids K_T ≈ K_s (small difference). For ideal gases K_T = P and K_s = γP.

Speed of sound:

Liquids: c = √(K_s / ρ)

Ideal gas: c = √(γ R T) = √(γ P / ρ)

Use K_s (isentropic) for the speed of sound, not K_T. For water at 20°C: c = √(2.18×10⁹ / 998) ≈ 1477 m/s.

Where:

K = bulk modulus [Pa]
β = compressibility = 1/K [Pa⁻¹]
ΔP = applied pressure increase [Pa]
|ΔV/V₀| = magnitude of relative volume decrease (dimensionless)
ρ = fluid density [kg/m³]
c = speed of sound [m/s]
γ = ratio of specific heats (≈ 1.4 for air)