Bulk Modulus

Summary
Calculate Bulk Modulus from Differential Change in Pressure and Volume
Calculate Bulk Modulus from Youngs Modulus and Poisson’s Ratio
Typical Values of Some Materials
See Also

Summary

The bulk modulus measures a substance’s elastic resistance to change in volume when under uniform loading in all directions.

It can be thought of as an extension of the Youngs Modulus into three dimensions.

The formula for bulk modulus is:

(1) $\begin{align*}K = -V(dP/dV)\end{align*}$

Where V = initial volume, dP = change in pressure, dV = change in volume.

K can be alternatively calculated if the Youngs Modulus (also known as the Modulus of Elasticity) and the Poisson’s Ratio of the material are known. Here,

(2) $\begin{align*}K = \frac{E}{3(1-2v)}\end{align*}$

Where E = Youngs Modulus and $v$ = Poisson’s Ratio.

Bulk Modulus of Elasticity Calculator

Bulk Modulus of Elasticity Calculator using Youngs Modulus and Poisson’s Ratio

Typical Values of Some Materials

This table contains typical bulk modulus value ranges for different materials.

Material	Bulk Modulus
Material	(GPa)
Aluminium	64 – 78
Aluminium Alloys	64 – 88
Boron Carbide (B₄C)	200 – 240
Brass	105 – 115
Brick	5 – 27
Bronze	104 – 125
Carbon (Diamond)	550 – 670
Concrete	6 – 28
Copper	108 – 142
Cork	0.01
Glass	33 – 45
Gold	125
Iron	119 – 167
Magnesium	35
Nickel	158 – 175
Nylon	3 – 8
Platinum	236 – 283
Rubber	257
Silver	96 – 106
Solder (Tin-Lead)	33 – 58
Steel	138 – 179
Stone (Granite)	22 – 58
Stone (Limestone)	3 – 22
Stone (Marble)	39 – 58
Tin	42 – 60
Titanium	93 – 111
Tungsten	307 – 314
Zinc	70 – 72

Calculate bulk modulus using differential change:
Formula:	$K = -V \frac{dP}{dV}$
	K = bulk modulus V = initial volume dP = change in pressure dV = change in volume
Initial Volume	m³
Change in Pressure	Pa
Change in Volume	m³

Result:

Calculate bulk modulus using Youngs Modulus and Poisson’s Ratio:
Formula:	$K = \frac{E}{3(1-2v)}$
	K = bulk modulus E = Youngs modulus (elastic modulus) $v$ = Poisson’s ratio
Youngs Modulus
Poisson’s Ratio

Result: