Bulk Modulus

Bulk Modulus

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

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:

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

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:

Typical Values of Some Materials

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

Material Bulk Modulus
(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

See Also