Bulk Modulus Calculator
This bulk modulus calculator works out how strongly a material resists being compressed, from the pressure you apply and the volume change that results. Enter the pressure increase, the original volume and the amount that volume shrinks, and the calculator returns the bulk modulus in both gigapascals and megapascals, the fractional volume change as a percentage, and the compressibility, which is just the reciprocal of the bulk modulus. Bulk modulus is the pressure needed to produce a given fractional reduction in volume, so a high figure means the material is stiff against squeezing: water sits around 2.2 GPa, hydraulic oil a little lower, steel about 160 GPa and diamond above 400 GPa. It is the property that decides how much a hydraulic fluid springs back under load, how fast sound travels through a liquid, and how far a sealed volume compresses at depth in the ocean. The defaults describe a 1000 litre volume squeezed by 4.5 litres under a 10 MPa pressure rise, which lands close to the bulk modulus of water at about 2.22 GPa. Enter your own test figures to characterise a fluid or solid, or work backwards by rearranging the same relationship if you already know the modulus and want the volume change under a given pressure. Use it for hydraulics, materials work, or any problem where how much something compresses under pressure matters.
Bulk modulus is the pressure change divided by the fractional volume change; the volume and its change just need to share the same units. Assumes elastic, small-strain compression at constant temperature. Estimate only.
How it works
The fractional volume change is the volume decrease divided by the original volume, a dimensionless number. The bulk modulus is the applied pressure change divided by that fractional change, so it carries the units of the pressure you enter, here megapascals, which we also show as gigapascals by dividing by 1000. Compressibility is the reciprocal of the bulk modulus and describes how readily the material yields to pressure. Because the fractional change is a ratio, the original volume and its change can be in any matching units, litres, cubic metres or millilitres, and the modulus comes out the same.
Worked example
A 1000 litre volume is squeezed by 4.5 litres when the pressure rises by 10 MPa. The fractional volume change is 4.5 divided by 1000, which is 0.0045 or 0.45 percent. The bulk modulus is 10 divided by 0.0045, which is 2222.2 MPa, or 2.222 GPa when divided by 1000. The compressibility is one divided by 2.222 GPa, about 0.450 per GPa, close to the value for water.
Related calculators
- Stress Strain Calculator: stress and strain from load.
- Young's Modulus Calculator: stiffness in tension.
- Hookes Law Calculator: spring force and extension.
- Shear Stress Calculator: shear from force and area.
- Density Calculator: mass, volume and density.
Frequently asked questions
What is the bulk modulus formula?
Bulk modulus K is the applied pressure change divided by the fractional decrease in volume: K = delta P divided by (delta V over V). A larger bulk modulus means the material resists compression more strongly. For a pressure rise of 10 MPa that shrinks a 1000 litre volume by 4.5 litres, K is 10 divided by 0.0045, which is about 2222 MPa or 2.22 GPa.
What is a typical bulk modulus?
Water has a bulk modulus of about 2.2 GPa, mineral oil around 1.5 to 2 GPa, steel about 160 GPa and diamond over 400 GPa. Gases have very low bulk modulus because they compress easily. The higher the figure, the less the material's volume changes under pressure.
How does bulk modulus relate to compressibility?
Compressibility is simply the reciprocal of the bulk modulus. A material with a high bulk modulus has a low compressibility and barely changes volume under pressure. So a bulk modulus of 2.22 GPa corresponds to a compressibility of about 0.45 per GPa, meaning a fractional volume loss of 0.45 percent for every GPa of pressure applied.
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