Bulk Modulus Calculator
Enter the initial volume, the change in pressure applied, and the resulting change in volume to calculate the bulk modulus of a material or fluid. Switch the solve-for mode to find any unknown from the other three. All major pressure units (Pa, kPa, MPa, GPa, psi, atm) and volume units (m3, cm3, L, ft3) are supported. The result updates as you type.
Formula
Worked example
1 L of water (V0 = 0.001 m3) is compressed with dP = 100 MPa. Using B = 2150 MPa (bulk modulus of water): strain = dP/B = 100/2150 = 0.04651, dV = 0.04651 x 0.001 = 4.651e-5 m3 = 0.04651 L. Compressibility beta = 1/2150 MPa = 4.65e-4 MPa-1.
What is bulk modulus?
Bulk modulus (symbol B or K) is a measure of a material's resistance to uniform compression. It is defined as the ratio of the applied pressure change to the resulting fractional volume decrease: B = -dP / (dV/V0). The minus sign follows the physics convention that compression (positive pressure) reduces volume (negative dV); using the absolute compression convention, both dP and dV are entered as positive numbers. A high bulk modulus means the material is nearly incompressible: steel has B of about 160 GPa, meaning you need enormous pressure to change its volume by even a fraction of a percent. Air at atmospheric pressure has B of only about 100 kPa, which is why air is easy to compress.
How to use this calculator
Choose "Solve for" at the top to pick which quantity you want to find: bulk modulus, pressure change, or volume change. Enter the known values in the fields that appear, select units from the drop-downs, and the result updates instantly. "Solve for bulk modulus" is the most common mode: measure or look up your initial volume, apply a known pressure increment, record the resulting volume change, and plug all three in. The show-your-work panel (Steps tab) walks through the calculation with your exact numbers so you can verify every intermediate value. The "auto unit" output formats the result in the most readable prefix (Pa, kPa, MPa, GPa).
Compressibility and its relationship to bulk modulus
Compressibility (beta) is simply 1/B: the fractional volume decrease per unit pressure increase. It has units of inverse pressure (1/Pa or 1/GPa). A highly compressible substance like a gas has a large beta and a small B; an incompressible substance like diamond has a tiny beta and a huge B. Engineers in hydraulics and fluid power systems often work with compressibility directly because it governs how much fluid volume changes when system pressure rises, which affects response time and energy losses. At high pressures (above a few hundred MPa), bulk modulus itself becomes pressure-dependent and must be measured experimentally rather than treated as a material constant.
Bulk modulus, Young's modulus and Poisson's ratio
For an isotropic elastic solid the three common moduli are linked. Given Young's modulus (E) and Poisson's ratio (nu): B = E / (3 * (1 - 2*nu)). This means that a material approaching nu = 0.5 (nearly incompressible, like rubber) has a bulk modulus much larger than its Young's modulus, while a more compressible material with nu near 0 has B of the same order as E. The shear modulus G = E / (2*(1+nu)) completes the triplet. For fluids, the concept of Young's modulus does not apply, but bulk modulus and compressibility remain well-defined through the pressure-volume relationship.
Bulk modulus of common materials (room temperature)
| Material | Bulk modulus (GPa) | Class |
|---|---|---|
| Air (isothermal, 20 deg C) | 0.000101 | Gas |
| Air (adiabatic, 20 deg C) | 0.000142 | Gas |
| Water (pure, 20 deg C) | 2.15 | Liquid |
| Seawater (35 ppt, 20 deg C) | 2.34 | Liquid |
| Mercury | 28.5 | Liquid |
| Ethanol | 0.9 | Liquid |
| Silicone rubber | 1.5 | Polymer/rubber |
| Concrete | 30 | Construction |
| Glass (soda-lime) | 46 | Ceramic |
| Limestone | 70 | Rock/mineral |
| Granite | 50 | Rock/mineral |
| Aluminum | 76 | Metal |
| Copper | 140 | Metal |
| Iron (cast) | 100 | Metal |
| Steel (mild) | 160 | Metal |
| Titanium | 110 | Metal |
| Diamond | 443 | Ceramic |
Approximate values. Actual values vary with temperature, purity, grain structure, and measurement method.
Frequently asked questions
What is the bulk modulus formula?
The formula is B = dP / (dV/V0), using the compression convention where dP and dV are both entered as positive numbers for compression. In the strict physics sign convention it is B = -dP / (dV/V0) because compression reduces volume. Rearranging: dP = B * dV / V0, and dV = dP * V0 / B. Compressibility is beta = 1/B.
What units is bulk modulus measured in?
Bulk modulus has units of pressure: pascals (Pa), kilopascals (kPa), megapascals (MPa), gigapascals (GPa), or psi. For gases and soft materials, kPa or MPa is most convenient. For hard metals and ceramics, GPa is the standard. Steel has a bulk modulus of about 160 GPa, water about 2.15 GPa, and air (isothermal) about 100 kPa.
What is the difference between bulk modulus and Young's modulus?
Young's modulus (E) describes resistance to uniaxial (one-dimensional) stretching or compression, while bulk modulus (B) describes resistance to uniform compression from all directions simultaneously. For an isotropic solid they are related by B = E / (3*(1-2*nu)) where nu is Poisson's ratio. Fluids have a well-defined B but no Young's modulus because they cannot resist shear.
Why is the bulk modulus of water important?
Water's bulk modulus of about 2.15 GPa (at 20 deg C, atmospheric pressure) determines the speed of sound in water (about 1480 m/s), governs the response of hydraulic systems, and is central to oceanographic pressure models. It increases slightly with pressure and decreases with temperature, so deep-sea and high-pressure engineering applications use tabulated or fitted values rather than a single constant.
Can bulk modulus be negative?
No, for stable materials in their normal phase, bulk modulus is always positive because compression (increased pressure) must reduce volume. A negative bulk modulus would mean the material expands when compressed, which is mechanically unstable. Some exotic metamaterials and auxetic structures can exhibit locally negative responses in narrow frequency ranges, but that is a dynamic effect, not a static material constant.
How does temperature affect bulk modulus?
Bulk modulus generally decreases as temperature rises because thermal agitation weakens inter-atomic bonding. For metals the effect is moderate (a few percent over a wide temperature range) but for liquids it can be significant: water's bulk modulus peaks near 50 deg C and falls off on both sides. For gases, isothermal bulk modulus equals the absolute pressure (B = P), while adiabatic bulk modulus is gamma * P where gamma is the heat capacity ratio, so both rise with pressure.