Calculate the compressibility factor Z from pressure, volume, moles, and temperature, converting common gas law units automatically.
Compressibility Formula
The following formula is used to calculate the compressibility factor (Z) of a gas.
- Where Z is the compressibility factor (dimensionless)
- P is the absolute pressure (pascals, Pa)
- V is the volume (m³)
- n is the amount of substance (moles, mol)
- R is the universal gas constant (8.31446261815324 J/(mol·K))
- T is the absolute temperature (K)
Use absolute pressure referenced to vacuum, measured in pascals (Pa) internally. Add the actual atmospheric pressure to a gauge-pressure reading before entering it. A zero-pressure result is only an algebraic limit, not a finite gas sample state.
Volume is a measure of the amount of space occupied by a three-dimensional object.
A mole (mol) is the SI unit for amount of substance and contains exactly 6.02214076 × 1023 specified entities (Avogadro’s constant). For a pure substance, the number of moles can be found from n = m/M, where m is mass and M is molar mass.
The gas constant is a physical constant used in the ideal gas law to relate the properties of gases, such as pressure, volume, and temperature.
Temperature (K) measures the thermal state of a system using an absolute scale (Kelvin). Absolute temperature must be greater than 0 K.
What is the Compressibility Factor (Z)?
The compressibility factor Z is a dimensionless number that describes how much a real gas deviates from ideal-gas behavior:
- If Z = 1, the gas behaves ideally.
- If Z < 1, attractive intermolecular forces tend to dominate (gas is “more compressible” than ideal under those conditions).
- If Z > 1, repulsive effects/finite molecular volume tend to dominate (gas is “less compressible” than ideal under those conditions).
Note: This is different from thermodynamic “compressibility” (such as isothermal compressibility, κT), which is defined using derivatives like κT = - (1/V)(∂V/∂P)T. This page’s equation and calculator are specifically for the compressibility factor Z.
Compressibility Example
How to calculate compressibility?
- First, determine the pressure.
Measure the absolute pressure of the gas.
- Next, determine the volume.
Measure or calculate the volume occupied by the gas at that pressure.
- Next, determine the number of moles.
Determine the amount of substance (moles) of the gas.
- Next, determine the temperature.
Measure the absolute temperature of the gas (in K, or convert to K).
- Finally, calculate the compressibility factor (Z).
Calculate Z using Z = (P × V) / (n × R × T).
FAQ
Compressibility describes how a material’s volume changes under pressure. In thermodynamics, it is often expressed as isothermal compressibility κT = −(1/V)(∂V/∂P)T.
The compressibility factor Z is a dimensionless measure of real-gas deviation from ideal-gas behavior. It is defined as Z = (P × V)/(n × R × T); for an ideal gas, Z = 1.
This calculator computes the compressibility factor by rearranging the ideal gas law: Z = (P × V)/(n × R × T). (Thermodynamic compressibility, such as κT, is calculated differently.)
