What is the compressibility factor Z?

The compressibility factor Z (also called the compression factor or gas deviation factor) measures how much a real gas deviates from ideal gas behaviour. It is defined as Z = PV / (nRT), where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is absolute temperature. An ideal gas always has Z = 1. A value below 1 means the gas is more compressible than ideal (attractive intermolecular forces dominate), while a value above 1 means it is less compressible than ideal (repulsive forces dominate at very high pressures).

What units does this calculator use?

You can enter pressure in atmospheres (atm) or pascals (Pa), volume in litres (L) or cubic metres (m3), and temperature in Kelvin (K) or Celsius (degC). The calculator converts everything to SI base units internally and uses R = 8.314462 J/(mol K) for Pa/m3 calculations or R = 0.082057 L atm/(mol K) for atm/L calculations. Temperature in Celsius is converted to Kelvin by adding 273.15.

When is Z less than 1 and when is it greater than 1?

At moderate pressures, Z is typically less than 1 for most real gases because attractive intermolecular forces pull molecules together, reducing the pressure the gas exerts compared to an ideal gas (meaning a smaller volume than ideal). At very high pressures, Z rises above 1 because molecules are forced close enough that their finite size and repulsive forces become dominant, making the gas harder to compress than an ideal gas. At very low pressures and high temperatures, all gases approach ideal behaviour and Z approaches 1.

Compressibility Factor (Z) Calculator

Calculate the compressibility factor Z for a real gas using Z = PV / (nRT). A value of Z = 1 indicates ideal behaviour. Values below 1 show attractive forces dominate; values above 1 show repulsive forces dominate at high pressures.

Enter pressure, volume, amount, and temperature in your preferred units. The calculator converts everything internally and shows how far your gas deviates from ideal.

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Standard formula Z = PV / (nRT). R = 8.314462 J mol^-1 K^-1 (SI) or 0.082057 L atm mol^-1 K^-1.

1. Gas Conditions

Pressure (P)

atm

Volume (V)

Amount of gas (n)

mol

Temperature (T)

2. Units

Pressure unit

Volume unit

Temperature unit

Decimal places in result

Compressibility Factor Result

Compressibility Factor Z
-
Dimensionless

Ideal Gas Volume

nRT/P (same units as input)

Deviation from Ideal

(Z - 1) as percentage

Behaviour

Relative to ideal gas

Calculation Breakdown

Pressure (P)-

Volume (V)-

Amount (n)-

Temperature (T)-

Gas constant (R)-

PV (numerator)-

nRT (denominator)-

Z = PV / nRT-

Interpretation

Ideal gas Z1.0000 (exact)

Your Z-

Z < 1: attractive forces-

Z > 1: repulsive forces-

Volume vs ideal-

Overall deviation-

Result: Enter values above to calculate.

Worked Example (matching the calculator defaults)

Given: P = 10 atm, V = 2.0 L, n = 1 mol, T = 300 K

Using R = 0.082057 L atm mol^-1 K^-1:

nRT = 1 × 0.082057 × 300 = 24.6171 L atm

PV = 10 × 2.0 = 20.0000 L atm

Z = PV / nRT = 20.0000 / 24.6171 = 0.8124

Z < 1: this gas is more compressible than ideal. Attractive intermolecular forces are dominant at these conditions, pulling molecules closer together so the actual volume is smaller than the ideal gas prediction of 2.4617 L.

What is the Compressibility Factor?

The compressibility factor Z (also called the gas deviation factor or compression factor) is a dimensionless number that describes how much a real gas deviates from ideal gas behaviour. It is defined by the equation:

Z = PV / (nRT)

where P is the absolute pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the absolute temperature in Kelvin. For a perfect (ideal) gas, Z = 1 exactly. Real gases deviate from this value depending on temperature, pressure, and the nature of the gas molecules.

Why Z Differs from 1

The ideal gas law assumes molecules have no volume of their own and exert no forces on each other. Real molecules break both assumptions:

Attractive forces (Z < 1): At moderate pressures, van der Waals attractions between molecules pull them together. The gas exerts less pressure than ideal for a given volume, or equivalently occupies a smaller volume than an ideal gas would at the same pressure. Z falls below 1.
Repulsive forces (Z > 1): At very high pressures, molecules are packed so tightly that their finite physical size becomes important. They cannot be compressed as easily as an ideal gas because they take up space. Z rises above 1.
Low pressure / high temperature (Z approaching 1): When molecules are far apart and moving fast, both effects become negligible and all gases approach ideal behaviour.

The Formula

Starting from the ideal gas law PV = nRT, the compressibility factor is simply the ratio of the real gas PV product to the ideal gas PV product:

Z = PV / (nRT)

Rearranging, the real gas equation of state is:

PV = ZnRT

This means the ideal gas law with a correction factor Z. Engineers use this in petroleum and natural gas work to calculate how much gas a reservoir or pipeline actually holds under real conditions.

Units and Gas Constant

Pressure unit	Volume unit	R value
Pa (pascals)	m³	8.314462 J mol^-1 K^-1
atm	L	0.082057 L atm mol^-1 K^-1
bar	L	0.083145 L bar mol^-1 K^-1

Temperature must always be in Kelvin (K = degC + 273.15) because the ideal gas law requires absolute temperature. Using Celsius will give a completely wrong result.

Typical Z Values for Common Gases

Gas	Conditions	Approximate Z
Nitrogen (N2)	25 degC, 1 atm	1.0000
Carbon dioxide (CO2)	25 degC, 1 atm	0.9950
Methane (CH4)	25 degC, 100 atm	0.877
Hydrogen (H2)	25 degC, 100 atm	1.068
Ammonia (NH3)	25 degC, 10 atm	0.956
Water vapour	200 degC, 1 atm	0.985

Note: hydrogen and helium have Z > 1 even at moderate pressures because their quantum mechanical properties cause repulsive interactions to dominate earlier than for most other gases.

Applications

The compressibility factor is used extensively in natural gas engineering to calculate reservoir capacity, pipeline capacity, and gas meter correction factors. It also appears in thermodynamics, chemical engineering process design, and atmospheric science. For most everyday engineering purposes at near-atmospheric pressures, Z is close enough to 1 that the ideal gas law is a good approximation.

Related Calculators

Maths and Stats Calculators: full index of maths, science, and engineering tools.
Charles's Law Calculator: volume and temperature relationship for gases at constant pressure.
Ideal Gas Law Calculator: solve PV = nRT for any unknown.
Moles Calculator: convert mass to moles using molar mass.
Equilibrium Constant (Keq) Calculator: calculate Keq from concentrations.

Method: Z = PV / (nRT) using R = 0.082057 L atm mol^-1 K^-1 (atm/L inputs) or R = 8.314462 J mol^-1 K^-1 (Pa/m³ inputs). All unit conversions applied before calculation. Source: NIST Chemistry WebBook, "Compressibility Factor" definition; IUPAC Green Book (2007) Section 2.11.

This calculator is for educational and scientific estimation purposes. For critical engineering applications such as natural gas pipeline and reservoir calculations, use validated equation-of-state software with appropriate correlations for the specific gas mixture.