This calculator works out the compressibility factor Z for a real gas, the number engineers and chemists use to describe how far a gas's actual behaviour departs from the ideal gas law. Using the formula Z = PV / (nRT), it compares the pressure-volume product you measure against what an ideal gas would produce at the same temperature and amount. You enter pressure (in atm, Pa, kPa, bar or psi), volume (in litres, cubic metres, millilitres or cubic centimetres), the amount of gas in moles, and temperature (in Kelvin or Celsius), then choose how many decimal places to show. The calculator converts everything into consistent units before calculating. It returns the compressibility factor Z itself, the ideal gas volume the same conditions would predict, the percentage deviation from ideal behaviour, and a plain-English behaviour reading showing whether attractive or repulsive intermolecular forces dominate. A full calculation breakdown shows each step from PV and nRT through to the final ratio, alongside an interpretation panel and a worked example matching the default values. Remember that temperature must be entered as an absolute value, since using Celsius directly in the formula gives a meaningless result. This tool is intended for educational and general scientific estimation; for critical applications such as natural gas pipeline or reservoir calculations, use validated equation-of-state software designed for the specific gas mixture involved.
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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
atm
L
mol
K
2. Units
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.
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.
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