# Compressibility Factor Calculator

Created by Rahul Dhari
Reviewed by Steven Wooding
Last updated: Sep 06, 2023

The compressibility factor calculator determines the compressibility factor using a version of the ideal gas law equation corrected for non-ideal gases. This factor is useful to determine the mass and volume of non-ideal gases. You can generate several results from the calculator to draw a compressibility factor chart. Read on to understand what is the compressibility factor and how to calculate it.

## How is the compressibility factor defined?

The behavior of an ideal gas can be generalized using the equation we know as ideal gas law. We discussed this concept thoroughly at our ideal gas law calculator, and we learned how to derive it at our combined gas law calculator. However, this equation can only be applied in specific conditions and for gases. Therefore, this equation was modified to account for the behavior of real gases. This operation was performed by including a dimensionless entity known as compressibility factor, $Z$. Mathematically, the ideal gas equation for a gas having volume $V$ and $n$ number of moles at pressure $P$, and temperature $T$ with gas constant $R$ is written as:

$Z = \frac{P\cdot V}{n\cdot R\cdot T}$

This transforms into a compressibility factor equation, where the compressibility factor $Z$ is included in the equation:

The compressibility factor is used to determine the deviation of thermodynamic properties of real gases from the ideal gas behavior. The term compressibility factor can also be defined as the ratio of the actual volume of a gas to the ideal volume of gas for a given temperature and pressure. Mathematically thats':

$Z = \frac{V_{\mathrm{actual}}}{V_{\mathrm{ideal}}}$

## How do I use the compressibility factor calculator?

Follow the below-mentioned steps to calculate the compressibility factor, $Z$.

• Step 1: Enter the gas pressure, $P$.
• Step 2: Give the gas volume, $V$.
• Step 3: Input the amount of substance in moles, $n$.
• Step 4: Insert the universal gas constant, $R$. The universal gas constant is set to its default value in SI units i.e. $8.314\ \mathrm{J/(K \cdot mol)}$. The value in FPS unit system is $10.73164\ \mathrm{(\psi\cdot ft^3)(lbm \cdot mol\ \degree R)}$.
• Step 5: Fill in the temperature of the gas, $T$.
• Step 6: The calculator will now use the compressibility factor equation to return the value of compressibility factor.

🙋 You may need some help with the conversions, here: take our temperature conversion tool and our pressure conversion calculator to quickly change between units!

## Example: Using the compressibility factor calculator

Find the compressibility factor for air at $1\ \mathrm{bar}$ and $293\ \mathrm{K}$ having volume $1\ \mathrm{m^3}$. Take the number of moles as $44.6$ and gas constant $R$ as $8.314\ \mathrm{J/(K\cdot mol)}$.

• Step 1: Enter the gas pressure, $P = 1\ \mathrm{bar}$.

• Step 2: Give the gas volume, $V = 1\ \mathrm{m^3}$.

• Step 3: Input the amount of substance in moles, $n = 44.6$.

• Step 4: The universal gas constant, $R$ is set to $8.314$ as default value.

• Step 5: Fill in the temperature of gas, $T = 293\ \mathrm{K}$.

• Step 6: The calculator will now use the compressibility factor equation to return the value of the compressibility factor.

$\begin{split} Z &= \frac{P\cdot V}{n\cdot R\cdot T}\\[1em] &=\frac{10^5\cdot1}{44.6\cdot 8.314\cdot 293} = 0.9204 \end{split}$

Now we know the compressibility factor, $Z$ for air at the above conditions is $0.9204$.You can also find the compressibility factor for several combinations of temperature and pressure to make a compressibility factor chart, as an example of which can be seen above.

At our Van der Waals equation calculator you can learn about another modification of the gas law that describes the the property of deviation of gases from ideal behavior.

## FAQ

### What is the compressibility factor of a gas?

The compressibility factor is the ratio of the actual volume of gas to the volume of an ideal gas.

Z = P × V / n × R × T = V(actual)/V(ideal)

### How do I calculate compressibility factor?

To calculate the compressibility factor:

1. Multiply no. of moles by universal gas constant and gas temperature.

2. Divide pressure by the preceding product.

3. Multiply the product by the volume of gas to obtain the compressibility factor.

Z = P × V / n × R × T

### What is the physical significance of the compressibility factor Z?

The compressibility factor Z is the deviation of properties of real gas from ideal gas behavior. It is used to modify properties of ideal gas to real gas.

### What is the compressibility factor equation?

The compressibility factor equation can be written as: Z = P × V / n × R × T, where Z is the compressibility factor, for pressure P, volume V, gas constant R, number of moles n, and temperature T.

Rahul Dhari
Pressure (P)
psi
Volume (V)
cu in
Number of moles (n)
mol
Gas constant (R)
J⋅K⁻¹⋅mol⁻¹
Temperature (T)
°F
Compressibility factor (Z)
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