# Ideal Gas Law Calculator

By Bogna Szyk
Last updated: May 21, 2021

This ideal gas law calculator will help you establish the properties of an ideal gas subject to pressure, temperature, or volume changes. Read on to learn about the characteristics of an ideal gas, how to use the ideal gas law equation, and the definition of the ideal gas constant.

## What is an ideal gas

An ideal gas is a special case of any gas that fulfills the following conditions:

• The gas consists of a large number of molecules that move around randomly.
• All molecules are point particles (they don't take up any space).
• The molecules don't interact except for colliding.
• All collisions between the particles of the gas are perfectly elastic.
• The particles obey Newton's laws of motion.

## Ideal gas law equation

The properties of an ideal gas are all summarized in one formula of the form:

`pV = nRT`

where:

• `p` is the pressure of the gas, measured in Pa;
• `V` is the volume of the gas, measured in m³;
• `n` is the amount of substance, measured in moles;
• `R` is the ideal gas constant; and
• `T` is the temperature of the gas, measured in Kelvins.

To find any of these values, simply enter the other ones into the ideal gas law calculator.

For example, if you want to calculate the volume of 40 moles of a gas under a pressure of 1013 hPa and at a temperature of 250 K, the result will be equal to:

`V = nRT/p = 40 * 8.3144598 * 250 / 101300 = 0.82 m³`.

## Ideal gas constant

The gas constant (symbol R) is also called the molar or universal constant. It is used in many fundamental equations, such as the ideal gas law.

The value of this constant is `8.3144626 J/(mol·K)`.

The gas constant is often defined as the product of Boltzmann's constant `k` (which relates the kinetic energy and temperature of a gas) and Avogadro number (the number of atoms in a mole of substance):

`R = NAk = (6.02214076 × 1023 /mol) * (1.38064852 × 10-23 J/K) = 8.3144626 J/(mol·K)`

You might find this air pressure at altitude calculator useful, too.

Bogna Szyk Pressure (p)
Pa
Volume (V)
cu ft
Amount of substance (n)
mol
Temperature (T)
°F
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