Ideal Gas Law Calculator (Thermodynamics)

Calculate Pressure, Volume, Moles, or Temperature of an ideal gas using the PV = nRT equation.

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Thermodynamics: The Ideal Gas Law

Thermodynamics is the branch of physics that deals with heat, work, and temperature, and their relation to energy and the physical properties of matter. One of the most foundational equations in this field is the Ideal Gas Law, which describes the behavior of a hypothetical "ideal" gas under various conditions.

Whether you are engineering pressurized tanks, studying chemical reactions, or calculating atmospheric changes in weather balloons, understanding the relationship between pressure, volume, and temperature is essential.

Glossary of Thermodynamic Variables

  • Pressure (P): The force exerted by the gas per unit surface area of its container. High pressure means the gas molecules are hitting the walls with great force. Standard units include Atmospheres (atm) and Pascals (Pa).
  • Volume (V): The three-dimensional space that the gas occupies. Because gases expand to fill their container, the volume of the gas is the volume of the container. Measured in Liters (L) or Cubic Meters (m³).
  • Amount of Substance (n): Measured in Moles (mol). One mole represents approximately 6.022 × 10²³ individual molecules (Avogadro's Number) of the gas.
  • Temperature (T): The measure of the average kinetic energy of the gas particles. In thermodynamics, temperature must be measured in absolute units, which is why our calculator converts Celsius and Fahrenheit into Kelvin (K) behind the scenes.
  • Ideal Gas Constant (R): A universal physical constant that ties the other variables together. In standard SI units, R = 8.314 J/(mol·K).

The Ideal Gas Equation (PV = nRT)

The Ideal Gas Law combines several historical laws (Boyle's Law, Charles's Law, and Avogadro's Law) into one elegant equation. It states that the pressure multiplied by the volume is directly proportional to the number of moles multiplied by the temperature.

The Core Equation:

P × V = n × R × T

Example Walkthrough:

Imagine you have a sealed rigid tank containing 2 moles (n) of oxygen gas. The tank has a volume of 0.05 cubic meters (V), and it is sitting in a hot room at 300 Kelvin (T). What is the pressure inside the tank?

To solve for Pressure (P), we rearrange the equation to: P = (n × R × T) / V

P = (2 mol × 8.314 J/(mol·K) × 300 K) / 0.05 m³

P = 4988.4 / 0.05

P = 99,768 Pascals (or ~0.98 Atmospheres)

Algebraic Variations for Reverse-Solving

Our calculator allows you to leave any one input completely blank (or set to zero) and it will solve for it dynamically. Here are the rearranged formulas our logic engine uses to provide your answers:

  • To find Volume: V = (n × R × T) / P
  • To find Moles: n = (P × V) / (R × T)
  • To find Temperature: T = (P × V) / (n × R)

Note: The Ideal Gas Law assumes that gas molecules have no volume of their own and that there are no intermolecular forces attracting them to one another. While no gas is truly "ideal," this equation provides incredibly accurate estimates for real gases at high temperatures and low pressures!