Ideal Gas Law Calculator
Solve for pressure, volume, temperature, or moles of an ideal gas in seconds. Use this when working on chemistry, physics, or engineering problems involving gases at moderate conditions.
About this calculator
The ideal gas law combines Boyle's Law, Charles's Law, and Avogadro's Law into one equation: PV = nRT, where P is pressure (Pa), V is volume (m³), n is the number of moles, R is the universal gas constant (8.314 J/mol·K), and T is temperature in Kelvin. Rearranging for moles gives n = (P × V) / (R × T). This law assumes gas molecules have no intermolecular forces and occupy negligible volume — conditions well-approximated by many real gases at low pressure and high temperature. It is foundational in thermodynamics, chemical engineering, and atmospheric science. Deviations from ideal behavior are handled by more advanced equations such as van der Waals.
How to use
Suppose you have 2 m³ of gas at a pressure of 101,325 Pa and a temperature of 300 K. To find the number of moles, apply n = (P × V) / (R × T): n = (101,325 × 2) / (8.314 × 300) = 202,650 / 2,494.2 ≈ 81.25 mol. Enter 101325 in the Pressure field, 2 in the Volume field, and 300 in the Temperature field. The calculator instantly returns approximately 81.25 moles. This is useful when verifying gas quantities in a sealed container or reaction vessel.
Frequently asked questions
What is the ideal gas law formula and what does each variable mean?
The ideal gas law is expressed as PV = nRT. P is the absolute pressure in Pascals, V is the volume in cubic metres, n is the amount of substance in moles, R is the universal gas constant (8.314 J/mol·K), and T is the absolute temperature in Kelvin. Each variable must use consistent SI units for the formula to give correct results. Mixing units — for example using atmospheres for pressure without converting — is the most common source of error.
When does the ideal gas law break down and give inaccurate results?
The ideal gas law becomes inaccurate at very high pressures (above ~10 atm) or very low temperatures approaching a substance's boiling point, where intermolecular forces and finite molecular volume become significant. Real gases like CO₂ or NH₃ deviate more than noble gases because of stronger intermolecular attractions. In these conditions, the van der Waals equation or Redlich-Kwong equation provides better accuracy. For most everyday engineering and chemistry calculations at near-ambient conditions, the ideal gas law gives results accurate to within a few percent.
How do I convert temperature to Kelvin before using the ideal gas law calculator?
The ideal gas law requires absolute temperature in Kelvin (K), not Celsius or Fahrenheit. To convert from Celsius to Kelvin, add 273.15: T(K) = T(°C) + 273.15. To convert from Fahrenheit, first convert to Celsius with T(°C) = (T(°F) − 32) × 5/9, then add 273.15. For example, 25 °C becomes 298.15 K, and 32 °F becomes 273.15 K. Always double-check your temperature unit before entering it into the calculator to avoid large errors in the output.