Ideal Gas Law Calculator

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One Equation, Four Interlocking Variables

Pressure, volume, temperature, and quantity of gas don't vary independently — change one and, all else being equal, at least one of the others has to move in response. The ideal gas law ties all four together in a single equation, unifying Boyle's law, Charles's law, and Avogadro's law into one relationship that holds (approximately) for real gases across a wide range of everyday conditions.

The Formula

P × V = n × R × T

P is pressure (kPa), V is volume (L), n is the amount of gas in moles, T is absolute temperature (K), and R is the universal gas constant, 8.314 (kPa·L)/(mol·K). Solved for whichever variable you need, this single equation replaces having to remember Boyle's, Charles's, and Gay-Lussac's laws separately.

Where All Four Variables Matter Together

  • Scuba and gas cylinder calculations — figuring out how much breathable air a tank holds at a given pressure and temperature requires all four terms.
  • HVAC and refrigeration design — compressor sizing and refrigerant behavior are modeled using gas-law relationships across changing pressure and temperature.
  • Chemistry stoichiometry — converting between moles of a gaseous reactant and the volume it occupies is a direct application of PV = nRT.
  • Weather and atmospheric modeling — air pressure, density, and temperature at different altitudes are linked through the same equation.

A Reference Point: Standard Molar Volume

One of the most useful checks of this law is the volume occupied by exactly 1 mole of an ideal gas at standard temperature and pressure (0°C, 101.325 kPa):

V = nRT / P
V = (1 × 8.314 × 273.15) / 101.325
V = 22.4127 L

This is the well-known "22.4 liters per mole at STP" figure taught in introductory chemistry, derived directly from the ideal gas law rather than memorized separately.

How to Use This Calculator

  1. Choose what to solve for: Find Pressure (P), Find Volume (V), Find Moles (n), or Find Temperature (T).
  2. Enter the three known values from Volume (L), Moles (mol), Temperature (choosing Kelvin or Celsius), and Pressure (kPa), depending on which mode you selected.
  3. Select Calculate to see the unknown value along with the worked formula.

Related Calculations

For the pressure-only and temperature-only special cases of this same law, see the Boyle's Law Calculator and the Charles's Law Calculator.