Ideal Gas Law Calculator (PV=nRT)

Using the ideal gas law PV=nRT, enter 3 of pressure, volume, amount of substance (moles), and temperature to calculate the remaining value.

Usage tips

  • Always enter temperature as absolute temperature (Kelvin, K). Entering a Celsius value directly will produce an incorrect result.
  • The gas constant used here is R=0.082057 L·atm/(mol·K). Pressure is unified in atm and volume in L.
  • This equation is an approximation that assumes an "ideal gas." At high pressure and low temperature, real gases may deviate from this behavior.
  • Switching the "value to calculate" hides that field's input and automatically calculates it from the other three values.

Frequently asked questions

The equation of state PV=nRT assumes the physical relationship that pressure and volume approach zero as temperature approaches 0 (absolute zero, where molecular motion theoretically stops). This relationship does not hold on relative temperature scales such as Celsius or Fahrenheit, so absolute temperature (K) must be used.

An ideal gas is a theoretical model that assumes molecular volume is negligible and that no intermolecular forces act. Real gases show increasingly significant effects from intermolecular forces and molecular volume at high pressure and low temperature, causing larger deviations from the ideal gas equation.

The value of the gas constant R depends on the unit system used. This tool unifies pressure in atm, volume in L, and temperature in K, so it uses R=0.082057 L·atm/(mol·K) corresponding to these units. When calculating in SI units (Pa·m³), R=8.314 J/(mol·K) is used instead.

The amount of substance represents the number of atoms or molecules, measured in mol. One mole refers to a collection of particles equal to Avogadro's number (about 6.02×10²³). If you know a gas's mass and its molar mass (molecular weight), you can find the number of moles by dividing mass by molar mass.
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Side Note — How the gas laws were unified

The ideal gas equation of state PV=nRT actually combines several laws that were discovered separately between the 17th and 19th centuries into a single equation. Boyle's law (P×V constant at constant temperature), Charles's law (V/T constant at constant pressure), and Avogadro's law (equal volumes of gas at the same temperature and pressure contain the same number of molecules, regardless of the type of gas) were each independently discovered empirical rules that were unified into one equation by the mid-19th century.

This unification is credited to the French engineer Émile Clapeyron. In 1834, he combined Boyle's law and Charles's law to publish an equation of the form PV=RT (per mole), which was later refined by incorporating Avogadro's law into today's PV=nRT form.

The "ideal gas" assumption merely neglects the interactions between gas molecules and the size of the molecules themselves, but under conditions close to standard temperature and pressure, it reproduces the behavior of real gases surprisingly well. This combination of simplicity and practicality is why, nearly 200 years later, it remains one of the first things taught in chemistry and physics education.

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