Ideal Gas Law Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The ideal gas law is written PV = nRT, solved here for pressure: P = nRT ÷ V. For 1 mole of gas at 0 °C occupying 22.4 L (standard conditions), the pressure is about 101.38 kPa, very close to 1 atmosphere.
Explanation
The ideal gas law relates four quantities that describe the state of a gas: its pressure (P), its volume (V), the amount of substance it contains (n, in moles), and its absolute temperature (T, in kelvins), through the universal gas constant R (8.314 J/(mol·K)). This law generalizes two more specific, well-known relationships: Boyle's law, which describes a change at constant temperature, and Charles's law, which describes a change at constant pressure — both are special cases of the full ideal gas law, applicable whenever all four quantities can vary at once. This calculator solves the equation for pressure, expressed in kilopascals (kPa) when volume is in liters and temperature in kelvins — a choice of units that lets you use R = 8.314 directly with no extra conversion. The ideal gas law remains an approximation, valid for a gas at moderate pressure and not-too-extreme temperature; it departs from reality for real gases under extreme conditions, where more complex models (the van der Waals equation, for instance) become necessary.
Example: 1 mole of gas at 0 °C in a volume of 22.4 L
Inputs
Amount of substance: 1 mol. Temperature: 0 °C. Volume: 22.4 L.
Calculation
0 °C = 273.15 K. Pressure = (1 × 8.314 × 273.15) ÷ 22.4 ≈ 2,270.97 ÷ 22.4 ≈ 101.38 kPa — very close to 101.325 kPa (1 atmosphere), the expected pressure under standard temperature and pressure conditions.
Result
This gas's pressure is about 101.38 kPa, close to one atmosphere.
Frequently asked questions
Why use R = 8.314 directly with no unit conversion?
Because one kilopascal times one liter equals exactly one joule (1 kPa·L = 1 J), the same unit used to express R. By working in kPa for pressure and liters for volume, R = 8.314 can therefore be used directly, with no extra conversion factor to apply.
What's the difference between this law and Boyle's law or Charles's law?
The ideal gas law (PV = nRT) is the complete relationship between all four quantities. Boyle's law (P₁V₁ = P₂V₂) and Charles's law (V₁/T₁ = V₂/T₂) are special cases of it, obtained by holding temperature or pressure constant, respectively, between two states. This calculator solves the full law for a single gas state, rather than a change between two states.
Why isn't the result exactly 101.325 kPa (1 atmosphere)?
Because the standard molar volume of 22.4 L is itself a commonly used rounded value taught in schools; the more precise molar volume of an ideal gas under standard conditions is about 22.414 L. The gap obtained (101.38 kPa versus 101.325 kPa) comes from this initial rounding, not a calculation error.