Ideal Gas Law Calculator
Solve the ideal gas law PV = nRT for pressure, volume, moles, or temperature, with pressure and volume in the units you actually use.
How to use this calculator
- 1Choose which quantity you want to find.
- 2Enter the other three, choosing convenient units for pressure, volume, and temperature.
- 3The calculator converts everything to SI, applies PV = nRT, and converts the answer back.
How it works
The ideal gas law
P × V = n × R × T P = pressure (Pa), V = volume (m³) n = amount of gas (mol), T = absolute temperature (K) R = 8.314 J/(mol·K), the universal gas constant temperature must be in kelvin, never Celsius
The ideal gas law ties together everything about a gas's state: squeeze it (raise P) and the volume falls; heat it (raise T) and it expands or its pressure climbs; add more gas (raise n) and it pushes harder. The single constant R makes the relationship exact for an idealised gas. It contains the older gas laws as special cases — Boyle's, Charles's, and Avogadro's — each of which holds one variable fixed and watches how the others trade off.
Worked example
One mole of any gas at 0 °C (273.15 K) and 1 atm occupies V = nRT ÷ P = (1 × 8.314 × 273.15) ÷ 101,325 ≈ 0.0224 m³, or 22.4 litres — the molar volume at standard temperature and pressure that every chemistry student memorises.
Ideal Gas Law Calculator: the complete guide
One equation, four variables
The ideal gas law is an equation of state: it fixes the relationship between a gas's pressure, volume, amount, and temperature, so that knowing any three determines the fourth. This is what makes it so useful — nearly every practical gas question is really one of these four unknowns, from how much a balloon expands as it warms to how many moles of gas fill a cylinder at a given pressure.
The one non-negotiable rule is that temperature must be absolute, measured in kelvin. Doubling the temperature from 20 °C to 40 °C does not double the pressure, because those are 293 K and 313 K — barely a 7% rise. Using Celsius directly is the single most common mistake, and it produces nonsense; the calculator converts for you to prevent it.
The gas laws it contains
Before the combined law, chemists discovered its pieces one variable at a time. Boyle's law (pressure and volume are inversely related at fixed temperature) explains why a syringe gets harder to push as you compress it. Charles's law (volume rises with temperature at fixed pressure) explains why a sealed bag of chips puffs up on a plane. Avogadro's law (equal volumes of gas hold equal numbers of molecules) underpins the whole mole concept.
The ideal gas law is simply all three fused into one statement with the constant R. Hold any variable fixed and the older law reappears. This is why it is worth learning as a single relationship: it is not one more formula but the parent of the others, and it handles cases none of them can alone.
Where 'ideal' stops being true
The law assumes molecules are point particles with no volume of their own and no attraction between them. Remarkably, real gases obey it closely at ordinary temperatures and pressures — the molecules are so small and so far apart that these assumptions barely matter. For most everyday and laboratory work, the ideal gas law is accurate to a percent or better.
It fails as a gas approaches conditions where it would condense: high pressure, low temperature. There the molecules are crowded close enough that their finite size and mutual attraction become significant, and the pressure or volume deviates measurably from the prediction. Real-gas equations such as van der Waals's add correction terms for exactly these two effects, but they are only needed near the edges of the gas phase.
Frequently asked questions
What is the ideal gas law?
PV = nRT, relating a gas's pressure (P), volume (V), amount in moles (n), and absolute temperature (T) through the gas constant R = 8.314 J/(mol·K). Knowing any three of the four variables lets you calculate the fourth.
Why must temperature be in kelvin?
Because the law is proportional to absolute temperature, and only the kelvin scale starts at absolute zero. Using Celsius would imply a gas has zero pressure at 0 °C, which is false. Always convert to kelvin first — this calculator does it automatically.
What volume does one mole of gas occupy?
About 22.4 litres at standard temperature and pressure (0 °C and 1 atm), and 24.0 litres at 25 °C. This 'molar volume' is the same for any ideal gas, which is a direct consequence of Avogadro's law built into the equation.
When does the ideal gas law stop working?
Near conditions where the gas would liquefy — very high pressure or very low temperature. There, molecular size and intermolecular attraction, which the law ignores, become significant. At everyday temperatures and moderate pressures, real gases follow it to within about one percent.