Skip to content
MasterMath

Ideal Gas Law Calculator

PV = nRT ties together pressure, volume, amount and temperature. Solve for whichever one you are missing.

Result

—

How this was worked out

    The formula

    P · V = n · R · T

    SymbolQuantityUnit
    PPressurePa
    VVolumem³
    nMolesmol
    TTemperatureK

    What it means

    The ideal gas law treats gas particles as points with no volume and no attraction between them. Real gases depart from it, but under ordinary conditions the approximation is remarkably good.

    How to work it out by hand

    1. Convert the temperature to kelvin: always kelvin, never Celsius
    2. Use consistent units for pressure and volume
    3. Rearrange for whichever quantity you need

    What is worth knowing

    Using Celsius instead of kelvin is the classic error, and it is not a small one: the law is proportional to absolute temperature, so 0 °C would predict zero pressure. Add 273.15 first, every time. The law fails where its assumptions do — at high pressure, where particle volume stops being negligible, and at low temperature, where attractions matter and the gas is close to condensing. Van der Waals' equation patches both, at the cost of two extra constants per gas.

    Frequently asked questions

    Why must the temperature be in kelvin?

    Because the law is proportional to absolute temperature. Using Celsius would predict zero pressure at 0 °C, which is nonsense.

    What is R?

    The gas constant, 8.314 J/(mol·K) in SI units. Its value depends on which units you use for pressure and volume.

    When does the ideal gas law fail?

    At high pressure and low temperature, where the volume of the particles and the attractions between them stop being negligible.

    What is standard temperature and pressure?

    Commonly 0 °C and 1 bar, at which one mole of an ideal gas occupies 22.7 litres. Older definitions use 1 atm and give 22.4.