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Ideal Gas Law Calculator

Solve the ideal gas law PV = nRT for pressure, volume, moles or temperature with automatic unit conversion (atm, kPa, bar, psi, L, m³, °C, K, °F).

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    Ideal Gas Law formula

    PV = nRT
    SymbolQuantitySI unitMeaning
    PPressurePaAbsolute pressure of the gas
    VVolumem³Volume occupied by the gas
    nAmount of gasmolAmount of gas in moles
    TTemperatureKAbsolute temperature

    What is Ideal Gas Law?

    Ideal Gas Law: For an ideal gas, the product of pressure and volume equals the amount of gas times the gas constant times the absolute temperature. — Émile Clapeyron, 1834

    The ideal gas law combines Boyle's, Charles's, Gay-Lussac's and Avogadro's laws into one equation of state. R = 8.314462618 J/(mol·K), or 0.082057 L·atm/(mol·K), is the universal gas constant. This calculator works internally in SI units, so you can mix any of the units on offer.

    Real gases behave ideally at low pressure and high temperature, where molecules are far apart and intermolecular forces are negligible. Air at room conditions deviates by less than 0.1%. Near condensation or at very high pressures, use a real-gas model such as van der Waals.

    How to use this calculator

    1. Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
    2. Enter the known values. Scientific notation such as 1.6e-11 is accepted.
    3. Select a unit for each value. Units are converted to SI automatically.
    4. The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.

    Worked example

    What pressure does 1 mol of gas exert in 22.414 L at 0 °C?

    1. T = 273.15 K, V = 0.022414 m³.
    2. P = nRT/V = 1 × 8.314 × 273.15 / 0.022414 = 101 325 Pa = 1.00 atm.

    This is the familiar molar volume at STP.

    Frequently asked questions

    Which value of R should I use?

    Any value works if the units match. The calculator handles this for you by converting everything to SI and using R = 8.314 J/(mol·K).

    Why must temperature be in kelvin?

    The law is proportional to absolute temperature. 0 °C is not "zero temperature", so Celsius values give wrong answers. Enter °C or °F if you like and the calculator converts them to kelvin.

    Should I use gauge or absolute pressure?

    Absolute pressure. Gauge pressure (e.g. a tyre gauge) must have atmospheric pressure (≈101.3 kPa) added first.