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Calcimator

Ideal Gas Law Calculator

Solve PV = nRT for any unknown variable — pressure, volume, moles, or temperature. Includes isothermal P-V curve visualization.

Inputs

L
mol
K

Results

Result

1.00066

Solved VariablePressure (P)
Pressure1.00066 atm
Pressure101.39 kPa
Volume22.4 L
Moles1 mol
Temperature273.15 K
Temperature0 °C
Molar Density0.04464 mol/L

The ideal gas law

  1. 1.Multiply moles, the gas constant and temperature
    nRT=1×0.0821×273.15=22.41

    This product is the total thermal energy available to the gas. R is the bridge between a count of molecules and an energy — it exists precisely so this multiplication has consistent units.

  2. 2.Divide by the volume
    P=22.4122.4=1

    Pressure is that energy spread over the space the gas occupies. Squeeze the same energy into less volume and the pressure rises in exact proportion.

Where the units go

  • mol × L·atm/(mol·K) × K ÷ L mol · K · L→atm
Émile Clapeyron combined Boyle's, Charles' and Avogadro's separate observations into one equation of state, introducing the constant that carries the relationship between the amount of gas and its energy.
Émile Clapeyron, 'Mémoire sur la puissance motrice de la chaleur', Journal de l'École Polytechnique, vol. 14·1834
How to Use This Calculator
  1. Select which variable to solve for (pressure, volume, moles, or temperature).
  2. Enter the known values for the other three variables with appropriate units.
  3. Review the calculated result using the ideal gas law: PV = nRT.
  4. Use this for standard conditions — real gases deviate at high pressure or low temperature.

How the result changes with Volume (V)

Volume (V)Result
10,0000.00224
35,0000.00064
65,0000.00034
90,0000.00025

What each input means

Solve For
Select which variable to solve for — the other three are inputs
Pressure (P)
Gas pressure in atmospheres (1 atm = 101.325 kPa)
Volume (V)
Gas volume in liters (22.4 L = 1 mol ideal gas at STP)
Moles (n)
Amount of gas in moles
Temperature (T)
Absolute temperature in Kelvin (0°C = 273.15 K)

How this is calculated

Formula

PV = nRT

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Solve For = 1, Pressure (P) = 1, Volume (V) = 22.4, Moles (n) = 1 = 5 input(s) provided
  2. Calculate Result
    Result
    1.00066 = 1.00066
  3. Calculate Solved Variable
    Solved Variable
    Pressure (P) = Pressure (P)
  4. Calculate Pressure
    Pressure = P
    1.00066 = 1.00066

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