Ideal Gas Law Calculator (PV=nRT)

Solve the ideal gas law PV = nRT for any one unknown variable. Enter three of the four variables (pressure, volume, moles, temperature) and calculate the missing one.

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Leave one field blank to solve for it.

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How to Use

  1. 1
    Select the unknown variable

    Choose which quantity you want to find: pressure (P), volume (V), moles of gas (n), or temperature (T). The other three are your inputs.

  2. 2
    Enter the three known values

    Input the known quantities in consistent units. The gas constant R = 8.314 J/(mol·K) requires pressure in Pa, volume in m³, and temperature in Kelvin.

  3. 3
    Calculate and interpret results

    Click Calculate. The tool solves PV = nRT for the unknown and displays the result with unit conversions between common engineering and SI units.

About

The ideal gas law PV = nRT is the cornerstone equation of gas-phase chemistry, unifying the relationships between pressure, volume, temperature, and moles of gas into a single compact expression. First synthesized in the 19th century from Boyle's, Charles's, and Avogadro's laws, it describes the behavior of an idealized gas whose molecules have no volume and interact only through perfectly elastic collisions.

In practice, the ideal gas law gives accurate results for most common gases (air, nitrogen, oxygen, hydrogen) under ordinary laboratory and industrial conditions. It underlies calculations in stoichiometry involving gaseous reactants and products, in thermodynamics of engines and refrigeration cycles, in meteorology and atmospheric science, and in industrial processes from distillation to combustion engineering.

The law also provides the conceptual foundation for more sophisticated models. Recognizing where real gases deviate — near phase transitions, at extreme pressures, or when molecules have strong dipole moments — builds physical intuition essential for understanding equations of state, fugacity, and compressibility factors used in chemical engineering. This calculator solves for any one of the four variables, making it equally useful for classroom problem sets and quick engineering estimates.

FAQ

What assumptions does the ideal gas law make?
The ideal gas law (PV = nRT) assumes gas molecules have negligible volume compared to the container and exert no intermolecular forces on each other. These assumptions hold well at low pressure (below a few atmospheres) and high temperature (well above the boiling point of the substance). Real gases deviate most at high pressures and low temperatures where intermolecular attractions and molecular volume become significant, requiring corrections from equations of state like van der Waals or the Peng-Robinson equation.
What is the value of the universal gas constant R?
The universal gas constant R = 8.314 J/(mol·K) = 8.314 Pa·m³/(mol·K). In other unit systems: R = 0.08206 L·atm/(mol·K), R = 62.36 L·mmHg/(mol·K), and R = 1.987 cal/(mol·K). Always verify which value of R matches the units you are using. The most common source of error in ideal gas calculations is mixing incompatible unit systems for P, V, and R.
What does STP mean and what volume does one mole of gas occupy there?
IUPAC defines Standard Temperature and Pressure (STP) as 0°C (273.15 K) and 100 kPa (changed from 101.325 kPa in 1982). At STP, one mole of an ideal gas occupies 22.414 L. The older standard (SATP, 25°C, 100 kPa) gives a molar volume of 24.789 L/mol. Be aware that textbooks published before 1982 may use 1 atm as standard pressure, giving 22.414 L/mol, which is still commonly cited.
How does the ideal gas law relate to Boyle's, Charles's, and Gay-Lussac's laws?
The ideal gas law unifies three earlier empirical laws. Boyle's Law (PV = constant at fixed T and n) describes isothermal compression. Charles's Law (V/T = constant at fixed P and n) describes isobaric heating. Gay-Lussac's Law (P/T = constant at fixed V and n) describes isochoric pressure change. Each is a special case of PV = nRT with two variables fixed, revealing how the three original laws are not independent but aspects of a single underlying relationship.
When should I use the van der Waals equation instead?
Use the van der Waals equation (P + a/V²)(V - b) = nRT when working with real gases at pressures above 10 atm, temperatures near the boiling point, or when high accuracy is required. The parameters a (intermolecular attraction) and b (excluded volume) are tabulated for common gases. CO₂, SO₂, and H₂O deviate significantly from ideal behavior even at moderate conditions; He and H₂ are nearly ideal over a wide range because of their low polarizability.
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