What is an ideal gas?
An ideal gas is a simplified model for describing gas behaviour. It assumes that gas particles move randomly, occupy negligible volume, and do not attract or repel one another except during perfectly elastic collisions. No real gas follows this model perfectly, but many gases behave closely enough under ordinary conditions for the ideal gas law to give useful results.
The approximation becomes less reliable at very high pressures, very low temperatures, or near condensation. Under those conditions, molecular size and intermolecular forces become significant. For moderate conditions, however, PV = nRT provides a fast way to connect pressure, volume, amount of gas, and temperature.
This calculator accepts common pressure, volume, and temperature units instead of forcing you to convert everything manually. It normalises pressure to pascals, volume to cubic meters, and temperature to kelvin, performs the calculation, then displays pressure and volume results in your selected units.
Ideal gas law equation
The ideal gas law is:
PV = nRT
where P is pressure, V is volume, n is the amount of gas in moles, R is the ideal gas constant, and T is absolute temperature in kelvin.
The calculator uses these rearranged forms:
pressure = amount × gas constant × temperature ÷ volume
volume = amount × gas constant × temperature ÷ pressure
amount = pressure × volume ÷ (gas constant × temperature)
temperature = pressure × volume ÷ (amount × gas constant)
How the unit conversion works
Pressure conversion
The selected pressure is multiplied by its pascal conversion factor.
pressure in pascals = entered pressure × pressure conversion factor
For 1 atm: 1 × 101,325 = 101,325 Pa.
Volume conversion
The selected volume is multiplied by its cubic-meter conversion factor.
volume in cubic meters = entered volume × volume conversion factor
For 22.414 L: 22.414 × 0.001 = 0.022414 m³.
Temperature conversion
Temperature requires a scale conversion rather than a simple multiplication.
For Celsius:
T(K) = T(°C) + 273.15
For Fahrenheit:
T(K) = (T(°F) - 32) × 5/9 + 273.15
For kelvin:
T(K) = T(K)
For Rankine:
T(K) = T(°R) × 5/9
How to use the ideal gas law calculator
Step One: Enter pressure and choose its unit
Enter a pressure such as 1 atm, 101.325 kPa, or 14.696 psi. Select the matching unit from the pressure dropdown.
Step Two: Enter volume and choose its unit
Enter the gas volume in m³, L, mL, cm³, ft³, in³, or US gallons, then select that unit.
Step Three: Enter moles and temperature
Enter the amount of gas in moles. Then enter the temperature and choose °C, K, °F, or °R.
Step Four: Read the converted results
The calculator converts the inputs to compatible SI units, applies PV = nRT, and displays pressure and volume in the units you selected. For 1 mol at 1 atm and 0°C with a volume of 22.414 L, the result is approximately 1 atm, 22.414 L, 1 mol, and 273.15 K.
Worked example: pressure from mixed units
Suppose 0.1 mol of gas occupies 1,000 L at 50°F.
Step One: Convert volume
1,000 L × 0.001 = 1 m³.
Step Two: Convert temperature
T(K) = (50 - 32) × 5/9 + 273.15 = 283.15 K.
Step Three: Apply the pressure formula
P = nRT ÷ V
P = 0.1 × 8.31446261815324 × 283.15 ÷ 1
Step Four: Read the pressure
P ≈ 235.40 Pa. You can display that result in Pa, kPa, atm, psi, or any other pressure unit by changing the selected pressure unit.
Ideal gas constant
The ideal gas constant is the universal constant R:
R = 8.31446261815324 J/(mol·K)
It is related to Avogadro’s constant and Boltzmann’s constant:
R = Nâ‚k
where Nâ‚ = 6.02214076 × 10²³ mol⁻¹ and k = 1.380649 × 10⁻²³ J/K. Their product gives the molar gas constant.
Other unit systems use different numerical values. For example, R ≈ 0.082057 L·atm/(mol·K) works with liters and atmospheres. This calculator uses the SI value internally and handles the conversions for you.
Related gas-law relationships
At constant temperature and amount, pressure and volume follow Boyle’s law:
PV = constant
At constant volume and amount, pressure is proportional to absolute temperature:
P/T = constant
At constant pressure and amount, volume is proportional to absolute temperature:
V/T = constant
These are idealised isothermal, isochoric, and isobaric relationships.
FAQs
Why must temperature be converted to kelvin?
Kelvin is an absolute temperature scale. Celsius and Fahrenheit have arbitrary zero points, so using them directly in PV = nRT would produce incorrect results.
Can I use psi and liters together?
Yes. Select psi for pressure and liters for volume. The calculator converts both to pascals and cubic meters before calculating.
Can I use Fahrenheit or Celsius?
Yes. Select °F or °C from the temperature dropdown. The calculator converts either scale to kelvin internally.
What happens if I enter 0 K?
Zero kelvin is the theoretical absolute zero. The ideal gas law becomes physically limiting there, so use a temperature above 0 K for ordinary calculations.
When does the ideal gas law become inaccurate?
It becomes less accurate at high pressure, low temperature, and near condensation, where real molecular volume and intermolecular forces can no longer be ignored.
References
- NIST, Fundamental Physical Constants: https://www.nist.gov/pml/fundamental-physical-constants
- NIST/CODATA, recommended constants: https://physics.nist.gov/cuu/pdf/wallet_2022.pdf