The ideal gas law
The ideal gas law is PV = nRT. Solving for pressure gives P = nRT / V, where n is moles, T is absolute temperature in kelvin, V is volume in liters, and R is the gas constant 0.082057 L·atm/(mol·K). One mole at 273.15 K in 22.414 L yields about 1.00 atm — standard temperature and pressure.
The law combines three older observations: Boyle's law (pressure inversely proportional to volume), Charles's law (volume proportional to absolute temperature) and Avogadro's law (volume proportional to moles). Multiplying them together and inserting a single proportionality constant R produces PV = nRT. The n in PV = nRT is an amount in moles, which the moles calculator works out from mass.
How to use this calculator
Enter the amount of gas in moles, the temperature in kelvin, and the volume in liters. The pressure comes out in atmospheres (atm). Temperature must be in kelvin — add 273.15 to a Celsius reading first, or the result will be wrong.
Volume must be non-zero, and both temperature and moles must be positive for a physically meaningful answer. If your volume is in millilitres, divide by 1,000 first; if it is in cubic metres, multiply by 1,000. Getting the volume unit wrong is the single most common cause of a pressure figure that looks absurd. Pressure must be absolute rather than gauge, so check the value with the pressure calculator before entering it.
About the gas constant
The value of R depends on the units chosen. Using atm, liters, moles and kelvin, R = 0.082057 L·atm/(mol·K). The law assumes an ideal gas — molecules with no volume and no attraction — which is a close approximation at ordinary temperatures and pressures. Density of the gas can be explored with the density calculator.
The same constant appears as 8.314 J/(mol·K) in SI units; only the unit system differs, not the physics.
Frequently asked questions
- What is the ideal gas law?
- PV = nRT, relating pressure, volume, moles and temperature through the gas constant R.
- How do I solve for pressure?
- Rearrange to P = nRT / V. One mole at 273.15 K in 22.414 L gives about 1.00 atm.
- What value of R should I use?
- With atm, liters, moles and kelvin, use R = 0.082057 L·atm/(mol·K).
- Why must temperature be in kelvin?
- The law requires absolute temperature. Convert Celsius to kelvin by adding 273.15.
- When does the ideal gas law stop working?
- It breaks down at high pressure and low temperature, where molecules are close enough that their own volume and mutual attraction matter. Near condensation, real gases deviate noticeably and equations such as van der Waals give better predictions.