Ideal Gas Law Calculator

The ideal gas law is PV = nRT. P is the absolute pressure, V is the volume, n is the amount of gas in moles, T is the absolute temperature in kelvin and R is the gas constant. It ties four measurable quantities together, so any one can be found from the other three.

To calculate it by hand, choose the unknown and rearrange. Pressure is P = nRT / V, volume is V = nRT / P, temperature is T = PV / (nR) and amount is n = PV / (RT). Put every value in matching units, multiply and divide, and check that the units cancel.

The calculator does the unit work for you. Choose what to solve for, enter the other three values with their units, and read the answer in the unit you picked. The same result is also shown in every other pressure, volume and temperature unit.

R is the same for every ideal gas. Since the 2019 redefinition of the SI it is exactly the Avogadro constant times the Boltzmann constant, 8.31446261815324 joules per mole kelvin, and NIST lists it as 8.314 462 618 J per mole kelvin. The calculator uses the full value.

The number changes with the units of pressure and volume. In litres and atmospheres it is 0.0820574, in litres and kilopascals it is 8.31446, in litres and bar it is 0.0831446. The gas constant table lists them. To find R from measurements, rearrange to R = PV / (nT): one mole at 273.15 K and 1 atm fills 22.414 L, so R = 22.414 / 273.15 = 0.08206 L atm per mole kelvin.

Mixing a value of R in one unit system with pressure or volume in another is the most common reason a hand calculation is off by 100 or 1,000. Converting everything to SI avoids it.

Pressure must be absolute, not gauge. A gauge shows the pressure above the surrounding air, so add about 1 atm, 101.325 kPa or 14.696 psi before using it. The calculator accepts atm, kPa, bar, mmHg and psi, converting through pascals with 1 atm equal to exactly 101,325 Pa. It treats mmHg as the torr, so 760 mmHg is exactly 1 atm.

Temperature must be absolute too. Celsius becomes kelvin by adding 273.15, and Fahrenheit by subtracting 32, multiplying by 5/9 and adding 273.15. Zero kelvin is the lowest possible temperature, so the calculator rejects anything at or below it.

Volume can be litres, cubic metres or millilitres. One cubic metre is 1,000 litres. The molar volume table shows what one mole occupies under common reference conditions such as 0 C and 1 atm, 22.414 L, or 25 C and 1 bar, 24.789 L.

Most real problems give grams, not moles. Switch the amount to mass, enter the molar mass in grams per mole and the calculator uses n = m / M. When you solve for the amount, it reports both the moles and the mass, together with the gas density in grams per litre.

Density at a given pressure and temperature is rho = PM / (RT). For dry air, M is about 28.96 g per mole, which gives 1.204 g per litre at 20 C and 1 atm. Specific volume is the reciprocal, volume per unit mass. The mass form of the law, PV = mRT, uses a specific gas constant equal to R divided by the molar mass, about 287.1 J per kilogram kelvin for air.

The gas density table lists molar mass and density for ten common gases at 25 C and 1 atm. Molar masses come from conventional atomic weights, such as 1.008 for hydrogen, 12.011 for carbon, 14.007 for nitrogen and 15.999 for oxygen.

The ideal gas law contains the older gas laws. Hold the amount and temperature fixed and it becomes Boyle's law, P1V1 = P2V2. Hold the amount and pressure and it becomes Charles's law, V1/T1 = V2/T2. Hold the amount and volume and it becomes Gay-Lussac's law, P1/T1 = P2/T2. Avogadro's law, V1/n1 = V2/n2, fixes pressure and temperature. Together they give the combined gas law, P1V1/T1 = P2V2/T2.

To find what a change in temperature does, solve for the state before, then re-solve for the state after with the same amount. For a rigid container, pressure scales with the kelvin temperature, so a container at 1 atm and 20 C reaches 129.0 kPa at 100 C. The heated container table lists more cases.

Never treat these figures as permission to heat a sealed vessel. Pressure rises quickly, and containers have ratings that must not be exceeded.

An ideal gas has point-like particles with no attraction between them. Real gases behave that way when the pressure is low and the temperature is well above the boiling point, because the molecules are far apart. Air, nitrogen, oxygen, argon and helium at room conditions are close to ideal.

The approximation weakens at high pressure, where molecule size matters, and near condensation, where attractions matter. Water vapour, ammonia and carbon dioxide near their liquid points deviate more. For those cases a real gas equation of state, such as van der Waals, or a compressibility factor, is more accurate.

As a rule of thumb, treat results as good to a percent or so near one atmosphere and room temperature, and as rougher estimates at tens of atmospheres. The calculator uses the ideal law only.

The results are an estimate for education and planning. They assume an ideal gas, a uniform temperature and a steady state, and they do not include moisture, gas mixtures that react, leaks or vessel flexing. For compressed gas cylinders, boilers or anything under pressure, follow the manufacturer's rating, the safety data sheet and local rules, and have a qualified person check the design.

For converting temperature scales, use the temperature converter. To work out how much a quantity changed in percent, see the percentage calculator, and to estimate a value between two table entries, try the linear interpolation calculator.