What is the ideal gas law?

The ideal gas law states that PV = nRT, linking the pressure, volume, amount and temperature of a gas through the gas constant R. It combines the three earlier gas laws — Boyle's, Charles's and Gay-Lussac's — into one relationship, and it holds for any gas at ordinary pressures and temperatures regardless of which gas it is. That last point is remarkable: helium and carbon dioxide follow the same equation.

What is the value of the gas constant R?

R is exactly 8.31446261815324 J/(mol·K). Since the 2019 SI redefinition it is not measured but defined, because it equals Avogadro's constant multiplied by the Boltzmann constant, and both of those are now fixed numbers. In other units it is 0.08206 L·atm/(mol·K), which is the form used when working in litres and atmospheres, and 8.314 kPa·L/(mol·K). This calculator works in SI internally, so you can mix input units freely.

Why must temperature be in kelvin?

Because the equation requires an absolute scale, where zero genuinely means zero thermal energy. Celsius and Fahrenheit both put their zero at an arbitrary point, so ratios between them are meaningless — 20 °C is not twice as hot as 10 °C in any physical sense, but 400 K really is twice 200 K. Using Celsius directly is the single most common mistake in gas calculations, and it produces answers that are wrong by a wide margin rather than slightly off.

What is molar volume at STP?

At IUPAC standard conditions of 0 °C and 100 kPa, one mole of any ideal gas occupies 22.711 litres. The older standard used 1 atmosphere instead of 100 kPa and gives the more familiar 22.414 litres, which is where the textbook figure of 22.4 comes from. IUPAC changed the standard pressure in 1982, so both numbers are in circulation and it is worth checking which one a given course expects.

How do I calculate the amount of gas from pressure and volume?

Rearrange to n = PV ÷ RT. A 12 litre scuba tank at 200 bar and 20 °C contains n = 200,000 × 0.012 ÷ (8.314 × 293.15) ≈ 98.5 moles of air. Convert everything to SI first: pressure in pascals, volume in cubic metres and temperature in kelvin. Note that a bar is 100,000 Pa while an atmosphere is 101,325 Pa — they differ by about 1.3 percent, which matters at high pressures.

What are Boyle's, Charles's and Gay-Lussac's laws?

They are the ideal gas law with two quantities held fixed. Boyle's law holds n and T constant, giving PV = constant — halve the volume and the pressure doubles. Charles's law holds P and n constant, giving V ∝ T, which is why a balloon shrinks in the cold. Gay-Lussac's law holds V and n constant, giving P ∝ T, which is why tyre pressure rises after a long drive. Each is a special case rather than a separate rule.

Why does pressure rise when a gas is heated?

Heating a gas makes its particles move faster — specifically, the root-mean-square speed rises with the square root of temperature, so quadrupling the temperature doubles the speed. Faster particles hit the container walls both more often and harder, and pressure is simply the total force of those collisions per unit area. In a sealed rigid container the volume cannot change, so all of that extra collision force shows up as higher pressure.

When does the ideal gas law stop working?

It assumes gas particles occupy no volume themselves and exert no forces on one another. Both assumptions hold well at ordinary conditions but fail when a gas is heavily compressed, where the particles' own volume becomes significant, or cooled towards its condensation point, where attractive forces start to matter. Deviations become noticeable above roughly 10 atmospheres. The van der Waals equation adds correction terms for both effects.

Does the identity of the gas matter?

Not for the ideal gas law itself. One mole of helium and one mole of carbon dioxide occupy the same volume at the same pressure and temperature, which is Avogadro's insight. Identity only enters when you convert between moles and mass, which needs the molar mass, or when you calculate particle speed, since heavier molecules move more slowly at the same temperature. It also affects how soon a real gas departs from ideal behaviour.

Ideal Gas Law Calculator (PV = nRT)

Enter any three of pressure, volume, amount of gas and temperature, and this calculator returns the fourth using PV = nRT. It handles the units chemistry actually uses — atmospheres, bar, kilopascals, mmHg and psi for pressure, litres or cubic metres for volume, and kelvin, Celsius or Fahrenheit for...

PV = nRT

Three values entered — solving for volume.

PPRESSURE

VVOLUME

solved: 24.4654 L

nAMOUNT OF GAS

TTEMPERATURE

= 298.15 K — the equation always uses the absolute scale

COMMON SITUATIONS

VOLUME

24.4654 L

MOLAR VOLUME

24.465 L/mol

MOLECULES

6.022e+23

AT STP THIS IS

22.711 L

Pressure

101.325 kPa

In atmospheres

1.0000 atm

Volume

24.4654 L

Amount

1.00000 mol

Temperature

298.15 K

In Celsius

25.00 °C

STEPS

Convert to SI: P = 101,325.00 Pa, V = 0.024465 m³, T = 298.15 K.

R is exactly 8.31446261815324 J/(mol·K) — the product of Avogadro's constant and the Boltzmann constant, both fixed by definition.

V = nRT / P = 1.00000 × 8.3145 × 298.15 ÷ 101,325.00 = 0.024465 m³

WHERE PRESSURE COMES FROM

Pressure is not an input, it is a consequence. Gas particles push on the walls by colliding with them, so anything that makes collisions more frequent or more forceful raises the pressure — more particles, a hotter gas, or a smaller container. Particle speed here follows √T, which is the real relationship: quadruple the temperature and the particles move twice as fast.

MOLAR VOLUME AT STANDARD CONDITIONS

IUPAC STP · 0 °C, 100 kPa

22.711 L/mol

Classic STP · 0 °C, 1 atm

22.414 L/mol

SATP · 25 °C, 100 kPa

24.790 L/mol

Yours

24.465 L/mol

The familiar 22.4 L/mol is the older standard, at one atmosphere. IUPAC moved to 100 kPa in 1982, which gives 22.711 L/mol — so textbooks and exam boards do not always agree on which figure to use.

HOW HIGH A PRESSURE IS THAT?

Ideal, not real. This model assumes particles have no volume of their own and do not attract one another. That holds well at ordinary pressures and temperatures, and breaks down when a gas is compressed hard or cooled towards its condensation point — which is exactly when it stops behaving like a gas.

Created with❤️byeaglecalculator.com

HOW TO USE

1
Enter any three of the four boxes — pressure, volume, amount of gas in moles, and temperature. Known values get a solid black border; the one you leave blank is outlined in gold and fills in automatically.
2
Pick units beside each field. Pressure in Pa, kPa, bar, atm, mmHg or psi; volume in litres, millilitres or cubic metres; amount in moles; temperature in kelvin, Celsius or Fahrenheit.
3
If you enter a temperature in Celsius or Fahrenheit, check the small grey line beneath it — that shows the kelvin value the equation is actually using. Temperature is where most errors in this topic come from.
4
Watch the simulation to see why pressure behaves as it does. Change the amount, the volume or the temperature and the particle count, box size and particle speed respond — pressure is the result of all three, not an independent input.

THE FORMULAS

Ideal gas lawPV = nRT

Solve for pressureP = nRT / V

Solve for volumeV = nRT / P

Solve for amountn = PV / RT

Solve for temperatureT = PV / nR

Gas constantR = 8.31446261815324 J/(mol·K)

Combined gas lawP₁V₁/T₁ = P₂V₂/T₂

MoleculesN = n × 6.02214076 × 10²³

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Last updated: July 29, 2026 · R exact per SI · Eagle-eyed accuracy for every calculation.