Ideal Gas Law Calculator
Solve PV = nRT for pressure, volume, moles or temperature with any units (atm, kPa, psi, L, °C, K) using R = 8.314462618 J/(mol·K), with every step shown.
Ideal Gas Law Calculator: with the default inputs, volume is 22.414 L.
Absolute pressure, not gauge. Not used when solving for P.
Not used when solving for V.
Moles of gas = mass ÷ molar mass. Not used when solving for n.
Converted to kelvin internally. Not used when solving for T.
- Solved for
- V = 22.414 L
- Pressure
- 1 atm
- Amount of gas
- 1mol
- Temperature
- 273.15 K
- Volume per mole (L/mol)
- 22.41422.414 L/mol at 0 °C and 1 atm; 24.465 L/mol at 25 °C and 1 atm.
- Number of molecules
- 6.022 × 10²³ molecules
Assumptions
- Ideal-gas behaviour: point molecules with no intermolecular forces.
- Pressures are absolute, not gauge.
- R = 8.314462618 J/(mol·K); 1 atm = 101,325 Pa exactly.
| R | Units | Use it when |
|---|---|---|
| 8.314462618 | J/(mol·K) = m³·Pa/(mol·K) | Everything in SI: pascals, cubic metres. This is what the calculator uses. |
| 0.082057366 | L·atm/(mol·K) | Chemistry classes: litres and atmospheres |
| 8.314462618 | L·kPa/(mol·K) | Litres and kilopascals — numerically the same as the SI value |
| 62.3636 | L·mmHg/(mol·K) | Pressures quoted in mmHg or torr |
| 1.987204 | cal/(mol·K) | Thermochemistry in calories |
| 10.7316 | ft³·psi/(lb-mol·°R) | US engineering units |
Every row is the same constant. Picking the wrong one is the single most common mistake in PV = nRT: the numbers you feed in must match the units of the R you use.
| Conditions | Volume per mole (L) | Who uses it |
|---|---|---|
| 0 °C, 1 atm (101.325 kPa) | 22.414 | The classic 22.4 L/mol taught in schools |
| 0 °C, 1 bar (100 kPa) | 22.711 | IUPAC STP since 1982 |
| 25 °C, 1 atm | 24.4654 | Room-temperature laboratory work |
| 20 °C, 1 atm | 24.0551 | NTP, common in engineering |
| 15 °C, 1 atm | 23.6448 | Natural-gas and HVAC standard conditions |
Molar volume does not depend on which gas it is — that is the whole content of Avogadro's law. Real gases sit a fraction of a percent off these figures at ordinary pressures.
How this is worked out
The formula
P V = n R T P = absolute pressure (Pa) V = volume (m³) n = amount of gas (mol) R = 8.314462618 J/(mol·K) (= 0.082057 L·atm/(mol·K)) T = absolute temperature (K) = °C + 273.15 Rearranged: V = nRT/P, P = nRT/V, n = PV/(RT), T = PV/(nR)
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Solve for
- Choose one of 4 options.Volume (V) · Pressure (P) · Amount of gas (n, moles) · Temperature (T)
- Pressure (P)
- Absolute pressure, not gauge. Not used when solving for P.in atm, kPa, Pa, bar, psi, mmHg · 0 or more · defaults to 1
- Volume (V)
- Not used when solving for V.in L, mL, m³, ft³, gal · 0 or more · defaults to 22.4
- Amount (n)
- Moles of gas = mass ÷ molar mass. Not used when solving for n.0 or more · defaults to 1
- Temperature (T)
- Converted to kelvin internally. Not used when solving for T.in K, °C, °F · 0 or more · defaults to 273.15
What you get back
- Volumemain answer
- Solved for
- Pressure
- Amount of gas
- mol
- Temperature
- Volume per mole (L/mol)
- 22.414 L/mol at 0 °C and 1 atm; 24.465 L/mol at 25 °C and 1 atm.
- Number of molecules
What this assumes
- Ideal-gas behaviour: point molecules with no intermolecular forces.
- Pressures are absolute, not gauge.
- R = 8.314462618 J/(mol·K); 1 atm = 101,325 Pa exactly.
About this calculator
PV = nRT ties together the four things you can measure about a gas — pressure, volume, amount and temperature — with one universal constant. Choose which quantity to solve for, enter the other three in whatever units you have, and the calculator converts to SI, substitutes into the rearranged equation, and converts back. The steps show every conversion, including the one students most often forget.
The kelvin trap
Temperature in a gas law must be absolute. 20 °C is 293.15 K, and using 20 instead would make the calculated volume 15 times too small. The same goes for pressure: it must be absolute, so a tire gauge reading of 32 psi is really 32 + 14.7 = 46.7 psi absolute. The calculator accepts °C, °F or K and does the shift for you, but check that pressures you type are absolute.
Numbers worth remembering
- One mole of ideal gas at STP (0 °C, 1 atm) occupies 22.41 L; at 25 °C and 1 atm it is 24.47 L. (IUPAC now defines STP as 1 bar, which gives 22.71 L — check which your course uses.)
- R = 8.314 J/(mol·K) in SI, or 0.08206 L·atm/(mol·K) if you work in liters and atmospheres. Both describe the same constant.
- One mole is 6.022 × 10²³ molecules — the molecules output uses this to turn moles into a count.
Reading the results
All four quantities are listed so you can switch display units on each; the one you solved for is repeated in the headline text. Volume per mole is a quick sanity check against the STP value above.
Where the model breaks
The ideal gas law assumes molecules take up no space and don't attract each other. That works within about 1% for air, nitrogen, helium and most gases near room conditions. It drifts at high pressure (tens of atmospheres), at low temperature near the boiling point, and for polar or heavy molecules (water vapour, CO₂, refrigerants). There the van der Waals equation or a compressibility factor Z corrects it, and for anything close to condensing you need steam tables rather than a formula.
Frequently asked questions
▸What is the value of R in the ideal gas law?
R = 8.314462618 J/(mol·K), exact since the 2019 SI redefinition. In liter-atmosphere units it is 0.0820574 L·atm/(mol·K); in liter-kilopascal units, 8.3145 L·kPa/(mol·K).
▸Why must temperature be in kelvin?
Because the law says volume is proportional to temperature — halve T and V halves. That is only true measured from absolute zero, not from the freezing point of water. Add 273.15 to Celsius.
▸What is the volume of one mole of gas at STP?
22.41 L at 0 °C and 1 atm (101.325 kPa). Under IUPAC's 1 bar definition of STP it is 22.71 L. At room temperature (25 °C, 1 atm) it is 24.47 L.
▸How do I find the moles of a gas?
n = PV ÷ RT with P in pascals, V in cubic meters and T in kelvin; or divide the gas's mass by its molar mass if you know the mass instead.
▸When is the ideal gas law not accurate?
At high pressures, near condensation temperatures, and for strongly interacting molecules. Air at room conditions is within about 0.1%; CO₂ at 50 atm is off by roughly 20%. Use a compressibility factor or the van der Waals equation there.
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