Ideal gas law calculator.
Leave exactly one of P, V, n and T empty.
Ideal gas law: PV = nRT, with R = 8.314462618 J/(mol·K). Enter three values and leave one empty. Use absolute pressure and absolute temperature (K). Example: 1 mol at 0 °C and 101.325 kPa fills 22.414 L.
Pressure, volume, amount of gas and temperature — leave one blank and the calculator solves for it. Works in kPa, atm, bar, psi, L, m³, ft³, K, °C and °F.
How the math works
PV = nRT P = nRT ÷ V V = nRT ÷ P n = PV ÷ (RT) T = PV ÷ (nR) R = 8.31446261815324 J/(mol·K) (exact since 2019)
R is the product of the Avogadro constant and the Boltzmann constant. Both have exact defined values in the SI since 20 May 2019, so R is exact too.
Molar volume of an ideal gas
| Conditions | Volume of 1 mol |
|---|---|
| 0 °C, 100 kPa (IUPAC STP) | 22.711 L |
| 0 °C, 101.325 kPa (1 atm) | 22.414 L |
| 20 °C, 101.325 kPa (NTP) | 24.055 L |
| 25 °C, 100 kPa (SATP) | 24.79 L |
"Standard conditions" have more than one definition. Always state the temperature and pressure you use.
When the ideal gas law is not accurate
- High pressure: above about 10 atm, real gases deviate. Use a compressibility factor Z: PV = ZnRT.
- Low temperature: near the condensation point, real gases deviate.
- Gauge pressure: the law needs absolute pressure. Add atmospheric pressure (about 101.3 kPa) to a gauge reading.
- °C or °F: the law needs absolute temperature. The calculator converts to kelvin for you.
Common questions
What is the ideal gas law?
PV = nRT. P is absolute pressure, V is volume, n is the amount of gas in moles, R is the gas constant and T is absolute temperature in kelvin.
What is the value of R?
R = 8.31446261815324 J/(mol·K). It is exact in the 2019 SI. Other forms are 0.082057 L·atm/(mol·K) and 8.314 L·kPa/(mol·K).
What volume does 1 mole of gas occupy?
At 0 °C and 1 atm (101.325 kPa), 22.414 L. At 0 °C and 100 kPa (IUPAC STP), 22.711 L.
Why must temperature be in kelvin?
The law is a proportion to absolute temperature. At 0 °C the gas still has a volume, so °C or °F would give wrong answers. The calculator converts automatically.
Does it work for air?
Yes, closely, at normal temperatures and pressures. Use the mean molar mass of dry air, 28.9644 g/mol (U.S. Standard Atmosphere, 1976), to convert moles to grams.
When should I not use it?
At high pressure (above about 10 atm), at low temperature near condensation, or for steam near saturation. Use real-gas data for those cases.
Sources
- Gas constant: NIST CODATA — R = NAk = 8.31446261815324 J mol⁻¹ K⁻¹ (exact).
- SI definitions: BIPM SI Brochure (9th edition, 2019).
Disclaimer. The ideal gas law is an approximation. For high-pressure vessels, use real-gas data and follow the applicable pressure-vessel code.