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Ideal Gas Calculator | Compute Gas Variables Using PV = nRT

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Solve the ideal gas law PV = nRT for pressure, volume, moles or temperature, with unit conversions and the gas constant applied. Enter any three values and get the fourth — the essential tool for chemistry and physics gas problems, with temperature handled in kelvin automatically.

Last updated: June 2026 · Free · No sign-up required

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Quick reference

Gas constant RUse with units
0.082057 L·atm/(mol·K)atm, liters
8.314 J/(mol·K)Pa, m³ (SI)
62.36 L·Torr/(mol·K)Torr, liters
0.08314 L·bar/(mol·K)bar, liters

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Interpretation guide

Solve forRearranged
Pressure PP = nRT / V
Volume VV = nRT / P
Moles nn = PV / (RT)
Temperature TT = PV / (nR)

lightbulb Sealed flask: solving for pressure

A lab technician seals 0.10 mol of nitrogen in a 2.5 L flask at room temperature (25 °C). What pressure will the gauge show? First convert 25 °C to kelvin: 25 + 273.15 = 298.15 K, rounded to 298 K for this calculation.

Result: P = nRT ÷ V = (0.10 mol × 0.08206 L·atm/(mol·K) × 298 K) ÷ 2.5 L = 2.4454 ÷ 2.5 = 0.978 atm — about 0.978 atm.

What this means: Just under 1 atm, which makes sense: a flask of gas near room temperature and modest fill sits close to atmospheric pressure. The calculation also shows why kelvin matters — using 25 °C directly would give a wildly wrong answer.

Formula & methodology

Formula: PV = nRT (P pressure, V volume, n moles, R gas constant, T absolute temperature in K)

How the ideal gas law works

The tool applies PV = nRT, where P is pressure, V volume, n the number of moles, R the gas constant, and T the absolute temperature in kelvin. Enter any three of the four variables and the calculator solves for the fourth, converting pressure and temperature units automatically so the equation stays consistent.

Example: 2 moles of gas at 300 K and 1 atm occupy V = nRT ÷ P = 2 × 0.0821 × 300 ÷ 1 ≈ 49.3 liters.

Reading the result: the law assumes ideal behavior — negligible molecular volume and no intermolecular forces — which holds well at moderate pressures and temperatures. Real gases deviate at high pressure or low temperature, where the van der Waals equation becomes more accurate.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What is the ideal gas law?
The ideal gas law is PV = nRT, relating pressure (P), volume (V), number of moles (n), and absolute temperature (T) through the gas constant R. It describes how an idealized gas behaves and is accurate for most gases at ordinary temperatures and pressures, where intermolecular forces are negligible.
What value of R should I use?
Choose R to match your units. Use 0.082057 L·atm/(mol·K) for pressure in atmospheres and volume in liters, or the SI value 8.314 J/(mol·K) for pascals and cubic meters. Using the wrong R is the most common mistake — the numbers won't reconcile if the units don't match.
Why must temperature be in kelvin?
The gas law is proportional to absolute temperature, where 0 represents zero thermal energy. Celsius and Fahrenheit have arbitrary zero points, so using them would give wrong or even negative results. Always convert: kelvin = Celsius + 273.15 before plugging into PV = nRT.
How do you solve for each variable?
Rearrange PV = nRT: pressure P = nRT/V, volume V = nRT/P, moles n = PV/(RT), and temperature T = PV/(nR). Substitute the three known quantities (with consistent units and T in kelvin) and compute the fourth.
When does the ideal gas law break down?
It becomes inaccurate at high pressures and low temperatures, where gas molecules are close enough that their volume and attractive forces matter. Near condensation, real gases deviate significantly, and the van der Waals equation — which adds correction terms for molecular size and attraction — gives better results.
Which gas variable can this page solve for?
Any one of the four: pressure, volume, moles, or temperature. Give it the other three and it rearranges PV = nRT automatically — for example, entering P, V, and n returns T in kelvin. Unit conversion is handled inline, so you can mix atmospheres with liters or pascals with cubic meters.
How does it handle the different values of the gas constant R?
It matches R to your units: 0.08206 L·atm/(mol·K) for atmospheres and liters, or 8.314 J/(mol·K) for pascals and cubic meters. Picking the wrong R is the most common gas-law mistake, so the page shows which value it used in the step-by-step working.
Can the ideal gas law fail for my numbers?
Yes — it assumes molecules have no volume and don't attract each other, which breaks down at high pressure or near condensation. If you're modeling a gas compressed to tens of atmospheres or cooled toward liquefaction, treat the result as an approximation and consider the van der Waals equation instead.
How precise is the arithmetic?
The algebra is exact for the ideal model — P = nRT/V computed with full floating-point precision, so the digits you see are correct for the inputs given. The real limit is physical, not mathematical: the answer is only as good as the ideal-gas assumption for your conditions.

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