CalcaTools

Ideal Gas Calculator

Ideal Gas Calculator is a free online calculator that helps you work out ideal gas quickly and accurately, right in your browser.

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

atm
L
atm
Results

Enter values above and click Calculate to see your result instantly.

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

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

school Free for classroom use

Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

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

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

PV = nRT links the pressure, volume, amount, and temperature of an ideal gas through the gas constant R. Temperature must be absolute (kelvin), and R must match your pressure and volume units.

Example

How many moles in 10 L at 1 atm and 300 K? n = PV / (RT) = (1 x 10) / (0.082057 x 300) = 10 / 24.62 = 0.406 mol.

Always convert Celsius to kelvin (K = °C + 273.15). Real gases deviate at high pressure or low temperature, where the van der Waals equation is more accurate.

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.