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Ideal Gas Calculator | Compute Gas Variables Using PV = nRT

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 Worked example

Let's say you are using the 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. Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula PV = nRT (P pressure, V volume, n moles, R gas constant, T absolute temperature in K) and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

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.
What does the Ideal Gas Calculator do?
Ideal Gas Calculator is a free online calculator that helps you work out ideal gas quickly and accurately, right in your browser. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Ideal Gas Calculator use?
The Ideal Gas Calculator applies the standard formula: PV = nRT (P pressure, V volume, n moles, R gas constant, T absolute temperature in K). The tool walks through each step of the calculation so you can verify the numbers yourself.
Is the Ideal Gas Calculator free and private?
Yes — the Ideal Gas Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Ideal Gas Calculator?
The Ideal Gas Calculator applies the standard formula: PV = nRT (P pressure, V volume, n moles, R gas constant, T absolute temperature in K). It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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