Ideal gas law calculator (PV = nRT)

The formula

$$PV = nRT$$

$P$ is pressure, $V$ volume, $n$ the amount of gas in moles, $T$ the absolute temperature in kelvin, and $R = 8.314\ \text{J/(mol·K)}$ is the molar gas constant.

Where it comes from

The ideal gas law stitches together three older experimental laws, each found by holding two quantities fixed and varying the others.

Boyle’s law (1662). At fixed temperature and amount, squeezing a gas raises its pressure in inverse proportion:

$$P \propto \frac{1}{V}$$

Charles’s law (1787). At fixed pressure, volume grows in proportion to absolute temperature:

$$V \propto T$$

Avogadro’s law (1811). At fixed temperature and pressure, equal volumes hold equal numbers of molecules, so

$$V \propto n$$

If $V$ is proportional to each of $1/P$, $T$ and $n$ separately, it is proportional to their product:

$$V \propto \frac{nT}{P} \quad\Rightarrow\quad V = R\,\frac{nT}{P}$$

The constant of proportionality is $R$. Multiplying both sides by $P$ gives $PV = nRT$.

The same result also falls out of kinetic theory: treat a gas as tiny particles bouncing elastically off the walls, add up the momentum they transfer per second, and the pressure comes out as $PV = \tfrac{1}{3}Nm\overline{v^2}$. Since the average kinetic energy of a particle is proportional to temperature, that again becomes $PV = nRT$.

Worked example

The volume of one mole of gas at 0 °C and 1 atm:

$$V = \frac{nRT}{P} = \frac{1 \times 8.314 \times 273.15}{101{,}325\ \text{Pa}} = 0.02241\ \text{m}^3 = 22.4\ \text{L}$$

Watch out for

• Temperature must be absolute. Using 25 instead of 298.15 K is the most common mistake; the calculator converts for you.
• Real gases deviate at high pressure and low temperature, where molecules take up space and attract each other. Below about 10 atm and well above the boiling point, the ideal law is usually within a few percent.

Sources

• CODATA 2018 value of the molar gas constant R (NIST)

Last checked November 11, 2026