Last updated: 2026-06-14

Understanding the ideal gas law

The ideal gas law describes how the pressure, volume, temperature, and amount of a gas are related. It treats gas particles as point masses with no attraction between them — an idealization that works remarkably well for real gases under everyday conditions. The law ties together three earlier gas laws into one compact equation.

The ideal gas law formula

$$PV = nRT$$

Symbol	Quantity	Unit (this calculator)
P	Pressure	atm
V	Volume	L
n	Amount of gas	mol
R	Gas constant	0.082057 L·atm/(mol·K)
T	Absolute temperature	K

Rearrange the equation to solve for any single variable:

• Pressure: $P = \dfrac{nRT}{V}$
• Volume: $V = \dfrac{nRT}{P}$
• Moles: $n = \dfrac{PV}{RT}$
• Temperature: $T = \dfrac{PV}{nR}$

Temperature must be on an absolute scale. This calculator accepts Celsius or Fahrenheit and converts to kelvin internally; using °C directly in the formula gives wrong answers.

The gas constant R

The universal gas constant appears in many forms depending on the units of pressure and volume:

R value	Units
8.314	J/(mol·K)
0.082057	L·atm/(mol·K)
8.314	L·kPa/(mol·K)
62.36	L·mmHg/(mol·K)

This calculator works internally in atm and litres, so it uses R = 0.082057 L·atm/(mol·K).

Worked example

What volume does 1 mole of an ideal gas occupy at 0 °C (273.15 K) and 1 atm?

$$V = \frac{nRT}{P} = \frac{1 \times 0.082057 \times 273.15}{1} = 22.414\ \text{L}$$

This is the famous molar volume at STP — about 22.4 litres per mole — which is why a mole of any gas fills roughly the same space at the same temperature and pressure.

The three laws it combines

Law	Statement	Held constant
Boyle's law	P ∝ 1/V	n, T
Charles's law	V ∝ T	n, P
Avogadro's law	V ∝ n	P, T

Holding any two of n, P, V, T fixed recovers one of these classic relationships from PV = nRT.

When real gases deviate

The ideal gas law assumes particles take up no space and do not attract one another. At low pressure and high temperature these assumptions hold and the law is accurate to a few percent. Near a gas's condensation point — high pressure or low temperature — attractions and particle volume matter, and more detailed models such as the van der Waals equation are needed.

Frequently Asked Questions (FAQ)

What is the ideal gas law?

The ideal gas law is PV = nRT, relating the pressure (P), volume (V), amount in moles (n), and absolute temperature (T) of a gas through the universal gas constant R. It combines Boyle’s law (P ∝ 1/V), Charles’s law (V ∝ T), and Avogadro’s law (V ∝ n) into a single equation. Given any three of the four variables, you can solve for the fourth.

What is the value of the gas constant R?

The universal gas constant R is 8.314 J/(mol·K) in SI units. When pressure is in atmospheres and volume in litres, R = 0.082057 L·atm/(mol·K), which is the value this calculator uses internally. Other common forms are 8.314 L·kPa/(mol·K) and 62.36 L·mmHg/(mol·K). The value you use must match the units of pressure and volume in your equation.

What volume does one mole of gas occupy?

At standard temperature and pressure defined as 0 °C (273.15 K) and 1 atm, one mole of an ideal gas occupies 22.414 L — the molar volume. At the IUPAC standard of 0 °C and 1 bar, it is 22.711 L, and at 25 °C and 1 atm it is about 24.47 L. These values follow directly from V = nRT ÷ P and explain why "22.4 litres per mole" is a familiar chemistry constant.

When does the ideal gas law break down?

The ideal gas law assumes gas particles have negligible volume and no intermolecular forces. These assumptions hold well at low pressure and high temperature, where particles are far apart. At high pressure or low temperature — near a gas’s condensation point — real gases deviate noticeably, and equations such as the van der Waals equation give better results. For everyday conditions, the ideal gas law is accurate to within a few percent.