Last updated: 2026-07-01

Understanding Avogadro's law

Avogadro's law describes how a gas expands when more of it is added and contracts when some is removed, as long as the temperature and pressure stay constant. It is one of the simple gas laws that together build up to the ideal gas law, and it captures a familiar idea: more gas takes up more room, in exact proportion to how much you add.

The Avogadro's law formula

$$\frac{V_1}{n_1} = \frac{V_2}{n_2}$$

Symbol	Quantity	Unit (this calculator)
V₁, V₂	Volume (states 1, 2)	L
n₁, n₂	Amount of gas (moles)	mol

At constant temperature and pressure the volume of a gas is directly proportional to the number of moles present. Rearranging the relationship lets you solve for whichever of the four quantities is unknown:

$$V_2 = V_1 \cdot \frac{n_2}{n_1}, \qquad n_2 = n_1 \cdot \frac{V_2}{V_1}$$

Counting particles, not mass

Avogadro's insight was that equal volumes of any gas — measured at the same temperature and pressure — contain equal numbers of molecules. That is why the amount is measured in moles rather than in grams. One mole is 6.022 × 10²³ particles, the Avogadro constant, so a mole of oxygen and a mole of helium occupy the same volume under the same conditions even though they weigh very different amounts.

Because the law is a direct proportion between volume and moles, only the ratio matters: doubling the moles doubles the volume, and halving the moles halves it.

Worked example

A sealed, flexible container holds 1.0 L of gas and contains 0.50 mol. More of the same gas is pumped in until it holds 1.25 mol, with the temperature and pressure unchanged. What is the new volume?

Apply the law and solve for the final volume:

$$\begin{aligned} V_2 &= V_1 \cdot \frac{n_2}{n_1} \\ &= 1.0 \times \frac{1.25}{0.50} \\ &= 2.5\ \text{L} \end{aligned}$$

The volume grows to 2.5 L. The amount of gas increased by a factor of 2.5 (from 0.50 to 1.25 mol), and the volume increased by exactly the same factor.

Where Avogadro's law appears

• Inflating a balloon or a bicycle tyre: adding more air (more moles) increases the volume at roughly constant pressure.
• A loaf of bread rises as yeast produces more carbon dioxide gas inside the dough.
• Breathing: drawing more air into the lungs increases their volume at nearly constant temperature and pressure.

Each of these adds or removes gas while temperature and pressure stay close to constant, which is what makes Avogadro's law the right description.

Avogadro's law and the other gas laws

Avogadro's law is the case of the ideal gas law, $PV = nRT$, where only the amount of gas and the volume change while pressure and temperature stay fixed. Boyle's law is the constant-temperature, constant-amount case relating pressure and volume, and Charles's law is the constant-pressure, constant-amount case relating volume and temperature. When pressure and temperature both change as well, use the Combined Gas Law Calculator; when you need an absolute quantity such as pressure from moles, temperature and volume, use the Ideal Gas Law Calculator.

Frequently Asked Questions (FAQ)

What is Avogadro's law?

Avogadro's law states that at constant temperature and pressure, the volume of a gas is directly proportional to the amount of gas (its number of moles): V₁/n₁ = V₂/n₂. Adding gas expands the volume in the same proportion, and removing gas shrinks it. Given three of the four values, the fourth follows directly.

Why is the amount measured in moles?

Avogadro's law counts particles, not mass. One mole is 6.022 × 10²³ particles (the Avogadro constant), so expressing the amount in moles lets the proportion compare like with like: doubling the moles doubles the volume regardless of which gas it is. This is the same reason equal volumes of two different gases at the same temperature and pressure contain equal numbers of molecules.

Where does Avogadro's law show up in everyday life?

Inflating a bicycle tyre or a balloon is the clearest case: pushing in more air (more moles) increases the volume at roughly constant pressure. A rising loaf of bread expands as yeast produces more carbon dioxide gas. Breathing works the same way — drawing more air into the lungs increases their volume. Each of these adds or removes gas at nearly constant temperature and pressure.

How does Avogadro's law relate to the other gas laws?

Avogadro's law holds temperature and pressure constant and links volume to the amount of gas. Boyle's law holds temperature and amount constant and links pressure to volume (P₁V₁ = P₂V₂). Charles's law holds pressure and amount constant and links volume to temperature (V₁/T₁ = V₂/T₂). All of them combine into the ideal gas law, PV = nRT, which contains Avogadro's law as the case where only n and V change.