Solve V₁/n₁ = V₂/n₂ instantly. Enter any three values and the calculator fills in the fourth, at constant temperature and pressure.
Computed from the other three values.
Final Volume
V₂ = 12.5 L
V₂ = V₁ × n₂ / n₁ = (5 L × 0.5 mol) / 0.2 mol = 12.5 L
Avogadro’s law states that the volume of a gas is directly proportional to the amount of gas it contains, measured in moles, when temperature and pressure are held constant. In equation form: V ∝ n, or equivalently V/n = constant. For two states of the same gas — or even two different gases — at the same temperature and pressure, this gives the two-point form V₁/n₁ = V₂/n₂.
Definition
Avogadro’s law states that equal volumes of gas, at the same temperature and pressure, contain equal numbers of molecules — regardless of which gas it is. Pump in more gas at fixed T and P, and the volume expands to match, in exact proportion to the amount added.
The law is named after Amedeo Avogadro, who hypothesised in 1811 that equal volumes of gas at the same temperature and pressure contain equal numbers of molecules, regardless of the gas’s identity. That was a striking claim at the time — it meant volume alone, under matched conditions, was a stand-in for a molecule count, decades before anyone could measure molecules directly. It's a very different relationship from the one on our Charles' law solver, which holds the amount of gas fixed and instead relates volume to temperature.
Avogadro’s law is a special case of the Ideal Gas Law, PV = nRT: when pressure P and temperature T are both fixed, dividing both sides by n and rearranging leaves V/n = RT/P = constant on the right — Avogadro’s law exactly. The ideal gas law is the more general tool precisely because it treats n as a full variable alongside P, V, and T, rather than assuming it's fixed.
The formula V₁/n₁ = V₂/n₂ works with volume in any consistent unit — litres, millilitres, cubic metres, or cubic feet — as long as both volumes use the same one for the comparison to mean anything. If your two volumes started out in different units, run them through the volume converter first so V₁ and V₂ are easy to compare by eye before you even open this calculator. Amount of gas is always in moles, so there's no unit dropdown for n₁ and n₂ — just a plain positive number.
Rearranged for whichever value is unknown: V₂ = V₁ × n₂ / n₁, V₁ = V₂ × n₁ / n₂, n₂ = n₁ × V₂ / V₁, and n₁ = n₂ × V₁ / V₂. The calculator above picks the right rearrangement automatically based on which field you leave blank.
A useful constant falls straight out of Avogadro’s law: since V/n is the same for any ideal gas at a given temperature and pressure, there's a single "molar volume" that applies universally under those conditions. At standard temperature and pressure — 0 °C and 1 atm, abbreviated STP — that molar volume works out to about 22.4 L/mol. One mole of helium, one mole of nitrogen, and one mole of carbon dioxide all occupy roughly the same 22.4 L at STP, even though their molecules have very different masses. What's actually equal is the count of molecules — about 6.022 × 10²³ of them, known as Avogadro's number — packed into that volume, not their combined weight.
| Symbol | Meaning | Unit |
|---|---|---|
| V₁ | Initial volume | L, mL, m³, ft³ |
| n₁ | Initial amount of gas | mol |
| V₂ | Final volume | L, mL, m³, ft³ |
| n₂ | Final amount of gas | mol |
Example 1
A balloon holds V₁ = 5 L of gas containing n₁ = 0.2 mol. More gas is pumped in until n₂ = 0.5 mol, at the same temperature and pressure. Find the new volume.
The amount of gas increased two-and-a-half-fold, from 0.2 to 0.5 mol, and the volume grew by exactly the same factor — 5 L to 12.5 L — the direct proportionality Avogadro’s law predicts.
Example 2
At standard temperature and pressure, one mole of ideal gas occupies 22.4 L. Starting from V₁ = 22.4 L with n₁ = 1 mol, how much volume would n₂ = 3 mol occupy at the same T and P?
Tripling the moles triples the volume, landing right at 67.2 L — exactly three times the 22.4 L/mol molar volume constant, confirming the proportional relationship holds.
Avogadro’s law is the odd one out among the classic single-variable gas laws, because it's the only one that lets the amount of gas itself change. Boyle’s law holds temperature and moles fixed and relates pressure to volume. Charles’ law holds pressure and moles fixed and relates volume to temperature. Avogadro’s law flips that around: it holds temperature and pressure fixed, and relates volume to the moles those other two laws treat as a constant.
The combined gas law calculator handles pressure, volume, and temperature all changing together, but it still assumes a fixed amount of gas — the moles term drops out of P₁V₁/T₁ = P₂V₂/T₂ entirely. If the amount of gas itself is what's changing in your scenario — gas being added to or removed from a container — Avogadro’s law, not the combined gas law, is the tool to reach for. And if pressure, volume, temperature, and moles are all in play at once, the ideal gas law calculator is the fully general version that covers every combination.
Avogadro’s law states that the volume of a gas is directly proportional to the amount of gas (in moles) when temperature and pressure are held constant: add more gas at the same T and P, and the volume grows in exact proportion.
V₁/n₁ = V₂/n₂, where V₁ and n₁ are the initial volume and amount of gas, and V₂ and n₂ are the final volume and amount of gas, both measured at the same temperature and pressure.
Molar volume is the volume one mole of gas occupies at a given temperature and pressure. At standard temperature and pressure (0 °C, 1 atm), that volume is about 22.4 L/mol for any ideal gas — a direct consequence of Avogadro’s law, since the volume-per-mole ratio V/n stays constant regardless of which gas it is.
Use V₂ = V₁ × n₂ / n₁, keeping temperature and pressure fixed. If n₂ is larger than n₁, the volume grows by the same factor — that’s the direct proportionality Avogadro’s law describes.
Avogadro’s law is a special, two-point case where temperature and pressure are both held constant and only volume and moles change. The ideal gas law, PV = nRT, is the general relationship between all four variables — pressure, volume, moles, and temperature — with no restriction on which ones move.
Closely, at ordinary temperature and pressure — most common gases behave near-ideally under everyday lab conditions. Deviations show up at very high pressure or very low temperature, where intermolecular forces and molecular volume start to matter, similar to the corrections the Van der Waals equation applies.
Because V/n is the same constant for every ideal gas at a given temperature and pressure, two different gases occupying the same volume under the same conditions must contain the same number of molecules — regardless of what the gas actually is or how heavy its molecules are.
Need a different variable held constant, or want to convert your inputs first? These companion tools cover the rest of the gas law family.