The Avogadro's law calculator above solves V₁ ÷ n₁ = V₂ ÷ n₂, the relationship between the volume of a gas and the amount of gas present when pressure and temperature are both held fixed. Enter any three of the four quantities and it returns the fourth, along with the molar volume, the change in volume and the amount of gas that had to be added or removed.
Arb Digital publishes the whole gas law family as separate tools, and this page is the member that solves for amount of substance. Each of the others holds something different constant: the Boyle's law calculator holds temperature and amount fixed and relates pressure to volume; the Charles's law calculator holds pressure and amount fixed and relates volume to temperature; the Gay-Lussac's law calculator holds volume and amount fixed and relates pressure to temperature; the combined gas law calculator holds only the amount fixed and links all three; and the ideal gas law calculator holds nothing fixed and solves PV = nRT outright. This page is the one that lets the amount change.
What This Avogadro's Law Calculator Does
Avogadro's law states that at fixed pressure and temperature the volume of a gas is directly proportional to the number of moles present. Add gas and the volume grows in exact proportion; remove gas and it shrinks the same way. The ratio V ÷ n is therefore a constant for a given pressure and temperature, and that constant is the molar volume.
The remarkable part of the law is what it leaves out. It makes no reference to which gas you have. Equal volumes of two different gases at the same pressure and temperature contain the same number of molecules, whether they are hydrogen or sulphur hexafluoride. Mass differs enormously between those two; molecule count does not.
The tool solves in all four directions, reports the molar volume so you can see the proportionality constant directly, and gives the change in volume both absolutely and as a percentage. If you supply a molar mass it also converts the change in moles into a change in mass, because a cylinder is filled by weight rather than by mole count.
How to Use It
- Confirm pressure and temperature really are constant. This is the assumption the whole law rests on. A vessel that heats up as it fills is not a constant-temperature process.
- Pick which quantity you are solving for. The corresponding input box is ignored, so you do not need to clear it.
- Keep both volumes in the same unit. The law is a ratio, so litres against litres or cubic metres against cubic metres both work, but litres against millilitres does not.
- Use moles, not mass, for the amount. If you have a mass, divide by the molar mass first, or use the molar mass box to see the mass equivalent of the answer.
- Read the molar volume as a sanity check. At ordinary room conditions it should land near 24 litres per mole, and a wildly different figure usually means a unit slip.
The Formula: How Avogadro's Law Is Calculated
The law is V ∝ n at constant pressure and temperature, which for two states becomes V₁ ÷ n₁ = V₂ ÷ n₂. Rearranged for each unknown: V₂ = V₁n₂ ÷ n₁, n₂ = n₁V₂ ÷ V₁, V₁ = V₂n₁ ÷ n₂, and n₁ = n₂V₁ ÷ V₂.
OpenStax Chemistry 2e, section 9.2 on relating pressure, volume, amount and temperature, states the law directly: for a confined gas, volume and number of moles are directly proportional if pressure and temperature both remain constant. The same section shows how Boyle's, Charles's, Amontons's and Avogadro's laws combine into PV = nRT, which is worth reading because it makes clear that the four laws are four slices of one relationship rather than four separate discoveries.
The mole itself is now defined by fixing the Avogadro constant. The NIST CODATA value for the Avogadro constant is exactly 6.02214076 × 1023 per mole, an exact number since the 2019 redefinition of the SI base units rather than a measured one.
Work the defaults by hand. Starting with 2.00 L of gas containing 0.500 mol, the molar volume is 2.00 ÷ 0.500 = 4.00 L/mol. Going to 0.800 mol at the same pressure and temperature gives V₂ = 2.00 × 0.800 ÷ 0.500 = 3.20 L. The volume has grown by 1.20 L, which is a 60 per cent increase, exactly matching the 60 per cent increase in moles from 0.500 to 0.800. If the gas were oxygen at 32 g/mol, the 0.300 mol added would weigh 9.60 g.
Molar Volume and the Two Different STPs
Because V ÷ n is fixed at a given pressure and temperature, that ratio has a name: the molar volume. It is the volume one mole of any ideal gas occupies under those conditions, and it is where the familiar textbook numbers come from.
There are two of them, and mixing them up is a classic exam mistake. At 0 °C and 100 kPa, the modern IUPAC standard conditions, one mole occupies 22.711 L. At 0 °C and 101.325 kPa, the older one-atmosphere convention, it occupies 22.414 L. Both come straight from RT ÷ P and differ only because the pressure convention changed. At 25 °C and 100 kPa, which is closer to a real laboratory, the figure is about 24.8 L/mol.
The useful habit is to derive the molar volume rather than recall it. Divide the gas constant times the absolute temperature by the pressure and you have it, in whatever units you are working in, with no risk of quoting a value for conditions you are not actually at. The ideal gas law calculator does that step for you.
Why Gas Identity Does Not Enter the Calculation
Avogadro's hypothesis was radical when he proposed it in 1811 and was largely ignored for fifty years, because it seemed obvious that a heavy molecule should take up more room than a light one. It does not, and the reason is that gas volume is almost entirely empty space.
In a gas at ordinary conditions the molecules occupy something on the order of a thousandth of the volume they move around in. What sets the volume is not the size of the molecules but how far apart they stay, and that spacing is fixed by the balance between thermal energy and the pressure pushing in. Both of those are held constant here, so the spacing is constant, so the volume simply counts molecules.
This is why a mole of hydrogen and a mole of sulphur hexafluoride occupy the same volume at the same conditions despite a mass ratio of more than seventy to one. It is also why gas density varies so widely between gases while gas molar volume does not: density is molar mass divided by molar volume, and only the numerator changes. Use the molar mass calculator to get the molar mass for a formula when you need to move between amount and mass.
Where the Proportionality Fails
Avogadro's law is exact for an ideal gas and approximate for a real one. The two assumptions behind it are that molecules have no volume of their own and that they do not attract each other, and both fail as gases are compressed or cooled.
At high pressure the finite size of the molecules starts to matter, and the gas occupies more volume than the law predicts because the molecules themselves take up space. At low temperature attraction between molecules pulls them closer than the ideal case, and the volume comes out lower. Near the point where a gas condenses, the law stops being a useful description at all.
The practical rule is that ordinary gases at around atmospheric pressure and room temperature follow the law closely enough that the error is smaller than most measurement error. Move to tens of atmospheres, or near the boiling point, and a compressibility factor becomes necessary. The compressibility factor calculator handles that correction, and the partial pressure calculator is the right tool once you have a mixture rather than a single gas.
One more limit is worth stating plainly: the law says nothing about chemical change. If the gas reacts, the number of moles changes for reasons that have nothing to do with adding or removing material, and you need the stoichiometry before this calculation means anything.
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Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using it when temperature or pressure changed — Avogadro's law holds both constant. If either moved, the combined gas law or the ideal gas law is the right tool.
- Putting mass in the moles box — the proportionality is with amount of substance, not mass. Two gases of equal mass have very different mole counts and therefore very different volumes.
- Mixing volume units between the two states — the ratio only cancels if both sides use the same unit. Litres against millilitres gives an answer wrong by a thousand.
- Quoting 22.4 litres per mole for room temperature — that figure is for 0 °C at one atmosphere. At 25 °C the molar volume is nearer 24.8 L/mol, which is a ten per cent difference.
- Applying it across a chemical reaction — if the gas reacts, the mole count changes through stoichiometry rather than through adding material, and this relationship no longer describes what happened.
Related Free Tools From Arb Digital
Work through the rest of the family with the Boyle's law calculator for pressure against volume, the Charles's law calculator for volume against temperature, the Gay-Lussac's law calculator for pressure against temperature, the combined gas law calculator when all three move, and the ideal gas law calculator for PV = nRT itself. For the substance side, use the molar mass calculator. For mixtures use the partial pressure calculator, and for non-ideal behaviour use the compressibility factor calculator. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
It states that at constant pressure and temperature the volume of a gas is directly proportional to the number of moles present. Written for two states it is V one over n one equals V two over n two, so doubling the amount of gas doubles the volume.
Each law holds different quantities constant. Boyle's holds temperature and amount and links pressure to volume. Charles's holds pressure and amount and links volume to temperature. Gay-Lussac's holds volume and amount and links pressure to temperature. The combined gas law holds only amount fixed, and the ideal gas law holds nothing fixed. Avogadro's is the one that lets the amount change.
No. Equal volumes of any two ideal gases at the same pressure and temperature contain the same number of molecules, regardless of molecular mass or size. That is the whole content of Avogadro's hypothesis, and it holds because a gas is mostly empty space.
It is the volume one mole occupies at a stated pressure and temperature, equal to the constant ratio of volume to moles. At 0 degrees Celsius and 100 kilopascals it is 22.711 litres per mole; at 0 degrees Celsius and one atmosphere it is 22.414 litres per mole; at 25 degrees Celsius and 100 kilopascals it is about 24.8.
Not directly. The proportionality is with amount of substance, so convert mass to moles by dividing by the molar mass first. If you enter a molar mass in this tool it will show you the mass equivalent of the change in moles, which is what you would actually weigh out.
When the gas stops behaving ideally, which happens at high pressure where molecular volume matters and at low temperature where intermolecular attraction matters. Near condensation it fails outright. At around atmospheric pressure and room temperature the error is usually smaller than measurement error.
Because the 2019 revision of the SI defined the mole by fixing the Avogadro constant at exactly 6.02214076 times ten to the twenty-third per mole. It is a defined value rather than a measured one, in the same way the speed of light is.
This tool is provided for educational and study use. It applies ideal gas behaviour at constant pressure and temperature, and does not account for non-ideal compressibility, condensation, dissolution or chemical reaction, so treat its output as a chemistry result rather than a process design value.
