Avogadro's Law Calculator
Solve V₁/n₁ = V₂/n₂ for any missing volume or amount of gas at constant temperature and pressure. Leave one field blank, enter the other three, and get an instant result with full step-by-step working.
Avogadro's Law Solver
What Is Avogadro's Law?
Avogadro's Law captures a surprisingly simple idea: at a given temperature and pressure, volume depends only on how much gas you have. Not on what kind of gas it is. Add more moles of gas into a flexible container and its volume grows in direct proportion; remove gas and volume shrinks the same way.
Written as V₁/n₁ = V₂/n₂, this is the same simple direct-proportion shape as Charles' Law, but with moles standing in for temperature. It is also the theoretical basis for the concept of molar volume: since volume per mole is the same constant for any ideal gas at fixed T and P, one mole of any gas at standard temperature and pressure occupies the same 22.4 L.
Avogadro's Law, together with Boyle's, Charles', and Gay-Lussac's Laws, combines into the full ideal gas law, PV = nRT. Try that calculator when you need to solve for pressure, volume, moles, or temperature all at once.
Volume grows in a straight line through the origin as the amount of gas increases.
Real-World Examples of Avogadro's Law
Pumping in more gas at the same temperature and pressure grows the balloon's volume proportionally.
Every time you use a hand pump to inflate a balloon, bicycle tire, or inflatable pool toy, you are adding moles of gas at roughly constant outside pressure and temperature. And the object's volume grows in step with how much gas you have added.
In chemistry labs, Avogadro's Law justifies why stoichiometric gas-phase reactions can be tracked by volume instead of mass: if two gases react in a 1:2 mole ratio at the same temperature and pressure, they will also combine in a 1:2 volume ratio, since volume and moles track each other exactly.
It also explains why a fixed-size scuba tank can hold vastly different amounts of breathable air depending on fill pressure: more moles of gas are compressed into that same rigid volume, which is really Boyle's Law and Avogadro's Law working together.
How the Calculator Works
Worked Example: Avogadro's Law in Practice
Problem: A balloon holds 1.20 L of gas containing 0.0500 mol at room temperature and pressure. How much gas (in moles) would be needed to inflate it to 4.00 L under the same conditions?
Roughly 3.33 times more gas (0.1667 mol versus the original 0.0500 mol) is needed to reach 3.33 times the volume, exactly the direct proportionality Avogadro's Law predicts. Try the Molar Volume Calculator next to see how many liters that amount of gas would occupy at standard conditions instead of arbitrary room conditions.
Common Mistakes When Applying Avogadro's Law
The most common mistake is applying Avogadro's Law when temperature or pressure is secretly changing between the two states being compared, for instance, adding gas to a container while it also warms up. V₁/n₁ = V₂/n₂ only holds when temperature and pressure are both truly fixed; if either changes, use the ideal gas law instead.
A second pitfall is mixing up which quantity is volume and which is moles when rearranging the formula, especially when a problem gives mass instead of moles directly. Always convert mass to moles (using the substance's molar mass) before applying Avogadro's Law. The relationship is defined in terms of moles of particles, not grams of substance, and different gases have very different molar masses for the same mass of material.
A third mistake is assuming Avogadro's Law means equal masses of different gases occupy equal volumes, it does not. It's specifically equal numbers of moles (equal numbers of particles) that occupy equal volumes at fixed temperature and pressure; a mole of light helium and a mole of heavy carbon dioxide occupy the same volume, but a gram of each would not, since they have very different molar masses.