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 vs. Moles at Constant T, P 1 2 Moles (n) Volume (V)

Volume grows in a straight line through the origin as the amount of gas increases.

Real-World Examples of Avogadro's Law

Inflating with a Pump Fewer moles More moles

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

1. Pick the unknown
Select V₁, n₁, V₂, or n₂ as the value you want solved.
2. Fill in the rest
Enter the other three values in any supported unit.
3. Get instant results
The answer and a full substitution walkthrough appear immediately.

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?

Given: V₁ = 1.20 L, n₁ = 0.0500 mol, V₂ = 4.00 L. Find: n₂. Avogadro's Law: V₁/n₁ = V₂/n₂ → n₂ = V₂n₁ / V₁ n₂ = (4.00 × 0.0500) / 1.20 n₂ ≈ 0.1667 mol

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.

Avogadro's Law 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 number of moles of gas present: V₁/n₁ = V₂/n₂. Double the amount of gas at the same temperature and pressure, and its volume doubles too. It is named after Amedeo Avogadro, who proposed it in 1811.
What is the formula for Avogadro's Law?
The formula is V₁/n₁ = V₂/n₂, where V₁ and n₁ are the initial volume and moles, and V₂ and n₂ are the final volume and moles. Rearranged: V₂ = V₁n₂/n₁, or n₂ = n₁V₂/V₁. This calculator solves for whichever of the four values you leave blank.
How is Avogadro's Law different from Boyle's, Charles', and Gay-Lussac's Laws?
Boyle's, Charles', and Gay-Lussac's Laws all describe a fixed amount of gas as pressure, volume, or temperature change. Avogadro's Law is the odd one out: it holds pressure and temperature constant and instead varies the amount of gas itself (moles), showing that volume depends on quantity of gas in the same simple, direct way it depends on temperature.
What units does this Avogadro's Law calculator support?
Volume can be entered in m³, L, mL, cm³, dm³, ft³, in³, or gal (US). Moles can be entered in mol, mmol, or kmol. Mix units freely across the four fields. The calculator converts internally before solving.
How does Avogadro's Law relate to molar volume?
Avogadro's Law implies that equal volumes of any ideal gas, at the same temperature and pressure, contain equal numbers of moles. Which is exactly why one mole of any ideal gas occupies the same volume (22.4 L at STP) regardless of what gas it is. See our dedicated Molar Volume Calculator to explore that relationship directly.
What is a real-world example of Avogadro's Law?
Inflating a balloon with a hand pump adds more gas molecules (more moles) at roughly constant atmospheric pressure and room temperature, and the balloon's volume grows in direct proportion to how much gas you have pumped in, a hands-on demonstration of V ∝ n.
How did Avogadro arrive at this law without being able to count molecules directly?
In 1811, Amedeo Avogadro proposed his hypothesis purely from careful measurements of how gas volumes combined in chemical reactions, decades before anyone could observe individual molecules. He reasoned that if equal volumes of different gases always combined in simple whole-number ratios, the simplest explanation was that equal volumes contained equal numbers of particles, a genuinely bold inference that took nearly 50 years to be widely accepted by other chemists.
How do I know if a problem needs Avogadro's Law or the ideal gas law?
If you are comparing two states of gas where only volume and the amount of gas change (temperature and pressure both fixed), Avogadro's Law alone is enough. If temperature or pressure also change, or if you need to find an absolute value like pressure or moles rather than just a ratio, use the ideal gas law (PV = nRT) instead.

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