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Long before anyone knew gases were made of molecules, experimenters in the 1600s and 1700s were measuring how gases responded when you squeezed them, heated them or sealed them in a container. The patterns they found are called the gas laws, and each one holds one property constant while two others change.
They’re still the clearest way to understand how gases behave.
Boyle’s law: pressure and volume
At constant temperature, the pressure of a fixed amount of gas is inversely proportional to its volume.
P₁V₁ = P₂V₂
Robert Boyle published this in 1662 using a J-shaped glass tube with air trapped in the short end. Pouring mercury into the long end compressed the air, and he found that doubling the pressure halved the volume.
Why it happens: gas pressure comes from molecules hitting the container walls. Squeeze the same molecules into half the space and they hit each wall twice as often.
Where you see it: pushing the plunger of a sealed syringe gets harder the further you push. A diver’s lungs would expand dangerously if they held their breath while ascending, because the surrounding pressure drops — which is why divers are taught never to do it.
Example: A balloon holds 4.0 L of air at 1.0 atm. It’s taken down to where the pressure is 2.5 atm (at constant temperature). New volume: V₂ = P₁V₁ ÷ P₂ = 1.0 × 4.0 ÷ 2.5 = 1.6 L.
Charles’s law: volume and temperature
At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature.
V₁ ÷ T₁ = V₂ ÷ T₂
Jacques Charles investigated this around 1787 (he was also a hot-air and hydrogen balloon pioneer), though he didn’t publish it; Joseph Louis Gay-Lussac published careful measurements in 1802 and credited Charles.
Why it happens: hotter molecules move faster and hit the walls harder. To keep the pressure the same, the gas must spread out into a larger volume.
Where you see it: a hot-air balloon rises because heated air expands and becomes less dense than the air around it. A balloon taken from a warm room into a freezer visibly shrinks.
Example: A gas occupies 2.00 L at 27 °C. What’s its volume at 127 °C, same pressure? Convert first: 300.15 K and 400.15 K. V₂ = 2.00 × 400.15 ÷ 300.15 = 2.67 L. (Using Celsius would give 2.00 × 127 ÷ 27 = 9.4 L, which is badly wrong.)
Gay-Lussac’s law: pressure and temperature
At constant volume, the pressure of a fixed amount of gas is directly proportional to its absolute temperature.
P₁ ÷ T₁ = P₂ ÷ T₂
(You’ll sometimes see this one attributed to Guillaume Amontons, who observed the relationship around 1700, and the naming varies between countries and textbooks.)
Why it happens: in a rigid container the gas can’t expand, so faster, harder-hitting molecules simply mean higher pressure.
Where you see it: aerosol cans warn you never to heat them. Tyre pressure drops on a cold morning and rises after a long drive. A pressure cooker’s sealed volume lets pressure climb as it heats.
Example: A tyre is at 220 kPa at 10 °C. After driving, the air inside reaches 40 °C. New pressure: 220 × 313.15 ÷ 283.15 = 243 kPa, about a 10% rise.
The combined gas law
The three laws fit together into one equation for a fixed amount of gas:
P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂
Each individual law is just this equation with one variable held constant — cancel T for Boyle, P for Charles, V for Gay-Lussac. So in practice you only need to remember this one.
Example: A weather balloon holds 5.00 m³ of helium at 100 kPa and 20 °C at ground level. At altitude the pressure is 30 kPa and the temperature −40 °C. What’s the new volume?
V₂ = P₁V₁T₂ ÷ (P₂T₁) = (100 × 5.00 × 233.15) ÷ (30 × 293.15) = 13.3 m³
The balloon nearly triples in size — which is exactly why weather balloons are launched only partly inflated.
Avogadro’s law and the ideal gas law
A fourth relationship completes the picture: at constant temperature and pressure, volume is proportional to the number of moles (Avogadro’s law, 1811). Combine it with the other three and you get the ideal gas law, PV = nRT, which works even when the amount of gas changes.
The rule that matters most
All gas law calculations need temperature in kelvin. Celsius and Fahrenheit have arbitrary zero points, so ratios of Celsius temperatures are meaningless. Add 273.15 to Celsius every time — it’s the most common source of wrong answers in this topic.
Pressure and volume can be in any units, as long as each appears in the same unit on both sides.
Quick answers
Which gas law has an inverse relationship? Boyle’s law. Pressure goes up as volume goes down.
What does “fixed amount of gas” mean? No gas enters or leaves. If gas is added or removed, use PV = nRT instead.
Do these laws work for all gases? For ideal gases exactly, and for real gases approximately — very well at ordinary temperatures and pressures.
Try it
The ideal gas law calculator has a combined gas law mode: leave one of the six boxes empty and it solves for it. For Boyle’s, Charles’s or Gay-Lussac’s law, give the constant quantity the same value in both states.
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