Last updated: 2026-07-01

Understanding Gay-Lussac's law

Gay-Lussac's law describes how the pressure of a sealed, fixed amount of gas rises when it is warmed and falls when it is cooled, as long as the volume stays constant. It is one of the simple gas laws that together build up to the ideal gas law, and it explains a familiar warning: never heat a sealed container of gas.

The Gay-Lussac's law formula

At constant volume the pressure of a gas is directly proportional to its absolute temperature. Rearranging the relationship lets you solve for whichever of the four quantities is unknown:

Always use absolute temperature

Gay-Lussac's law is a direct proportion, so it is only valid on a temperature scale that begins at true zero. The Celsius and Fahrenheit scales place their zero points arbitrarily, so ratios taken on them are physically meaningless — warming a gas from 10 °C to 20 °C does not double its pressure, even though the Celsius number doubled.

The Kelvin scale starts at absolute zero (−273.15 °C), so a doubling of kelvin corresponds to a genuine doubling of pressure. Convert every temperature to kelvin before applying the law: $T(\text{K}) = T(^{\circ}\text{C}) + 273.15$. This calculator accepts Celsius or Fahrenheit and performs the conversion to kelvin before taking the ratio.

Worked example

A sealed rigid canister holds gas at 100 kPa when it is at 27 °C. It is left in direct sun and warms to 77 °C. What is the new pressure inside, given the volume cannot change?

First convert both temperatures to kelvin: 27 °C = 300.15 K and 77 °C = 350.15 K. Then apply the law:

The pressure rises to about 116.7 kPa. Notice that the ratio 350.15/300.15 is roughly 1.17, so the pressure climbs by about 17% — the same fraction as the rise in absolute temperature.

Where Gay-Lussac's law appears

• Aerosol cans carry a "do not incinerate" warning because heating the fixed volume inside raises the internal pressure until the can can burst.
• Car tyres read a higher pressure after a long motorway drive, as friction warms the trapped air.
• A pressure cooker builds up steam pressure because the sealed pot holds a fixed volume while the contents are heated.

Each of these happens at roughly constant volume, which is what makes Gay-Lussac's law the right description.

Gay-Lussac's law and the other gas laws

Gay-Lussac's law is the constant-volume special case of the combined gas law, $P_1 V_1 / T_1 = P_2 V_2 / T_2$. Setting $V_1 = V_2$ cancels the volume terms and leaves $P_1/T_1 = P_2/T_2$. Boyle's law is the constant-temperature case relating pressure and volume, and Charles's law is the constant-pressure case relating volume and temperature. For a problem where volume also changes, use the Combined Gas Law Calculator instead; when you need an absolute quantity such as the number of moles, use the Ideal Gas Law Calculator.