Gay-Lussac's Law Calculator (P₁/T₁ = P₂/T₂)
By Santaji GadepatilinUpdated October 30, 2026
In a sealed, rigid container the pressure of a gas rises in direct proportion to its absolute temperature. This Gay-Lussac's law calculator finds the final pressure after heating or cooling — or the temperature that produces a given pressure — for gas cylinders, aerosol cans, tyres and sealed vessels.
How to use the Gay-Lussac’s law calculator
Enter the initial absolute pressure and temperature, and the final temperature. The calculator gives the final absolute pressure. Enter any three of the four values to solve for the fourth — for example, the temperature at which a vessel reaches its design pressure.
Gay-Lussac’s law formula
P1 ÷ T1 = P2 ÷ T2 ⇒ P2 = P1 × T2 ÷ T1
Temperatures are absolute (K = °C + 273.15) and pressures absolute.
Example
A sealed container holds gas at 200 kPa absolute and 20 °C. It is heated to 80 °C:
- T1 = 293.15 K, T2 = 353.15 K
- P2 = 200 × 353.15 ÷ 293.15 = 240.93 kPa absolute (139.6 kPa gauge)
Pressure of a gas sealed at 200 kPa(a) and 20 °C
| Temperature | P ÷ P₁ | Absolute pressure | Gauge pressure |
|---|---|---|---|
| -20 °C | 0.864 | 172.7 kPa | 71.4 kPa |
| 0 °C | 0.932 | 186.4 kPa | 85.0 kPa |
| 20 °C | 1.000 | 200.0 kPa | 98.7 kPa |
| 40 °C | 1.068 | 213.6 kPa | 112.3 kPa |
| 60 °C | 1.136 | 227.3 kPa | 126.0 kPa |
| 80 °C | 1.205 | 240.9 kPa | 139.6 kPa |
| 100 °C | 1.273 | 254.6 kPa | 153.3 kPa |
| 150 °C | 1.443 | 288.7 kPa | 187.4 kPa |
Notes
- Real gases follow the law well at moderate pressures; near condensation or at very high pressure use a compressibility factor.
- Liquids trapped in a closed pipe behave very differently — thermal expansion of a liquid can raise pressure by several bar per °C, which is why thermal relief valves are fitted.
- To change pressure, volume and temperature together, use the combined gas law calculator.
Frequently asked questions
What is Gay-Lussac's law?
At constant volume and amount of gas, pressure is proportional to absolute temperature — P₁ ÷ T₁ = P₂ ÷ T₂. It is also called Amontons's law or the pressure law.
Must I use absolute pressure?
Yes. Gauge pressure is measured from atmosphere, not from zero, so add atmospheric pressure (about 101.3 kPa) first. Temperatures are converted to kelvin automatically.
Why do aerosol cans warn against heat?
Pressure rises with absolute temperature. A can at 20 °C heated to 80 °C sees its pressure rise by about 20%, and much more if liquid propellant evaporates.
How is Gay-Lussac's law different from Charles's law?
Charles's law holds pressure constant and relates volume to temperature; Gay-Lussac's law holds volume constant and relates pressure to temperature.