Gay-Lussac's Law Calculator
Find final gas pressure at constant volume.
Results update as you type.
How it works
Gay-Lussac's law describes how the pressure of a fixed volume of gas changes with temperature, and this calculator finds the final pressure. You enter the initial pressure, the initial temperature, and the final temperature, both temperatures in kelvin, and it returns the final pressure. The law states that at constant volume, pressure is directly proportional to absolute temperature: heat a sealed rigid container and the pressure rises, cool it and the pressure falls. Doubling the absolute temperature doubles the pressure. This is why aerosol cans warn against heating, why tire pressure rises on hot days and after driving, and why sealed containers can burst if heated. It is one of the fundamental gas laws and a special case of the ideal gas law with volume and amount of gas held constant. The single most important rule is that temperature must be in kelvin, the absolute scale, not Celsius or Fahrenheit, because the proportionality only holds from absolute zero; using Celsius would give badly wrong answers. To convert, add 273.15 to a Celsius temperature. Pressure can be in any consistent unit since the calculation uses the temperature ratio. Enter the initial pressure and both temperatures in kelvin to compute the final pressure.
P₁/T₁ = P₂/T₂ → P₂ = P₁ × T₂ / T₁
Gay-Lussac's law states that for a fixed amount of gas at constant volume, pressure is directly proportional to absolute temperature. So the initial pressure divided by initial temperature equals the final pressure divided by final temperature. The final pressure equals the initial pressure times the ratio of final to initial temperature, which must be in kelvin.
Source:Chemistry (gas laws)
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Worked example
How to use this calculator
- 1
Enter your values
Enter initial pressure (p₁), initial temperature (t₁) and final temperature (t₂).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Final pressure (P₂) updates instantly as you type — no button to press.
Frequently asked questions
What is Gay-Lussac's law?
Gay-Lussac's law states that the pressure of a fixed amount of gas at constant volume is directly proportional to its absolute temperature. As temperature rises, pressure rises in proportion, and as it falls, pressure falls. It describes how sealed, rigid containers of gas respond to heating and cooling.
Why must temperature be in kelvin?
The proportionality between pressure and temperature holds only on an absolute scale that starts at absolute zero, which is kelvin. Celsius and Fahrenheit have arbitrary zero points, so using them breaks the ratio and gives wrong results. Always convert to kelvin by adding 273.15 to Celsius before applying the law.
How do you calculate the final pressure?
Multiply the initial pressure by the ratio of the final temperature to the initial temperature, with both temperatures in kelvin. So final pressure equals initial pressure times final temperature divided by initial temperature. Enter the three values and the calculator computes the final pressure, ensuring you use kelvin for both temperatures.
What are real-world examples?
Gay-Lussac's law explains why aerosol cans warn against incineration, since heating raises internal pressure until they burst, why car tire pressure increases on hot days and after driving heats the tires, and why pressure cookers and sealed vessels build pressure as they are heated at fixed volume.
How is it related to the other gas laws?
Gay-Lussac's law is the constant-volume case of the ideal gas law, just as Boyle's law is the constant-temperature case and Charles's law is the constant-pressure case. Together these combine into the combined gas law and ultimately the ideal gas law, which relates pressure, volume, temperature, and amount of gas all at once.