Gay-Lussac's Law Calculator
At constant volume and constant amount of gas, pressure divided by absolute temperature stays constant. Enter any 3 of P₁, T₁, P₂, T₂ below and the calculator solves the missing one instantly — temperatures you enter in °C or °F are converted to kelvin automatically, and you can mix pressure units freely.
Fill any 3 of the 4 fields — the empty one is solved automatically.
Gay-Lussac constant k = P₁/T₁ = — Pa/K
How it works — worked example
- Convert temperatures to kelvin first (already kelvin here): T₁ = 300 K, T₂ = 350 K. Never plug °C directly into the law.
- Compute the Gay-Lussac constant: k = P₁/T₁ = 100 kPa / 300 K = 0.333333 kPa/K.
- Rearrange for the unknown: P₂ = k × T₂ = 0.333333 × 350 = 116.667 kPa.
- Heating the gas from 300 K to 350 K raises the pressure from 100 kPa to 116.667 kPa — a factor of 350/300 = 1.1667, about 16.7% growth.
Assumptions: volume and the amount of gas stay constant (a rigid sealed container), and the gas behaves ideally. Real gases deviate at very high pressures or near condensation — see the FAQ.
Pressure unit reference
| Unit | = Pa | = kPa |
|---|---|---|
| Pa | 1 | 0.001 |
| kPa | 1,000 | 1 |
| bar | 100,000 | 100 |
| psi | 6,894.757 | 6.89476 |
| atm | 101,325 | 101.325 |
| mmHg | 133.322 | 0.133322 |
Exact definitions: 1 atm = 101,325 Pa; 1 bar = 100,000 Pa; 1 psi = 6,894.757293168 Pa; 1 mmHg = 133.322387415 Pa. So 1 atm = 14.6959 psi = 759.9999 mmHg (about 760).
Frequently asked questions
What is Gay-Lussac's law?
Gay-Lussac's law says that for a fixed amount of gas at constant volume, pressure is directly proportional to absolute temperature: P₁/T₁ = P₂/T₂. Heat a sealed rigid container and the pressure rises by the same fraction as the temperature in kelvin; cool it and the pressure falls. It was published by Joseph Louis Gay-Lussac in 1802 (Guillaume Amontons had found the same relationship around 1702, so it is also called Amontons's law), and it is one of the three classical gas laws.
Why must the temperature be in kelvin?
This is the classic trap: the law only works with an absolute scale. Heating gas from 20 °C to 80 °C is not a fourfold temperature increase — in kelvin it is 293.15 K to 353.15 K, a factor of only 1.2047, so the pressure rises by about 20.5%, not 300%. Plugging °C straight in gives nonsense. The calculator above converts °C and °F to kelvin for you before applying P₁/T₁ = P₂/T₂.
How do you calculate the final pressure (P₂)?
Rearrange the law to P₂ = P₁T₂ / T₁. Example: gas at 100 kPa and 300 K is heated to 350 K, so P₂ = 100 × 350 / 300 = 116.667 kPa — the pressure grows by the same 350/300 = 1.1667 factor as the absolute temperature. Enter any three values in the calculator above and it solves the fourth.
How do you find the final temperature (T₂)?
Use T₂ = T₁P₂ / P₁. Example: gas at 2 atm and 273.15 K (0 °C) is pressurized to 3 atm at constant volume, so T₂ = 273.15 × 3 / 2 = 409.725 K = 136.575 °C. The calculator shows the answer in whichever unit you pick — °C, °F or K — plus a full conversion table.
What pressure units can I use?
Pa, kPa, bar, psi, atm or mmHg — you can even mix units, e.g. P₁ in psi with P₂ in kPa, because everything is converted to SI internally. Exact definitions: 1 atm = 101,325 Pa = 101.325 kPa = 1.01325 bar; 1 bar = 100,000 Pa; 1 psi = 6,894.757293168 Pa; 1 mmHg = 133.322387415 Pa. So 1 atm = 14.6959 psi = 759.9999 mmHg (about 760). Temperature: °C, °F or K, converted to kelvin first (°F to kelvin is (T − 32) × 5/9 + 273.15, so 68 °F = 20 °C = 293.15 K).
What must stay constant for Gay-Lussac's law to apply?
Two things: the volume and the amount of gas. Think of a rigid sealed container — a gas cylinder, a pressure cooker, a car tire holding its shape — so no gas escapes and the volume cannot change. If the volume changes while you heat the gas, P₁/T₁ will not equal P₂/T₂ and the calculator’s consistency check will flag the mismatch (for varying volume at constant pressure, use Charles’s law instead; for varying pressure at constant temperature, use Boyle’s law).
Can temperature be zero or negative kelvin in the calculator?
No — all temperatures must be above absolute zero (> 0 K). Zero kelvin is unreachable in practice, and negative kelvin has no physical meaning here, so the calculator rejects both with an honest error. Pressures must be positive numbers as well.
How is Gay-Lussac's law different from Boyle's and Charles's laws?
Each classical gas law holds one variable constant and relates the other two. Gay-Lussac's law holds volume constant and relates pressure to temperature (P₁/T₁ = P₂/T₂). Boyle's law holds temperature constant and relates pressure to volume (P₁V₁ = P₂V₂). Charles's law holds pressure constant and relates volume to temperature (V₁/T₁ = V₂/T₂). When pressure, volume and temperature all change, combine them as P₁V₁/T₁ = P₂V₂/T₂ — together they are the ideal gas law PV = nRT.
Where is Gay-Lussac's law used in real life?
Anywhere a fixed amount of gas is heated or cooled in a rigid container: car tires reading higher pressure after driving on a hot day (and lower on cold mornings), pressure cookers and autoclaves, aerosol spray cans carrying a do-not-heat warning, scuba and welding gas cylinders left in the sun, and fire-suppression systems rated for temperature swings.
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