Gay-Lussac's Law Calculator

Gay-Lussac’s law states that the pressure of a fixed mass of gas is directly proportional to its absolute temperature when volume is held constant. In equation form: P ∝ T, or equivalently P/T = constant. For two states of the same gas at constant volume, this gives the two-point form P₁/T₁ = P₂/T₂. Every temperature in that equation has to be an absolute value in kelvin — plug in Celsius or Fahrenheit directly and the ratio breaks, which is why this calculator always converts to kelvin before dividing and shows that converted value in the substitution line. If you'd rather sanity-check a temperature by eye across scales first, the temperature converter handles that conversion on its own.

The law is named after Joseph Louis Gay-Lussac, who published the pressure–temperature relationship in 1808. It's the third of the three single-variable gas laws, alongside the Charles' law tool above and Boyle's law — and Gay-Lussac's name is attached to two related but distinct pieces of gas-law history. This exact pressure–temperature relationship is often credited to him, though some historians note the constant-volume observation had earlier roots with Guillaume Amontons. Separately, Gay-Lussac also published a version of what's now called the combined gas law, building on the constant-pressure work already associated with Jacques Charles. The two contributions are related but not the same thing, so it's worth keeping them apart when you see his name cited for either one.

Gay-Lussac’s law is a special case of the Ideal Gas Law, PV = nRT: when the amount of gas n and volume V are both fixed, P/T reduces to a constant — Gay-Lussac’s law exactly.

The relationship shows up anywhere a gas is sealed inside a container that can't expand or contract in response to heat: an aerosol can left in a hot car, the propellant inside a fire extinguisher, or the working gas in a constant-volume gas thermometer, where the pressure reading is used to infer temperature rather than the other way around. It's also the reason pressure-relief valves exist on sealed vessels — past a certain temperature rise, the pressure predicted by this law would exceed what the container can safely hold, so the valve vents gas before that happens.

The formula P₁/T₁ = P₂/T₂ works with pressure entered in kilopascals, atmospheres, millimetres of mercury, or pounds per square inch — pick whichever unit matches your source data, since the ratio cancels the unit either way. Temperature is different: both T₁ and T₂ must be absolute values, so every field is converted to kelvin internally regardless of whether you typed kelvin, Celsius, or Fahrenheit, and a value at or below absolute zero is rejected outright.

Rearranged for whichever value is unknown: P₂ = P₁ × T₂ / T₁, P₁ = P₂ × T₁ / T₂, T₂ = T₁ × P₂ / P₁, and T₁ = T₂ × P₁ / P₂. The calculator above picks the right rearrangement automatically based on which field you leave blank, and always displays a solved temperature in kelvin in the substitution line underneath the headline answer.

Gay-Lussac’s law holds volume and the amount of gas constant and relates pressure to temperature. That constant-volume condition is called an isochoric process, and it's a direct match: this is exactly the isochoric process — for the associated heat transfer at constant volume, see the isochoric process calculator.

Compare that with the other two single-variable laws. Charles’ law holds pressure constant and relates volume to temperature instead (an isobaric process), and Boyle’s law holds temperature constant and relates pressure to volume (an isothermal process). Each page assumes one variable stays fixed while the other two trade off.

If volume in your scenario isn't actually fixed — if pressure, volume, and temperature are all changing together — Gay-Lussac's law alone won't cover it. Use the combined gas law calculator instead, which merges this law with Boyle's and Charles' into one solver for all three variables at once.