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Gay-Lussac's Law Calculator

Calculate the pressure or temperature of a gas when the volume is held constant. Select what you want to solve for, and enter the remaining three variables.

1. Calculation Mode & Units
Final P₂
Final T₂
Initial P₁
Initial T₁
2. Gas Variables
3. Result
Final Pressure (P₂)
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Understanding Gay-Lussac's Law

Formulated by the French chemist Joseph Louis Gay-Lussac in the early 1800s, Gay-Lussac's Law (also known as the Pressure-Temperature Law) describes the direct relationship between the pressure and temperature of a gas when its volume is held strictly constant.

The Core Formula

The law states that the pressure of a fixed mass of gas is directly proportional to its absolute temperature:

$$P \propto T$$

When comparing the same gas under two different sets of conditions, the formula is written as:

$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$

Where:

  • $P_1$ and $T_1$: The initial pressure and absolute temperature.
  • $P_2$ and $T_2$: The final pressure and absolute temperature.

Why Absolute Temperature (Kelvin) is Required

While pressure can be measured in atmospheres (atm), pascals (Pa), or psi, the temperature must be calculated in an absolute scale, such as Kelvin. If you use Celsius or Fahrenheit, the mathematical proportions break down. For example, if a gas starts at $0^\circ\text{C}$, the equation would require dividing by zero, which is mathematically impossible. RapidCalc handles this conversion internally so you can input standard degrees safely.