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Gay-Lussac's Law Calculator

Enter the initial pressure and temperatures to get the final pressure.

How it is calculated

For a fixed amount of gas in a rigid container, pressure divided by absolute temperature stays constant: P1 ÷ T1 = P2 ÷ T2, so P2 = P1 × T2 ÷ T1. Enter the starting pressure P1 in any pressure unit, and both temperatures T1 and T2 in kelvin (K); the answer comes out in the same pressure unit as P1. The tool does not convert from °C or °F: you must add 273.15 to Celsius yourself. T1 must be above zero, T2 and P1 cannot be negative. The law assumes the volume and the amount of gas stay fixed and that the gas behaves ideally.

Worked example

A sealed container holds gas at 220 kPa and 20 °C. It is heated to 50 °C. Step 1: convert to kelvin: T1 = 20 + 273.15 = 293.15 and T2 = 50 + 273.15 = 323.15. Step 2: ratio T2 ÷ T1 = 323.15 ÷ 293.15 = 1.1023. Step 3: P2 = 220 × 1.1023 = 242.51 kPa. The pressure rises about 10% for a 30-degree rise.

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Common mistakes

  • Typing Celsius temperatures directly: 20 and 50 would give 550, more than double the true value of 242.51.
  • Using the law when the container can expand, such as a balloon or a tyre that flexes noticeably; volume is not constant there.
  • Mixing gauge pressure with absolute pressure: the law needs absolute pressure, so add the atmospheric pressure to a gauge reading first.
  • Expecting a correct answer when gas leaks or is added between the two states.
  • Applying it near condensation or liquefaction, where a gas no longer behaves ideally.

About this calculator

Gay-Lussac's Law states that for a fixed amount of gas held at constant volume, pressure is directly proportional to absolute temperature: P₁/T₁ = P₂/T₂, with temperatures in Kelvin — as a sealed gas heats up, its molecules strike the container walls harder and more often, raising pressure in direct proportion.

It's one of the components of the ideal gas law and explains everyday and industrial phenomena like why a sealed aerosol can or a car tire's pressure rises on a hot day, and why pressure vessels, autoclaves and gas cylinders need a rated temperature range — chemistry students and engineers use this relationship to predict a gas's final pressure after a temperature change without any volume change.

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Comments (1)

  • Editorial team

    Tyre pressure shows how the gauge reading enters. Take 32 psi gauge at 10 °C, so 46.7 psi absolute with 14.7 psi of air. At 30 °C, which is 303.15 K against 283.15 K, the tool returns 50.00 psi absolute, or about 35.3 on the gauge. A flexing tyre changes volume too, so treat it as an estimate. What container are you modelling?

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