Gay-Lussac's Law Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/8/2026
Gay-Lussac's law is calculated with P₂ = P₁ × T₂ ÷ T₁ (temperatures in kelvins), at constant volume. For 1 atm at 20°C heated to 80°C, the final pressure is about 1.2047 atm.
Explanation
Gay-Lussac's law describes the isochoric transformation of an ideal gas: at constant volume, a gas's pressure is directly proportional to its absolute temperature. Heating a gas enclosed in a rigid container (fixed volume) therefore increases its pressure, and conversely cooling it decreases it — this is the principle behind the risk of an aerosol can bursting when exposed to heat, or tires losing pressure in cold weather. As with the other ideal gas laws (see our Charles's law calculator, for the transformation at constant pressure, and our Boyle's law calculator, for the transformation at constant temperature), temperatures must be expressed in kelvins, not degrees Celsius, since the law relies on a direct proportionality that only holds starting from absolute zero (−273.15°C, where T = 0 K) — using Celsius degrees directly in the ratio would give a physically inconsistent result. This calculator performs this conversion automatically from temperatures entered in Celsius, more intuitive to work with day to day.
Example: 1 atm at 20°C, heated to 80°C
Inputs
Initial pressure: 1 atm. Initial temperature: 20°C (293.15 K). Final temperature: 80°C (353.15 K).
Calculation
Final pressure = 1 × 353.15 ÷ 293.15 ≈ 1.2047 atm.
Result
This gas's final pressure, at constant volume, is about 1.2047 atm.
Frequently asked questions
Why must temperatures be converted to kelvins rather than degrees Celsius?
Because Gay-Lussac's law expresses a direct proportionality between pressure and absolute temperature: doubling the absolute temperature doubles the pressure, at constant volume. This relationship only holds in kelvins, where zero corresponds to a true absence of thermal agitation (absolute zero). In degrees Celsius, where zero is arbitrary (water's freezing point), the same ratio would give a physically incorrect result.
What is the difference between Gay-Lussac's, Charles's, and Boyle's laws?
These are three special cases of the ideal gas law, each holding one quantity constant: Boyle's law holds temperature constant (pressure and volume vary inversely), Charles's law holds pressure constant (volume and temperature vary together), and Gay-Lussac's law holds volume constant (pressure and temperature vary together). Our ideal gas law calculator combines all three for the general case where nothing is fixed.
What physically happens at absolute zero?
Absolute zero (−273.15°C, or 0 K) theoretically corresponds to a complete absence of thermal agitation of the gas particles. At this temperature, Gay-Lussac's law predicts zero pressure, and the calculation becomes mathematically impossible in the other direction (dividing by an initial temperature of 0 K) — a limiting case that remains largely theoretical, since no real gas still behaves like an ideal gas at such extreme temperatures.