Gay-Lussac's Law Calculator — Pressure–Temperature Gas Law
Apply Gay-Lussac's Law to find an unknown pressure or temperature for a gas held at constant volume. Enter any three of P₁, T₁, P₂, T₂ and the calculator solves for the fourth.
kPa
K
kPa
K
P₁/T₁ = P₂/T₂ (kPa per K) — this stays constant at fixed volume
- 1
Initial state P₁ ÷ T₁
100 ÷ 300 = 0.3333 - 2
Final state P₂ ÷ T₂ (same constant)
150 ÷ 450 = 0.3333Gay-Lussac's law: at constant volume P/T is the same for both states.
How does this calculator work?
Gay-Lussac's Law: at constant volume, a gas's pressure is directly proportional to its absolute temperature — P₁/T₁ = P₂/T₂. Enter any three of P₁, T₁, P₂, T₂ (temperatures in Kelvin) and the calculator solves for the fourth. Doubling the Kelvin temperature doubles the pressure.
Formula
How this is calculated
Gay-Lussac's Law states that for an ideal gas kept at constant volume, the absolute pressure is directly proportional to the absolute temperature: P / T = constant. The physical reason is kinetic: higher temperature means gas molecules move faster, strike the container walls more often and with greater force, so pressure rises. Doubling the Kelvin temperature exactly doubles the pressure; halving it halves the pressure.
The calculator rearranges P₁/T₁ = P₂/T₂ to solve for whichever variable you leave blank. Temperatures must be in Kelvin (K = °C + 273.15, or K = °F − 32 × 5/9 + 273.15) because the law is valid only with absolute temperature; using Celsius would imply zero pressure at 0 °C, which is wrong. Pressure units can be anything — kPa, atm, psi, bar — as long as both P₁ and P₂ use the same unit.
This law assumes ideal gas behaviour and a perfectly rigid container. Real gases deviate at very high pressures or temperatures close to condensation, and any change in the amount of gas or the container volume breaks the constant-volume assumption. Gay-Lussac's Law is a special case of the combined gas law (P₁V₁/T₁ = P₂V₂/T₂) with V₁ = V₂.
Frequently asked questions
The law requires absolute temperature because pressure is proportional to molecular kinetic energy, which is zero at absolute zero (0 K). At 0 °C a gas still has substantial pressure, so using Celsius gives physically wrong answers. Always convert: K = °C + 273.15.
Common applications include: explaining why tyre pressure rises when a car heats up, why sealed aerosol cans can explode in a fire, pressure-relief valve design for boilers and gas cylinders, and predicting pressure changes in autoclave sterilisation or pressurised cooking.
Boyle's Law keeps temperature constant and relates pressure to volume (P∝1/V). Charles's Law keeps pressure constant and relates volume to temperature (V∝T). Gay-Lussac's Law keeps volume constant and relates pressure to temperature (P∝T). All three combine into the combined gas law.
Also known as
TG we-Calculate Editorial Team. (2026). Gay-Lussac's Law Calculator — Pressure–Temperature Gas Law [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/gay-lussacs-law-calculator
TG we-Calculate Editorial Team. "Gay-Lussac's Law Calculator — Pressure–Temperature Gas Law." TG we-Calculate. 2026. https://we-calculate.com/calculator/gay-lussacs-law-calculator.
TG we-Calculate Editorial Team, "Gay-Lussac's Law Calculator — Pressure–Temperature Gas Law," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/gay-lussacs-law-calculator
@misc{wecalculate_gay_lussacs_law_calculator, title = {Gay-Lussac's Law Calculator — Pressure–Temperature Gas Law}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/gay-lussacs-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
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