About the Gay-Lussac's Law Calculator
This Gay-Lussac's law calculator finds how the pressure of a gas changes with temperature when its volume is fixed — a sealed can, a rigid tank or a tyre that barely stretches. Choose the unknown (P₁, T₁, P₂ or T₂), enter the other three values and pick your units. Temperatures in Celsius or Fahrenheit are converted to kelvin automatically before the ratio is solved.
Students use it for gas-law homework; drivers and cyclists use it to see why tyre pressure rises on a hot day; and anyone storing aerosol cans or gas cylinders can estimate how much the pressure climbs as they warm. The chart plots pressure against temperature so you can see the straight-line relationship.
The law assumes an ideal gas, a fixed amount of gas and a constant volume. Real containers flex slightly and real gases deviate at high pressure, so treat results as good estimates. Tyre gauges read gauge pressure (pressure above the atmosphere); leave the gauge option on and the calculator adds 1 atm before solving and subtracts it afterwards.
With the default inputs, the answer is 36.7787. Change any value above to recalculate instantly.
How to use the gay-lussac's law calculator
- 1Choose which value you want to find.
- 2Select your temperature unit and pressure unit, and say whether the pressures are gauge readings.
- 3Enter the three known values.
- 4Read the answer and the kelvin conversions used in the working.
Formula and method
Gay-Lussac's law (also called Amontons's law) states that for a fixed amount of ideal gas at constant volume, pressure is directly proportional to absolute temperature. Faster-moving molecules hit the container walls harder and more often, so heating the gas raises the pressure in the same proportion as the kelvin temperature.
The calculator converts every temperature to kelvin (K = °C + 273.15; K = (°F − 32) × 5/9 + 273.15), solves the proportion, and converts a temperature answer back to your unit. Pressure can be in any unit because only the ratio matters, but both pressures must be absolute (not gauge) values in the same unit.
- P₁, P₂
- Initial and final absolute pressure
- T₁, T₂
- Initial and final absolute temperature (K)
Worked examples
Tyre warming from 20 °C to 50 °C
A 32 psi gauge reading is 32 + 14.696 = 46.696 psi absolute. P₂ = 46.696 × 323.15 ÷ 293.15 = 51.475 psi absolute, or about 36.78 psi on the gauge — a rise of roughly 4.8 psi for a 30 °C increase.
Temperature at which a rigid tank reaches 2.5 atm
Starting at 1 atm and 298.15 K, T₂ = 298.15 × 2.5 ÷ 1 = 745.38 K, which is 472.2 °C.
Cooling a sealed cylinder from 300 K to 250 K
P₂ = 200 × 250 ÷ 300 = 166.67 kPa. Cooling by one-sixth of the absolute temperature lowers the pressure by one-sixth.
Frequently asked questions
What is Gay-Lussac's law?+
Gay-Lussac's law says that at constant volume the pressure of a fixed amount of gas is directly proportional to its absolute temperature: P₁/T₁ = P₂/T₂. Double the kelvin temperature and the pressure doubles.
Why must temperature be in kelvin?+
The law is a direct proportion, which only works on a scale that starts at absolute zero. 0 °C is not zero thermal energy, so ratios of Celsius temperatures are meaningless. Kelvin starts at true zero.
What are real-life examples of Gay-Lussac's law?+
Tyre pressure rising after a long drive, aerosol cans warning against heating above 50 °C, pressure cookers, and gas cylinders left in the sun are all everyday examples of pressure increasing with temperature at constant volume.
How is Gay-Lussac's law different from Charles's law?+
Charles's law links volume and temperature at constant pressure; Gay-Lussac's law links pressure and temperature at constant volume. Boyle's law covers pressure and volume at constant temperature, and the combined gas law joins all three.
Should I use gauge or absolute pressure?+
Use absolute pressure. A gauge reads pressure above the atmosphere, so add about 14.7 psi or 101.3 kPa before calculating, then subtract it again to get the new gauge reading.