Gay-Lussac's Law Calculator
Solve P₁/T₁ = P₂/T₂ for any of the four variables — temperature is always converted to kelvin automatically. Two static 3D diagrams show a sealed rigid vessel heating up and the family of P–T lines through absolute zero, alongside charts of the classic straight-line relationship.
Reviewed by the ToolNestr Editorial Team — July 2026
Important: Gay-Lussac's law requires absolute temperature. Enter °C or K below — °C is converted to kelvin automatically before solving.
Two ideas that trip students up
1. Same rigid vessel, hotter gas, higher pressure
A cold, low-pressure sealed vessel with a fixed lid next to a hot, high-pressure one — the same fixed volume of gas at two different absolute temperatures. The lid never moves; only the pressure gauge changes.
2. Every line points to absolute zero
Straight P-vs-T lines for different gas samples all extrapolate back to the same point: P = 0 at 0 K. That shared intercept is the same reasoning that located absolute zero using Charles's law.
Gay-Lussac's law graphs
How it works
The core idea in one line: heat a gas sealed in a rigid, fixed-volume container and its pressure rises in direct proportion to its absolute temperature — but that proportion only works in kelvin, never Celsius.
P₁/T₁ = P₂/T₂
pressure ÷ absolute temperature is constant at fixed V and n
K = °C + 273.15
convert to kelvin before using the formula — always
P₂ = P₁ × T₂ / T₁
solve for the new pressure
Rearranged, P₁/T₁ = P₂/T₂ solves any of the four variables: P₂ = P₁T₂/T₁ and T₂ = T₁P₂/P₁. It only holds when volume and the amount of gas (moles) stay fixed — the container must be rigid — and temperature must be absolute (kelvin), since the direct proportionality breaks down completely if you use Celsius, whose zero point is arbitrary rather than physical.
Worked example 1 — heating a sealed gas canister
Given: A sealed, rigid gas canister holds gas at 1.00 atm and 20°C. It is heated at constant volume to 80°C. Find the new pressure.
Using Celsius directly (80 ÷ 20 = 4×) would badly overstate the pressure rise — the correct kelvin ratio gives only about a 20% increase.
Worked example 2 — an aerosol can left in a hot car
Given: An aerosol can is at 2.50 atm and 25°C. Left in a hot car, it warms at constant volume to 95°C. Find the new pressure.
The pressure climbs by roughly 23% — a real margin for a can rated for a specific working pressure, which is exactly why aerosol cans warn against heat exposure.
Gay-Lussac's law vs Boyle's law vs Charles's law
Gay-Lussac's law is the pressure–temperature pair: hold volume and moles fixed in a sealed, rigid container, and pressure tracks absolute temperature exactly.
| Law | Held constant | Relationship |
|---|---|---|
| Gay-Lussac's law | Volume, moles | P and T — directly proportional (P₁/T₁ = P₂/T₂) |
| Boyle's law | Temperature, moles | P and V — inversely proportional (P₁V₁ = P₂V₂) |
| Charles's law | Pressure, moles | V and T — directly proportional (V₁/T₁ = V₂/T₂) |
All three are special cases of the combined/ideal gas law PV = nRT, each freezing one variable to isolate the other two.
Where Gay-Lussac's law actually matters
🍲 Pressure cookers
A pressure cooker is a sealed, nearly rigid vessel. Heating the water inside raises the pressure of the trapped steam in direct proportion to absolute temperature, which is precisely what lets food cook faster at higher temperatures than boiling at normal atmospheric pressure.
🧴 Aerosol can safety warnings
Aerosol cans are sealed rigid containers holding pressurised gas. Warming them — in direct sunlight, a hot car, or near a flame — raises the internal pressure sharply, which is why every can carries an explicit warning against heat exposure and incineration.
🚗 Car tire pressure and ambient temperature
A tire is close to a fixed-volume container. On a hot day, or right after highway driving heats the air inside, tire pressure reads noticeably higher than on a cold morning — the same P/T proportionality, which is why manufacturers specify a "cold" tire pressure.
🏭 Industrial sealed containers
Storage tanks, gas cylinders and sealed process vessels in industrial settings are engineered with pressure relief valves precisely because heating a fixed volume of gas raises its pressure predictably — Gay-Lussac's law lets engineers calculate exactly how much a temperature swing will raise internal pressure.
Common misconceptions
"You can plug Celsius values straight into Gay-Lussac's law."
False — this is the single most common student error. The P ∝ T proportionality only holds for absolute temperature. You must convert every temperature to kelvin (K = °C + 273.15) before using P₁/T₁ = P₂/T₂, or the answer will be badly wrong.
"Gay-Lussac's law applies to any sealed container, regardless of whether it can expand."
False — it specifically requires constant volume, meaning a rigid container that cannot expand or contract. If the container can change size (like a balloon or a piston), volume is no longer fixed and you need the combined gas law, P₁V₁/T₁ = P₂V₂/T₂, instead.
"Gay-Lussac's law works even if volume changes too."
False — volume (and the amount of gas) must be held constant. That constraint is the entire premise of the law. If volume changes as well, the simple P/T proportionality no longer applies.
"Pressure and temperature are equal to each other."
False — they are proportional, not equal. P/T is a constant ratio, not P = T. Doubling the absolute temperature doubles the pressure; it does not make the pressure numerically equal to the temperature.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, Chemistry 2e — gas laws and Gay-Lussac's law (free, peer-reviewed). openstax.org
- • Brown, LeMay & Bursten, Chemistry: The Central Science — Chapter 10, Gases.
- • Zumdahl & Zumdahl, Chemistry — the gas laws and kinetic molecular theory.
Gay-Lussac's law assumes constant volume and a fixed amount of gas (n). Temperatures are converted to kelvin internally. Results are rounded for display.
How to use this calculator
Enter three values
Fill any three of P₁, T₁, P₂, T₂; the fourth solves live.
Mind the units
Toggle °C or K for each temperature field — conversion to kelvin happens automatically before solving.
Study the diagrams
The sealed-vessel diagram and the P–T line family below illustrate why pressure rises in a rigid container as temperature climbs.
Related tools
Frequently asked questions
What is Gay-Lussac's law?
Gay-Lussac's law states that at constant volume and a fixed amount of gas, pressure and absolute temperature are directly proportional: P₁/T₁ = P₂/T₂. Heat a sealed, rigid container and the pressure inside rises in direct proportion to the temperature in kelvin.
Why must temperature be in kelvin, not Celsius, for Gay-Lussac's law?
The proportionality P ∝ T only holds for absolute temperature. Celsius has an arbitrary zero point (the freezing point of water), so ratios of Celsius values are meaningless here — 40°C is not "twice as hot" as 20°C. Kelvin starts at absolute zero, where a gas's pressure would theoretically reach zero, so ratios of kelvin temperatures correctly track ratios of pressure. Always convert with K = °C + 273.15 before using the formula.
What has to stay constant for Gay-Lussac's law to apply?
Volume and the amount of gas (moles) must both stay fixed — the gas has to be sealed in a rigid container that cannot expand or contract. Gay-Lussac's law isolates the pressure–temperature relationship only when those two are held constant; if volume also changes, you need the combined gas law instead.
Why do pressure cookers and aerosol cans carry heat warnings?
Both are sealed, essentially rigid containers holding gas at some initial pressure. Heating them raises the internal pressure in direct proportion to absolute temperature — Gay-Lussac's law in action. Enough heat can push the pressure past what the container is rated for, which is exactly why aerosol cans warn against storage near heat and pressure cookers use calibrated relief valves.
How is Gay-Lussac's law different from Charles's law?
Charles's law holds pressure constant and relates volume to temperature (V₁/T₁ = V₂/T₂) in a container that can expand, like a balloon. Gay-Lussac's law holds volume constant instead and relates pressure to temperature (P₁/T₁ = P₂/T₂) in a sealed, rigid container that cannot change size. They are two different slices through the same ideal gas law, PV = nRT.