P₁ / T₁ = P₂ / T₂
Constant volume · T in Kelvin · P = absolute pressure
State 1 (Initial)
Pa
Enter pressure > 0.
°C
Enter a valid temperature.
State 2 (Final)
⭐ Solving for P₂
P₂ = P₁ × (T₂ / T₁)
°C
Enter a valid temperature.
State 1 (Initial)
Pa
Enter pressure > 0.
°C
Enter a valid temperature.
State 2 (Final)
⭐ Solving for T₂
T₂ = T₁ × (P₂ / P₁)
Pa
Enter pressure > 0.
State 1 (Initial)
⭐ Solving for P₁
P₁ = P₂ × (T₁ / T₂)
°C
Enter a valid temperature.
State 2 (Final)
Pa
Enter pressure > 0.
°C
Enter a valid temperature.
State 1 (Initial)
⭐ Solving for T₁
T₁ = T₂ × (P₁ / P₂)
Pa
Enter pressure > 0.
State 2 (Final)
Pa
Enter pressure > 0.
°C
Enter a valid temperature.
Result
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Sources & Methodology
Gay-Lussac’s Law verified against IUPAC standards and standard physical chemistry references.
LibreTexts Chemistry — Gay-Lussac’s Law
Open-access derivation, worked examples, and applications of Gay-Lussac’s Law in chemistry education.
NIST CODATA — Universal Gas Constant & SI Definitions
NIST reference for absolute zero (0 K = −273.15°C) and the basis of absolute temperature scale used in gas law calculations.
Law: P₁/T₁ = P₂/T₂ (constant volume, constant amount)
Find P₂: P₂ = P₁ × T₂/T₁ | Find T₂: T₂ = T₁ × P₂/P₁
Find P₁: P₁ = P₂ × T₁/T₂ | Find T₁: T₁ = T₂ × P₁/P₂
Temperature conversion: K = °C + 273.15 | K = (°F − 32) × 5/9 + 273.15
Pressure conversions: 1 atm = 101,325 Pa | 1 psi = 6,894.76 Pa | 1 bar = 100,000 Pa
Results shown in Pa, kPa, atm, psi — temperatures in K, °C, °F.
Find P₂: P₂ = P₁ × T₂/T₁ | Find T₂: T₂ = T₁ × P₂/P₁
Find P₁: P₁ = P₂ × T₁/T₂ | Find T₁: T₁ = T₂ × P₁/P₂
Temperature conversion: K = °C + 273.15 | K = (°F − 32) × 5/9 + 273.15
Pressure conversions: 1 atm = 101,325 Pa | 1 psi = 6,894.76 Pa | 1 bar = 100,000 Pa
Results shown in Pa, kPa, atm, psi — temperatures in K, °C, °F.
⏱ Last reviewed: April 2026
How to Use Gay-Lussac’s Law in 2026
Gay-Lussac’s Law describes how pressure and temperature are related in a sealed, rigid container. When you heat a gas in a fixed volume, the molecules move faster and hit the walls harder — pressure rises. When you cool it, pressure falls. The law is a direct consequence of the kinetic theory of gases and is one of the foundational gas laws in chemistry and physics.
The Formula and Worked Examples
P₁ / T₁ = P₂ / T₂ (T in Kelvin, P absolute)
Find P₂: P₂ = P₁ × (T₂/T₁)
Find T₂: T₂ = T₁ × (P₂/P₁)
Example 1 — tyre pressure:
Cold tyre: 220 kPa at 20°C (293.15 K). After driving to 60°C (333.15 K):
P₂ = 220 × (333.15/293.15) = 250.0 kPa
Example 2 — find temperature from pressure rise:
Gas at 293.15 K and 1 atm rises to 1.5 atm (sealed vessel):
T₂ = 293.15 × (1.5/1.0) = 439.7 K = 166.6°C
Find T₂: T₂ = T₁ × (P₂/P₁)
Example 1 — tyre pressure:
Cold tyre: 220 kPa at 20°C (293.15 K). After driving to 60°C (333.15 K):
P₂ = 220 × (333.15/293.15) = 250.0 kPa
Example 2 — find temperature from pressure rise:
Gas at 293.15 K and 1 atm rises to 1.5 atm (sealed vessel):
T₂ = 293.15 × (1.5/1.0) = 439.7 K = 166.6°C
Real-World Scenarios
| Scenario | P₁ | T₁ | T₂ | P₂ |
|---|---|---|---|---|
| Tyre after highway driving | 220 kPa | 20°C | 60°C | 250 kPa |
| Gas cylinder cooled (storage) | 10 MPa | 25°C | −40°C | 7.83 MPa |
| Pressure cooker seal | 101.3 kPa | 20°C | 120°C | 135.8 kPa |
| Aerosol can in hot car | 200 kPa | 20°C | 50°C | 220.5 kPa |
Why Kelvin Is Required
Pressure is proportional to absolute temperature in Kelvin. A gas at 10°C heated to 20°C does NOT double its pressure — it increases by only (293/283 − 1) = 3.5%. But a gas at 200 K heated to 400 K exactly doubles its pressure. Always convert: T(K) = T(°C) + 273.15. Using Celsius gives incorrect and potentially dangerous results in engineering applications.
💡 Gauge vs absolute pressure: Tyre gauges show gauge pressure (above atmospheric). Always add atmospheric pressure (101,325 Pa) before applying Gay-Lussac’s Law. A tyre reading 200 kPa gauge = 301.325 kPa absolute. Forgetting this conversion causes errors of approximately 25–50% in typical tyre pressure calculations.
Frequently Asked Questions
Gay-Lussac's Law states that at constant volume, the pressure of a fixed amount of gas is directly proportional to its absolute temperature: P/T = constant, or P1/T1 = P2/T2. Published in 1809 by Joseph Louis Gay-Lussac, it explains why sealed containers like tyres and aerosol cans increase in pressure when heated.
P1/T1 = P2/T2, with T in Kelvin and P as absolute pressure. Rearranged: P2 = P1 x (T2/T1) for final pressure; T2 = T1 x (P2/P1) for final temperature; P1 = P2 x (T1/T2) for initial pressure; T1 = T2 x (P1/P2) for initial temperature. This calculator solves all four.
Pressure is proportional to molecular kinetic energy, which is proportional to absolute temperature in Kelvin — not Celsius or Fahrenheit. Those scales have arbitrary zero points. Zero Kelvin (absolute zero, −273.15°C) is the true zero of molecular motion. Always convert: K = °C + 273.15.
P2 = P1 x (T2/T1) in Kelvin. Example: a tyre at 20°C (293.15 K) and 220 kPa driven to 60°C (333.15 K): P2 = 220 x (333.15/293.15) = 250 kPa. A 13.6% increase in Kelvin temperature gives a 13.6% pressure increase.
T2 = T1 x (P2/P1) in Kelvin. If a sealed vessel at 293.15 K (20°C) and 100 kPa is pressurised to 150 kPa: T2 = 293.15 x (150/100) = 439.7 K = 166.6°C. This is the temperature the gas must reach to produce that pressure increase.
Gay-Lussac's Law (P1/T1=P2/T2): pressure and temperature at constant volume. Boyle's Law (P1V1=P2V2): pressure and volume at constant temperature. Charles's Law (V1/T1=V2/T2): volume and temperature at constant pressure. Combined Gas Law: P1V1/T1 = P2V2/T2 unifies all three.
Tyre pressure increases 10-20% during highway driving. Aerosol cans carry heat warnings because sealed containers follow Gay-Lussac's Law. Pressure cookers reach predictable operating pressures at given temperatures. Gas cylinder storage facilities account for ambient temperature changes. Autoclave sterilisation relies on temperature-pressure relationships at constant volume.
Gauge pressure is measured above atmospheric pressure (what tyre gauges show). Gay-Lussac's Law requires absolute pressure. Convert: absolute = gauge + atmospheric (101,325 Pa). A tyre reading 200 kPa gauge = 301.325 kPa absolute. Using gauge pressure directly gives errors of 25-50% in typical calculations.
Isochoric means constant volume — a process where the gas cannot expand or compress. Rigid sealed containers (metal tanks, welded cylinders, sealed pressure vessels) are isochoric. Gay-Lussac's Law governs isochoric heating and cooling. No PV work is done — all heat input raises internal energy and thus temperature and pressure.
Very accurate at moderate pressures (below ~5 MPa) and temperatures well above the boiling point. Deviations occur at high pressure (above ~10 MPa) or near critical/boiling points where intermolecular forces matter. For precision engineering at extreme conditions, use real gas equations with compressibility factor Z: P = ZnRT/V.
Guillaume Amontons described the pressure-temperature relationship in 1702, over a century before Gay-Lussac's 1809 publication. Amontons also predicted absolute zero by extrapolating his data to zero pressure. The same law goes by both names — Amontons' Law in physics history, Gay-Lussac's Law in chemistry education.
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