Combined Gas Law Calculator
Solve for pressure, volume, or temperature using the combined gas law (P₁V₁/T₁ = P₂V₂/T₂).
Supports metric and imperial units.
The Combined Gas Law merges Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law into a single relationship that describes how pressure, volume, and temperature of a fixed amount of gas interact.
The formula: (P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
Where:
- P₁, P₂ = Initial and final pressure (must be in absolute units: kPa, atm, or psia — NOT gauge pressure)
- V₁, V₂ = Initial and final volume (any consistent unit: L, mL, m³, ft³, gallons)
- T₁, T₂ = Initial and final temperature in Kelvin (K = °C + 273.15, or K = (°F + 459.67) × 5/9)
Critical note on Kelvin: Temperature MUST be in Kelvin for this formula to work. Using Celsius or Fahrenheit will give wrong results. Kelvin starts at absolute zero (−273.15°C = −459.67°F), where gas molecules theoretically have zero kinetic energy.
The three sub-laws:
- Boyle’s Law (isothermal, T constant): P₁V₁ = P₂V₂ — pressure and volume are inversely proportional
- Charles’s Law (isobaric, P constant): V₁/T₁ = V₂/T₂ — volume and temperature are directly proportional
- Gay-Lussac’s Law (isochoric, V constant): P₁/T₁ = P₂/T₂ — pressure and temperature are directly proportional
Practical examples:
-
Car tire heating: A tire inflated to 32 psi (gauge) at 20°C — what pressure at 60°C?
- P₁ = 32 + 14.7 = 46.7 psia; T₁ = 293 K; T₂ = 333 K
- P₂ = 46.7 × 333/293 = 53.1 psia = 38.4 psi gauge
-
Scuba tank: A tank with 3,000 psi of air at 25°C — at −5°C (cold water)?
- P₂ = 3,000 × (268/298) = 2,698 psi (a ~10% reduction)
Metric pressure units:
- 1 atm = 101.325 kPa = 14.696 psi
- Standard conditions (STP): 0°C (273 K) and 1 atm (101.325 kPa)
- SATP: 25°C (298 K) and 100 kPa