Combined Gas Law Calculator

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:

1. 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

2. Scuba tank: A tank filled to 3,000 psi (gauge) at 25°C, taken into −5°C water?

   • P₁ = 3,000 + 14.7 = 3,014.7 psia; T₁ = 298 K; T₂ = 268 K
   • P₂ = 3,014.7 × 268/298 = 2,711 psia = 2,697 psi on the gauge, about 10% down
   • At tank pressures the 14.7 moves the answer by about a psi, which is why divers skip it. On the tyre above it is almost a third of the absolute pressure, and skipping it there gives 36.4 psi instead of 38.4.

Metric pressure units:

• 1 atm = 101.325 kPa = 14.696 psi
• Standard conditions (STP): 0°C (273.15 K) and 1 atm (101.325 kPa), the older definition most textbooks still use. IUPAC has defined STP at 100 kPa since 1982.
• SATP: 25°C (298.15 K) and 100 kPa