Combined Gas Law Calculator
Pick the unknown, fill in the other five, and see how pressure, volume and temperature trade off between two states of the same gas.
By Manzoor Ahmad, pharmacist · Updated What is the combined gas law formula?
P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂, with temperatures in kelvin. To find a new volume, V₂ = P₁V₁T₂ ÷ (T₁P₂). A 10 L balloon at 1 atm and 25 °C that rises to 0.5 atm and −20 °C expands to 10 × 1 × 253.15 ÷ (298.15 × 0.5) = 17.0 L.
Tap a letter to choose the unknown (highlighted).
State 1 (before)
State 2 (after)
The gas laws inside the combined gas law
| Law | Held constant | Equation | Everyday example |
|---|---|---|---|
| Boyle’s law | T, n | P₁V₁ = P₂V₂ | syringe, scuba diving, chip bag on a plane |
| Charles’s law | P, n | V₁/T₁ = V₂/T₂ | hot-air balloon, ball shrinking in the cold |
| Gay-Lussac’s law | V, n | P₁/T₁ = P₂/T₂ | tire pressure, pressure cooker, aerosol can |
| Combined gas law | n | P₁V₁/T₁ = P₂V₂/T₂ | weather balloon rising |
| Ideal gas law | — | PV = nRT | moles of gas in a tank (calculator) |
Solving steps
- List the six variables and mark the unknown.
- Convert every temperature to kelvin (°C + 273.15).
- Use the same pressure unit and the same volume unit for both states.
- Rearrange P₁V₁/T₁ = P₂V₂/T₂ for the unknown and substitute.
- Sanity-check: higher temperature or lower pressure should mean more volume.
Combined gas law FAQs
For a fixed amount of gas, P1V1 ÷ T1 = P2V2 ÷ T2, where P is pressure, V is volume and T is absolute temperature in kelvin. It combines Boyle's, Charles's and Gay-Lussac's laws.
Rearrange to V2 = P1V1T2 ÷ (T1P2). A balloon holding 10 L at 1 atm and 25 °C (298.15 K) that rises to 0.5 atm and −20 °C (253.15 K) expands to 10 × 1 × 253.15 ÷ (298.15 × 0.5) = 17.0 L.
Gas laws are proportional to absolute temperature. Using °C would make 0 °C look like zero energy and can give negative or infinite volumes. Add 273.15 to °C to get kelvin.
At constant temperature, P1V1 = P2V2: pressure and volume are inversely proportional. Halving the volume doubles the pressure.
At constant pressure, V1 ÷ T1 = V2 ÷ T2: volume is proportional to absolute temperature. Warming a gas from 273 K to 373 K increases its volume by about 37%.
At constant volume, P1 ÷ T1 = P2 ÷ T2. This is why a sealed aerosol can or a tire's pressure rises as it heats up.
Yes, as long as both states use the same unit; the units cancel. This calculator lets you pick any unit and converts internally.
The combined gas law compares two states of the same amount of gas. The ideal gas law, PV = nRT, relates one state to the number of moles, so use it when you need the amount of gas.
IUPAC defines standard temperature and pressure as 273.15 K (0 °C) and 100 kPa. Many textbooks still use 1 atm (101.325 kPa); check which your course uses.
At constant volume, P2 = P1 × T2 ÷ T1 using absolute pressure. A tire at 220 kPa gauge (321 kPa absolute) at 20 °C rises to about 343 kPa absolute (242 kPa gauge) at 40 °C.
It is accurate to within a few percent for most gases near room temperature and moderate pressure. It breaks down at very high pressure or near the condensation point.
Cabin pressure drops to about 0.75–0.8 atm at cruising altitude. With temperature roughly constant, Boyle's law says the trapped air expands by 25–33%.
Sources
Assumes ideal-gas behavior and a fixed amount of gas. Use absolute pressures: tire and cylinder gauges read pressure above atmospheric, so add about 101 kPa (14.7 psi).