About the Combined Gas Law Calculator
This combined gas law calculator handles a gas whose pressure, volume and temperature all change at once. Choose which of the six quantities — P₁, V₁, T₁, P₂, V₂ or T₂ — is unknown, enter the other five, and it solves P₁V₁/T₁ = P₂V₂/T₂. Temperatures can be entered in Celsius, Kelvin or Fahrenheit and are converted to kelvin automatically.
It is the go-to tool for general chemistry problems, correcting a measured gas volume to standard conditions (STP), and understanding what happens to a gas sample when it is moved, heated or compressed. Holding one variable steady turns it into Boyle's law (constant T), Charles's law (constant P) or Gay-Lussac's law (constant V), so it covers all three.
The equation assumes an ideal gas and a fixed amount of gas (no leaks). Use the same pressure unit and the same volume unit for both states; only temperature needs to be absolute, which the calculator handles for you.
With the default inputs, the answer is 5.4193. Change any value above to recalculate instantly.
How to use the combined gas law calculator
- 1Choose which of the six quantities is unknown.
- 2Select your pressure, volume and temperature units.
- 3Enter the five known values.
- 4Read the answer and compare the initial and final states in the table.
Formula and method
The combined gas law merges Boyle's, Charles's and Gay-Lussac's laws. For a fixed amount of ideal gas, the quantity PV/T stays constant, so the initial and final states can be set equal. Rearranging isolates any one variable, for example V₂ = P₁V₁T₂ / (T₁P₂).
It comes directly from the ideal gas law PV = nRT with the amount n held fixed. Temperatures must be absolute, so the calculator converts °C and °F to kelvin before solving and converts a temperature answer back. Pressure and volume can be in any unit provided both states use the same one.
- P₁, V₁, T₁
- Initial pressure, volume and absolute temperature
- P₂, V₂, T₂
- Final pressure, volume and absolute temperature
Worked examples
Compress and heat a gas
V₂ = 1 × 10 × 323.15 ÷ (298.15 × 2) ≈ 5.42 L. Doubling the pressure alone would halve the volume to 5 L, but warming by 25 °C expands it a little.
Correct a lab volume to STP
250 mL collected at 98.5 kPa and 22 °C corresponds to 98.5 × 250 × 273.15 ÷ (295.15 × 101.325) ≈ 224.9 mL at 0 °C and 1 atm.
Gay-Lussac's law: heating a sealed tank
With volume fixed, P₂ = 30 × 333 ÷ 293 ≈ 34.1 psi — a 40 K rise pushes pressure up about 13.7%.
Frequently asked questions
What is the combined gas law?+
The combined gas law, P₁V₁/T₁ = P₂V₂/T₂, relates the pressure, volume and absolute temperature of a fixed amount of gas between two states. It combines Boyle's, Charles's and Gay-Lussac's laws into one equation.
What is Gay-Lussac's law?+
Gay-Lussac's law states that at constant volume, pressure is proportional to absolute temperature: P₁/T₁ = P₂/T₂. Set V₁ = V₂ in this calculator to use it — that is why aerosol cans warn against heating.
Do temperatures need to be in kelvin?+
Yes. The gas laws are proportions that only hold on an absolute scale. This calculator accepts °C or °F and converts them to kelvin automatically before solving.
What are standard temperature and pressure (STP)?+
IUPAC defines STP as 0 °C (273.15 K) and 100 kPa, while many textbooks still use 0 °C and 1 atm (101.325 kPa). At 0 °C and 1 atm one mole of ideal gas occupies about 22.4 L.
When should I use the ideal gas law instead?+
Use PV = nRT when you need the amount of gas in moles, or when the amount changes. The combined gas law is simpler when you compare two states of the same sample.