Combined Gas Law formula
| Symbol | Quantity | SI unit | Meaning |
|---|---|---|---|
| P₁ | Initial pressure | Pa | Pressure in the initial state |
| V₁ | Initial volume | m³ | Volume in the initial state |
| T₁ | Initial temperature | K | Temperature in the initial state |
| P₂ | Final pressure | Pa | Pressure in the final state |
| V₂ | Final volume | m³ | Volume in the final state |
| T₂ | Final temperature | K | Temperature in the final state |
What is Combined Gas Law?
Combined Gas Law: For a fixed amount of gas, PV/T is constant. Holding T constant gives Boyle's law, holding P constant gives Charles's law, and holding V constant gives Gay-Lussac's law.
When a fixed quantity of gas changes state, the ratio PV/T stays the same. The combined gas law lets you predict the new pressure, volume or temperature after a change. It contains three classic special cases:
- Boyle's law (constant T): P₁V₁ = P₂V₂
- Charles's law (constant P): V₁/T₁ = V₂/T₂
- Gay-Lussac's law (constant V): P₁/T₁ = P₂/T₂
To use a special case, just enter the same value for the quantity held constant in both states.
How to use this calculator
- Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
- Enter the known values. Scientific notation such as
1.6e-11is accepted. - Select a unit for each value. Units are converted to SI automatically.
- The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.
Worked example
2.00 L of gas at 101.325 kPa and 25 °C is compressed to 200 kPa and warmed to 50 °C. What is the new volume?
- T₁ = 298.15 K, T₂ = 323.15 K.
- V₂ = P₁V₁T₂ / (T₁P₂) = 101.325 × 2.00 × 323.15 / (298.15 × 200).
- V₂ = 1.10 L.
Frequently asked questions
Does the amount of gas need to stay constant?
Yes. If gas is added or removed, use the ideal gas law PV = nRT for each state instead.
Can I use °C directly?
You can select °C in the unit menu, but the calculation always converts to kelvin. Plugging Celsius values straight into the formula by hand gives wrong results.