When a gas is squeezed, heated or released into a bigger space, its pressure, volume and temperature change together. As long as no gas gets in or out, those three quantities stay linked by a single ratio. This calculator uses the combined gas law to find any one of the six values, pressure, volume and temperature before and after, from the other five. Each value has its own unit menu, and temperatures are converted to kelvin automatically.
How to use the combined gas law calculator
- Choose what to Solve for: initial or final pressure, volume or temperature.
- Enter the Initial state: pressure in Pa, kPa, MPa, bar, mbar, atm, psi, Torr, mmHg or inHg; volume in L, mL, m³, cm³, ft³, in³ or gallons; temperature in °C, °F, K or °R.
- Enter the Final state in the same way, leaving the unknown blank.
- Pick the unit for the answer.
- Read the result, the pressure, volume and temperature ratios, the amount of gas implied by the first state, and which special case applies if one quantity stays constant.
Combined gas law formula
Rearranged for each unknown:
The initial values follow the same pattern with the subscripts swapped. Both temperatures must be absolute, and both pressures absolute.
Worked example
A balloon rising into thin, cold air
A sealed balloon holds 2.0 L of gas at 1.00 atm and 25 °C. It rises to where the pressure is 0.50 atm and the temperature is −20 °C.
Convert temperatures: T1 = 298.15 K, T2 = 253.15 K.
V2 = 1.00 × 2.0 × 253.15 ÷ (298.15 × 0.50) = 3.40 L
Halving the pressure alone would double the volume to 4.0 L, but the cold shrinks it by a factor of 0.849, giving 3.40 L. The sample is about 0.082 mol of gas.
Heating a closed container. A rigid 1 L can holds gas at 1.00 atm and 25 °C. Heat it to 125 °C without letting the volume change, and solve for the final pressure: with V1 = V2, P2 = 1.00 × 398.15 ÷ 298.15 = 1.34 atm, a Gay-Lussac’s law case. This is why aerosol cans carry warnings to keep them away from heat.
The gas laws it contains
| Held constant | Law | Relationship |
|---|---|---|
| Temperature | Boyle’s law | P1V1 = P2V2 |
| Pressure | Charles’s law | V1/T1 = V2/T2 |
| Volume | Gay-Lussac’s law | P1/T1 = P2/T2 |
| Nothing | Combined gas law | P1V1/T1 = P2V2/T2 |
When you enter equal values for one quantity, the calculator names the special case it reduces to. The dedicated Boyle’s law calculator and Charles’s law calculator add diagrams for those cases.
Limits of the law
The combined gas law assumes ideal behavior: molecules with no volume and no attraction for each other. Real gases follow it closely near room conditions but deviate at high pressures and near condensation, and below about 100 K most gases liquefy, which the calculator flags. It also assumes the amount of gas is fixed; if gas leaks or is added, use the ideal gas law calculator for each state instead. To change pressure or temperature units on their own, use the pressure converter or the temperature converter.
Frequently asked questions
What is the combined gas law?
For a fixed amount of gas, P₁V₁/T₁ = P₂V₂/T₂, with absolute pressure and temperature in kelvin. It combines Boyle's law (P and V at constant T), Charles's law (V and T at constant P) and Gay-Lussac's law (P and T at constant V) into one equation.
Why must temperature be in kelvin?
Gas volume and pressure are proportional to absolute temperature, which starts at absolute zero. On the Celsius scale, going from 10 °C to 20 °C does not double anything; in kelvin it is 283.15 K to 293.15 K, a 3.5% increase. The calculator converts °C, °F and °R for you.
Can I mix units such as atm and kPa?
Yes. Every pressure, volume and temperature has its own unit menu, and the calculator converts everything to SI before solving. You can enter P₁ in psi and P₂ in bar, or V₁ in mL and V₂ in liters.
How is this different from the ideal gas law?
The ideal gas law, PV = nRT, links one state of a gas to its amount in moles. The combined gas law compares two states of the same sample, so you do not need to know the amount. The calculator still reports the implied moles from the first state.
Does it matter whether I use gauge or absolute pressure?
Yes. The law needs absolute pressure. Tire and tank gauges read pressure above the atmosphere, so add about 14.7 psi or 101.3 kPa at sea level before entering the value; otherwise the ratios will be wrong.