The combined gas law brings together Boyle's, Charles's and Gay-Lussac's laws for a fixed amount of gas. Enter the starting pressure, volume and temperature and the new pressure and temperature to get the new volume.
Enter the initial pressure, volume and temperature.
Enter the final pressure and temperature.
Read the final volume.
Combined gas law: P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂
The combined gas law tracks what happens to a fixed amount of gas when its pressure and temperature both change. This calculator takes the starting pressure, volume and temperature, and the new pressure and temperature, and returns the new volume using P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂. It converts Celsius to kelvin automatically and shows how the formula reduces to Boyle's or Charles's law in special cases.
The law is part of Class 11 chemistry and physics. It explains why sealed chip packets puff up when carried to Leh or Shimla, why a balloon shrinks in a cold room, why tyre pressure rises after a long drive and why scuba divers must breathe out as they rise. Unlike the ideal gas law calculator, it needs no gas constant or number of moles, only the before and after conditions.
1. Write P₁, V₁ and T₁ for the starting state. Pressure and volume can be in any unit, as long as you use the same units for both states.
2. Convert both temperatures to kelvin: T = °C + 273.15.
3. Write P₂ and T₂ for the new state.
4. Rearrange P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂ to get V₂ = P₁ × V₁ × T₂ ÷ (T₁ × P₂).
5. Check the direction: higher pressure should shrink the gas, higher temperature should expand it.
6. If temperature is unchanged, this reduces to Boyle's law P₁V₁ = P₂V₂; if pressure is unchanged, to Charles's law V₁ ÷ T₁ = V₂ ÷ T₂.
Boyle found that at fixed temperature, PV is constant. Charles found that at fixed pressure, V is proportional to absolute temperature. Gay-Lussac found that at fixed volume, P is proportional to absolute temperature. If all three hold for a fixed amount of gas, then PV ÷ T must be constant too, whichever variables change. That constant is nR, from the ideal gas law, but because it cancels between the two states you never need to know n or R to use the combined law.
Gas volume at constant pressure is proportional to absolute temperature, which starts at absolute zero, −273.15 °C. Celsius has an arbitrary zero at the freezing point of water, so ratios in Celsius are meaningless. Warming a gas from 10 °C to 20 °C does not double its volume; in kelvin it goes from 283.15 K to 293.15 K, a rise of about 3.5%. Pressures in the formula must also be absolute, not gauge readings, for the same reason.
The law assumes the amount of gas is fixed, so no leaks and no reactions, and that the gas behaves ideally. It holds well for air and common gases at everyday pressures and temperatures. It fails near condensation, for example steam close to 100 °C at atmospheric pressure, and at very high pressures. Real containers also matter: a rigid cylinder keeps V fixed, while a balloon's rubber adds some pressure of its own, so the gas pressure inside differs slightly from the air outside.
Rahul seals a 0.5-litre packet of snacks in Delhi at 101 kPa and 30 °C and carries it to Leh, where the air pressure is about 65 kPa and it is 5 °C.
Convert to kelvin: T₁ = 303.15 K, T₂ = 278.15 K
P₁V₁/T₁ = P₂V₂/T₂ → V₂ = P₁V₁T₂ ÷ (T₁P₂): = 101 × 0.5 × 278.15 ÷ (303.15 × 65) = 0.7129 L
Special cases: Same T → Boyle's law P₁V₁ = P₂V₂; same P → Charles's law V₁/T₁ = V₂/T₂
Answer: Final volume V₂ 0.7129 L
Using Celsius temperatures directly in the ratio.
Using gauge pressure from a tyre gauge instead of absolute pressure.
Mixing units, such as P₁ in atm and P₂ in kPa.
Applying the law when gas is leaking or being added.
Forgetting that a flexible packet can only expand until its material stretches or bursts.
Class 11 gas law numericals.
Predicting how sealed packets, balloons and bottles behave at hill stations and in aircraft.
Estimating tyre pressure change between a cold morning and a hot afternoon.
Correcting measured gas volumes to standard conditions in labs.
Understanding breathing gas expansion in scuba diving.
Can I use atm or mmHg?
Yes, as long as P₁ and P₂ use the same unit.
Why kelvin?
Gas volume is proportional to absolute temperature; Celsius would give wrong ratios.