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Combined Gas Law Calculator

Enter any five values and leave one empty -- the calculator will solve for the missing value using P1V1/T1 = P2V2/T2. All temperatures must be in Kelvin.

Initial Conditions

Final Conditions

The combined gas law

The combined gas law is what falls out of PV = nRT when the amount of gas stays fixed. nR is a constant, so PV/T is also constant — meaning whatever value PV/T takes under the initial conditions, it takes the same value under any new conditions:

P₁V₁/T₁ = P₂V₂/T₂

This calculator takes any five of the six variables and solves for the missing one. The three most common scenarios — initial state to final state with all three changing, holding T constant (Boyle), holding P constant (Charles) — all use the same equation. Just plug in the known values and the law handles the special cases automatically.

The non-obvious part is unit handling. Pressure and volume units cancel cleanly across the equality, so any consistent choice works — atm with atm, mL with mL — but temperature has to be in Kelvin. The gas laws describe how kinetic energy scales with temperature, and only an absolute scale gives you the right ratios. If T₁ is 27 °C and T₂ is 327 °C, the physical ratio is 600 K / 300 K = 2, not 327/27. Convert before substituting.

The “fixed quantity” assumption matters too. If gas is added or removed between the two states, n changes and the ratio P₁V₁/T₁ no longer equals P₂V₂/T₂ — you need the full ideal gas law and have to solve for n on each side separately.

Worked examples

Boyle case (T constant): gas at 2.00 atm, 5.00 L, 298 K. Drop pressure to 1.00 atm at the same temperature. V₂ = (P₁V₁T₂)/(T₁P₂) = (2.00 × 5.00 × 298)/(298 × 1.00) = 10.0 L.

All three changing: 1.50 atm, 3.00 L, 300 K → 2.50 atm, ?, 400 K. V₂ = (1.50 × 3.00 × 400)/(300 × 2.50) = 1800/750 = 2.40 L.

Solving for T₂: 1.00 atm, 2.50 L, 273 K → 3.00 atm, 0.500 L, ? T₂ = (P₂V₂T₁)/(P₁V₁) = (3.00 × 0.500 × 273)/(1.00 × 2.50) = 163.8 K (about −109 °C).

Frequently Asked Questions

What is the combined gas law?
The combined gas law relates pressure, volume, and temperature of a fixed quantity of gas under two different sets of conditions: P₁V₁/T₁ = P₂V₂/T₂. It comes from PV = nRT — for a fixed amount of gas, PV/T equals nR, which is constant. So whatever PV/T equals before a change, it equals after. Boyle, Charles, and Gay-Lussac are special cases of this expression with one variable held constant.
What are the special cases of the combined gas law?
Hold T constant and you get Boyle's law: P₁V₁ = P₂V₂. Hold P constant and you get Charles's law: V₁/T₁ = V₂/T₂. Hold V constant and you get Gay-Lussac's law: P₁/T₁ = P₂/T₂. Each was discovered separately before the combined form pulled them together. In practice, you rarely need to remember the named laws — solve the combined form and let the constants on each side cancel.
Why must temperature be in Kelvin?
Gas behavior depends on absolute temperature — the kinetic energy of the molecules. Celsius and Fahrenheit are anchored to arbitrary reference points (water's freezing point, a brine bath), so doubling 25 °C to 50 °C does not double the molecular kinetic energy. Kelvin starts at absolute zero, where kinetic energy is zero, so ratios on the Kelvin scale match the underlying physics. Add 273.15 to °C to convert.
Does the combined gas law work for real gases?
It works well at moderate temperatures and pressures where intermolecular forces are weak and molecular volume is small compared to the container. Near condensation — high pressure or low temperature — real gases compress more than the law predicts (attractive forces dominate) or less (excluded volume dominates). The van der Waals equation adds two correction terms for these effects.
What units should I use for pressure and volume?
Any pressure unit works as long as both P₁ and P₂ use the same one. Same for volume. The units cancel in the ratio, so atm, kPa, mmHg, torr, or psi all give the same answer if you stay consistent. Temperature is the exception — it must always be in Kelvin, because the absolute zero point matters when you're taking ratios.