This combined gas law calculator solves P₁V₁/T₁ = P₂V₂/T₂ for any one missing value — the single equation that unites Boyle’s, Charles’s and Gay-Lussac’s laws for a fixed amount of gas.

–

Temperatures must be in Kelvin (°C + 273.15). Pressure and volume units just need to match on both sides — kPa with kPa, liters with liters.

One Law, Three Famous Special Cases

For a sealed, fixed amount of gas, the quantity PV/T never changes. Hold one variable constant and the combined law collapses into each historical law: temperature fixed → Boyle’s law (PV = constant); pressure fixed → Charles’s law (V/T); volume fixed → Gay-Lussac’s law (P/T). The combined law is simply all three allowed to move at once — and the stepping stone to the Ideal Gas Law, which adds the amount of gas itself. Part of our Chemistry Calculators collection.

Worked Example (Verified)

A gas occupies 2.0 L at 100 kPa and 300 K. It is compressed to 150 kPa and heated to 450 K. New volume?

  • V₂ = P₁V₁T₂ ÷ (T₁P₂) = (100 × 2.0 × 450) ÷ (300 × 150) = 90,000 ÷ 45,000 = 2.0 L
  • The squeeze (×1.5 pressure) and the heating (×1.5 absolute temperature) exactly cancel — a coincidence of the chosen numbers, and a clean way to see the two effects fight.
  • Check with Boyle alone first (100→150 kPa would shrink it to 1.33 L), then Charles alone (300→450 K would expand that to 2.0 L ✔)

The Kelvin Rule (Where Most Errors Live)

  • Gas laws measure temperature from absolute zero — always convert: K = °C + 273.15. Using 27 °C instead of 300 K is not a small error; it is a tenfold one.
  • Pressure units: consistent pairs only, but gauge vs. absolute matters in real engineering: a “30 psi” tire gauge reads ~44.7 psi absolute. Textbook problems assume absolute unless stated.
  • The amount of gas must truly be fixed — leaks, reactions or a breathing balloon opening break the law’s one assumption.

Related Tools

Frequently Asked Questions

What is the combined gas law formula?

P₁V₁/T₁ = P₂V₂/T₂, valid for a fixed amount of gas. Leave any one variable out and algebra isolates it — the calculator does exactly that.

Why must temperature be in Kelvin?

Because gas behavior scales with absolute temperature — molecular kinetic energy is proportional to kelvins, not to Celsius degrees, whose zero is arbitrary (the freezing point of water). Ratios computed in °C are simply wrong.

When do I use the combined gas law vs. the ideal gas law?

Combined: the same sealed sample in two states, amount unknown or irrelevant. Ideal (PV = nRT): whenever moles or mass of gas is known, given, or asked for.

Can pressure units be mmHg or atm?

Any unit at all, provided P₁ and P₂ share it (the units cancel in the ratio). Same for volume. Temperature is the exception — Kelvin, non-negotiable.

What if two variables are unknown?

One equation cannot determine two unknowns — you need another relationship (often the ideal gas law with a known mass, or a constant variable turning it into one of the three simpler laws).

Is this combined gas law calculator free?

Yes — free, instant, no sign-up.