Combined Gas Law Calculator

The combined gas law states that for a fixed mass of gas, the quantity PV/T stays constant, even as pressure, volume, and temperature all change at the same time. Written as a two-point equation, that's P₁V₁/T₁ = P₂V₂/T₂: the initial state on the left, the final state on the right. It's less a new law of its own than a merger of three others — Boyle’s law, Charles’ law, and Gay-Lussac’s law — into a single relation that doesn't require any one variable to be held still.

The derivation is really just algebra on the three single-variable laws. Boyle’s law says P₁V₁ = P₂V₂ when temperature is held constant. Charles’ law — covered on the main Charles law calculator — says V₁/T₁ = V₂/T₂ when pressure is held constant. Gay-Lussac’s law says P₁/T₁ = P₂/T₂ when volume is held constant. Each one is the combined gas law equation with one variable frozen out; unfreeze all three and you get P₁V₁/T₁ = P₂V₂/T₂ back, which is why the combined law is the natural tool once more than one thing is moving.

As with Charles’ and Gay-Lussac’s laws, temperature has to be on an absolute scale. A gas at 20 °C isn't "twice as hot" as a gas at 10 °C, but a gas at 200 K genuinely does have twice the average kinetic energy of one at 100 K — so this calculator always converts your temperature entries to Kelvin before running the ratio, the same absolute-zero safeguard the homepage's Charles' law calculator uses.

Rearranged for whichever value is unknown, the six forms are: P₂ = P₁V₁T₂ / (T₁V₂), V₂ = P₁V₁T₂ / (T₁P₂), T₂ = T₁P₂V₂ / (P₁V₁), P₁ = P₂V₂T₁ / (T₂V₁), V₁ = P₂V₂T₁ / (T₂P₁), and T₁ = P₁V₁T₂ / (P₂V₂). The calculator above picks the right one automatically based on which single field you leave blank.

Pressure can be entered in kilopascals, atmospheres, millimetres of mercury, or pounds per square inch; volume in litres, millilitres, cubic metres, or cubic feet; and temperature in Kelvin, Celsius, or Fahrenheit. If your two readings arrived in different units — say one temperature in °C and the other already in K, or one volume in litres and the other in cubic feet — running them through the temperature converter or the volume converter first makes it easy to sanity-check the numbers by eye before they go into the six fields above. The calculator does the same conversion internally regardless, so it isn't strictly necessary — it's just a good habit for catching typos.

The combined gas law is the right tool specifically when more than one of pressure, volume, and temperature changes between your two states. If only temperature is changing while pressure stays fixed, that's Charles' law, and the main Charles law calculator needs one fewer input to solve it. If only pressure and volume are changing at constant temperature, that's Boyle's law. If only pressure and temperature are changing at constant volume — a sealed rigid container being heated, for instance — that's Gay-Lussac's law. Using the matching single-variable calculator in any of those cases is simpler, since it asks for one less value and skips a multiplication step.

The combined gas law earns its keep once two or all three variables move together, like the weather balloon above where pressure, volume, and temperature all changed at once. What it can't handle is a change in the amount of gas itself — moles added or removed, gas leaking out, or a reaction consuming some of it. For that, step up to the Ideal Gas Law calculator, which adds the mole count n and the gas constant R into the mix via PV = nRT. Every combined-gas-law problem is really a special case of the ideal gas law where n happens to stay fixed — the same relationship Boyle's, Charles', and Gay-Lussac's laws each have to the combined law one level down.