Combined Gas Law Calculator

Leave any one of the six values blank and it solves for that one, converting units and checking the physics as it goes.

Advertisement
AD · 728×90 / 320×100
How to use this calculator

Fill in five of the six values and leave the one you want blank. Pick the units for each field; temperatures are converted to kelvin internally before anything is calculated, which is where most hand-worked answers go wrong. If a value would sit at or below absolute zero, it tells you instead of returning a number.

PV₁ / T₁ = PV₂ / T

One law instead of three

Before the combined gas law you had to remember three separate relationships: pressure against volume, volume against temperature, and pressure against temperature. Each held only if you froze the third variable.

P₁V₁ / T₁ = P₂V₂ / T₂

The combined law puts them together. Whatever the gas does, that whole expression keeps the same value, so knowing five of the six numbers is enough to find the sixth.

Kelvin is not optional

The most common mistake with this law is not algebra, it is units. Because the relationship is a ratio, temperature has to be measured from absolute zero. Use Celsius and 20 °C looks like twice 10 °C, which is simply false — 293 K is nowhere near twice 283 K.

The calculator converts everything to kelvin before touching the arithmetic, and refuses any value at or below absolute zero rather than quietly returning a nonsense number.

A worked example

Two litres of gas at 1 atm and 273 K, compressed to 2 atm and heated to 546 K:

V₂ = P₁V₁T₂ / (T₁P₂) = (1 × 2 × 546) / (273 × 2) = 2 L

Unchanged — doubling the pressure would have halved the volume, and doubling the temperature doubles it back. Worth trying with only one of the two changed, to see each effect on its own.

Advertisement
AD · Native

Frequently asked questions

What is the combined gas law?

It states that pressure times volume divided by temperature stays constant for a fixed amount of gas: P₁V₁/T₁ = P₂V₂/T₂. It merges Boyle's law, Charles's law and Gay-Lussac's law into one relationship, so you only need to remember the one.

Why must temperature be in kelvin?

Because the law is a proportion, and proportions need a scale that starts at true zero. Celsius and Fahrenheit both have arbitrary zero points, so using them makes the ratio meaningless — and at low temperatures it can produce negative volumes. Converting to kelvin first is the single most common fix for a wrong answer.

Worked example

A gas at 1 atm, 2 L and 273 K is compressed to 2 atm while being heated to 546 K. Rearranging: V₂ = P₁V₁T₂ / (T₁P₂) = (1 × 2 × 546) / (273 × 2) = 2 L. The doubled pressure and the doubled temperature cancel exactly.

What if the amount of gas changes?

Then this law does not apply, because it assumes a fixed number of moles. If gas is added or removed you need the ideal gas law, PV = nRT, which carries the amount explicitly.

How accurate is it for real gases?

Good enough for most everyday and classroom conditions. It drifts at very high pressures or near the point where a gas would liquefy, because real molecules take up space and attract each other, which the law ignores.