Combined Gas Law Calculator: P1 V1 / T1 = P2 V2 / T2

The gas laws joined into one: pressure, volume and temperature all changing.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}
  • P_2 = \frac{P_1V_1T_2}{T_1V_2}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the final pressure: final pressure = (starting pressure x starting volume x final temperature) / (starting temperature x final volume)
  2. Put the values in (every value in its SI unit): final pressure = (100 x 2 x 350) / (300 x 1.5)
  3. The answer: final pressure: 155.556 kPa
  4. The same answer in other units: 1.55556 bar; 1.53521 atm; 22.5614 psi

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is the combined gas law?

For a fixed amount of gas, the pressure times the volume divided by the absolute temperature stays constant.

When do I use it?

When the pressure, the volume and the temperature of a gas all change, for example a balloon rising into the atmosphere.

Do I need kelvin?

Yes, for the temperatures. The pressures and volumes can be in any units as long as they match.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any physics or chemistry text (the gas laws).

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