Boyle's Law Calculator: P1 V1 = P2 V2

How the pressure of a gas changes when its volume changes at a constant temperature.

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

  • P_1V_1 = P_2V_2
  • P_2 = \frac{P_1V_1}{V_2}
  • V_2 = \frac{P_1V_1}{P_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) / (final volume)
  2. Put the values in (every value in its SI unit): final pressure = (100 x 2) / (1)
  3. The answer: final pressure: 200 kPa
  4. The same answer in other units: 2 bar; 1.97385 atm; 29.0075 psi

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

Common questions

What is Boyle's law?

For a fixed mass of gas at constant temperature, the pressure times the volume stays constant.

How do I find the new pressure?

Multiply the old pressure by the old volume and divide by the new volume.

Do I use gauge pressure?

No. Use absolute pressure, which is the gauge pressure plus the atmospheric pressure.

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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