Boyle's Law Pressure-Volume

Find final gas pressure with Boyle's Law

Result

243.12

How it is calculated

Boyle's law says the product of pressure and volume stays constant for a fixed amount of gas at constant temperature: P1 × V1 = P2 × V2. The tool solves for the final pressure: P2 = P1 × V1 ÷ V2. The result is a bare number with no unit attached; it comes out in whatever pressure unit you used for P1 (kPa, atm, bar, psi). Likewise V1 and V2 can be in any volume unit, as long as both use the same one. All three values must be above zero. Use absolute pressure, not gauge pressure, and keep the temperature and the amount of gas unchanged. If the gas leaks, heats or condenses, the law no longer applies.

Worked example

A gas at 101.3 kPa occupies 6 litres and is compressed to 2.5 litres at the same temperature. Multiply the starting pressure by the starting volume: 101.3 × 6 = 607.8. Divide by the final volume: 607.8 ÷ 2.5 = 243.12, in kPa because P1 was entered in kPa. The volume fell to 42% of its start (2.5 ÷ 6), so the pressure rose by the factor 6 ÷ 2.5 = 2.4.

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Common mistakes

  • Entering gauge pressure (for example a tyre gauge reading). The law needs absolute pressure, which is gauge plus about 101.3 kPa at sea level.
  • Mixing volume units for V1 and V2, such as litres and millilitres.
  • Applying the law when the temperature changes. A gas that heats up during compression breaks the assumption.
  • Reading the result in the wrong unit. The tool does not label it; it is in the same unit as your P1.
  • Swapping V1 and V2 and getting a pressure drop where a rise was expected. Smaller final volume means higher pressure.

About this calculator

Boyle's Law states that for a fixed amount of gas at constant temperature, pressure and volume are inversely related: P₁V₁ = P₂V₂. Compress a gas into half its original volume and its pressure doubles; let it expand to double its volume and pressure drops by half — the product of the two always stays the same.

Divers use it to understand how the volume of air in their lungs and gear changes with depth (and why holding your breath while ascending is dangerous), engineers apply it when sizing gas cylinders and pneumatic systems, and it's one of the first gas laws taught in chemistry because it isolates the pressure-volume relationship before temperature and moles are added back in with the ideal gas law.

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