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Boyle's Law Calculator

Find the volume of a gas after a pressure change.

How it is calculated

Boyle's law says that for a fixed amount of gas at constant temperature, pressure times volume stays constant: P₁ × V₁ = P₂ × V₂. The tool solves for the new volume, V₂ = P₁ × V₁ / P₂, and shows it with four decimals. The two pressures must use the same unit (atm, kPa, bar and so on) and the answer comes out in whatever volume unit you used for V₁. All three values must be greater than zero. Pressure here must be absolute pressure, not gauge pressure. The law holds for ideal gases; real gases deviate at high pressure or very low temperature, and the temperature and amount of gas must not change.

Worked example

A gas occupies 6 L at 2 atm. It is compressed to 3 atm at the same temperature. V₂ = (2 × 6) / 3 = 12 / 3 = 4.0000 L. Pressure rose by a factor of 1.5, so volume fell to 1/1.5 of its value, which is two-thirds, and 6 × 2/3 = 4.

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Common mistakes

  • Using gauge pressure (the reading on a tyre gauge) instead of absolute pressure, which adds about 1 atm.
  • Mixing pressure units, such as P₁ in atm and P₂ in kPa.
  • Applying the law when the temperature changes; then the combined gas law is needed.
  • Mistaking the inverse relationship for a direct one and expecting volume to rise when pressure rises.
  • Using it when gas is added or leaks out, since the amount must stay fixed.

About this calculator

Boyle's law states that for a fixed amount of ideal gas at constant temperature, pressure and volume are inversely proportional: P₁V₁ = P₂V₂. Compress the gas into a smaller volume and its pressure rises proportionally; let it expand and pressure falls — a relationship discovered by Robert Boyle in 1662 and one of the founding gas laws that later combined into the ideal gas law (PV = nRT).

Chemistry and physics students use it as an entry point into gas behavior, but it's also practically important for scuba divers (understanding how air in the lungs and tank expands or compresses with depth, which is why divers are taught never to hold their breath while ascending), and for engineers working with compressed gas systems, syringes, and pneumatics. Enter the initial pressure and volume plus either the final pressure or final volume to solve for the other.

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