Thermodynamics & Heat
Basic

Boyle's Law

Pressure and volume are inversely related at constant T.

Formula

P1V1=P2V2P_1 V_1 = P_2 V_2

Variables

PPressure
VVolume

Example

Squeeze a gas to half its volume at fixed temperature and its pressure doubles.

How it works

Boyle's Law says that for a fixed amount of gas kept at the same temperature, lowering the volume makes the pressure rise, and increasing the volume makes the pressure fall. This happens because the gas molecules have the same average speed, so when they are confined to a smaller space they hit the container walls more often, creating greater pressure. The product of pressure and volume stays constant for the same sample of gas as long as temperature does not change.

When to use it

Use this formula when a gas is compressed or expanded without changing its temperature, such as in syringes, pistons, scuba gear, or sealed containers. It is also useful for any problem asking how pressure or volume changes for the same gas sample at constant temperature.

Worked example, step by step

A gas occupies 4.0 L at a pressure of 150 kPa. If the gas is compressed to 2.5 L at constant temperature, what is the new pressure? P1V1 = P2V2 (150 kPa)(4.0 L) = P2(2.5 L) 600 kPa·L = 2.5 L × P2 P2 = 600 ÷ 2.5 P2 = 240 kPa Final answer: the new pressure is 240 kPa.

Common mistakes to avoid

  • Using the formula when temperature changes, which breaks the condition for Boyle's Law
  • Mixing up the variables and multiplying or dividing in the wrong place
  • Forgetting to keep units consistent, such as using liters for one volume and milliliters for the other without converting

Did You Know?

Squeeze a gas into half the volume and its pressure doubles — Boyle showed this in 1662.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026