Boyle's Law Calculator
Find the final pressure of a gas after compression or expansion using Boyle's Law. Used in physics and chemistry when temperature is held constant and volume changes.
About this calculator
Boyle's Law states that for a fixed amount of gas at constant temperature, pressure and volume are inversely proportional. The relationship is expressed as P₁V₁ = P₂V₂, where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume. Rearranging to solve for final pressure gives: P₂ = (P₁ × V₁) / V₂. This inverse relationship means that if you halve the volume, pressure doubles. Boyle's Law applies to ideal gases and is a reasonable approximation for real gases at moderate temperatures and pressures. It is fundamental to understanding how syringes, bicycle pumps, and atmospheric pressure changes with altitude all work.
How to use
A gas sample starts at an initial pressure of 2 atm and an initial volume of 5 L. The gas is compressed to a final volume of 2 L. Using the formula: P₂ = (P₁ × V₁) / V₂ = (2 × 5) / 2 = 10 / 2 = 5 atm. Enter 2 in 'Initial pressure', 5 in 'Initial volume', and 2 in 'Final volume'. The calculator returns a final pressure of 5 atm — the pressure doubled when volume was more than halved, consistent with the inverse relationship.
Frequently asked questions
Why does pressure increase when volume decreases according to Boyle's Law?
When the volume of a gas container decreases, the same number of gas molecules must move within a smaller space. This means they collide with the container walls more frequently, which we measure as higher pressure. This inverse relationship holds as long as temperature and the amount of gas remain constant. It is described mathematically by Boyle's Law: P₁V₁ = P₂V₂. Real gases deviate slightly from this ideal behavior at very high pressures or very low temperatures.
What are the conditions required for Boyle's Law to apply?
Boyle's Law applies strictly when two conditions are met: the temperature of the gas must remain constant (an isothermal process), and the amount of gas (number of moles) must not change. If heat is added or lost, or if gas escapes from the system, Boyle's Law alone is not sufficient and you would need to use the combined gas law or ideal gas law instead. The law also assumes ideal gas behavior, which is a good approximation for many real gases at ordinary temperatures and pressures.
How is Boyle's Law used in real-world applications?
Boyle's Law underlies the operation of many everyday devices. A syringe works by expanding its volume to draw in fluid and compressing it to push the fluid out — a direct application of pressure-volume relationships. Scuba divers must understand it because air in their lungs expands as they ascend to lower pressure depths, which is why controlled breathing is critical to safety. It also explains how bicycle pumps and air compressors work, and why a sealed bag of chips puffs up at high altitude where outside pressure is lower.