Boyle's Law Calculator
Squeeze a Gas and Its Pressure Fights Back
Boyle's law describes one of the most tangible relationships in physics: at constant temperature, compressing a gas into a smaller space raises its pressure by exactly the same proportion. Push the plunger on a sealed syringe halfway in and the pressure inside doesn't just increase — it doubles. This inverse relationship between pressure and volume was established experimentally by Robert Boyle in 1662 and still holds for ideal gases today.
The Formula
The product of pressure and volume for a fixed amount of gas at a constant temperature never changes. Knowing any three of P1, V1, P2, and V2 lets you solve for the fourth.
Where Boyle's Law Applies
- Scuba diving — a lungful of air at depth expands as a diver ascends and pressure drops, which is why divers are trained never to hold their breath while surfacing.
- Medical ventilators and syringes — dosing and gas delivery devices rely on the predictable pressure-volume relationship of the gas being moved.
- Aerosol and pneumatic systems — compressed air tools and spray cans are sized and rated around how much a given gas charge will expand or compress.
- Weather balloons — as a balloon rises into lower-pressure air, its volume expands in the inverse proportion Boyle's law predicts.
A Worked Example
A 60 mL syringe filled with gas at 1 atmosphere is sealed and its plunger pushed in until the gas occupies just 20 mL:
P2 = (1 atm × 60 mL) / 20 mL
P2 = 3 atm
Compressing the gas to a third of its original volume triples its pressure — the inverse relationship holds exactly.
How to Use This Calculator
- Choose what to solve for: Find Final Pressure (P2) or Find Final Volume (V2).
- Enter the Initial Pressure (P1) and Initial Volume (V1).
- Enter the known final value — Final Volume (V2) if solving for pressure, or Final Pressure (P2) if solving for volume.
- Select Calculate to see the result along with the worked formula.
Related Calculations
For the temperature-driven counterpart to this relationship, see the Charles's Law Calculator, or combine pressure, volume, temperature, and quantity in one equation with the Ideal Gas Law Calculator.