About the Boyle's Law Calculator
This Boyle's law calculator finds the missing pressure or volume when a fixed amount of gas is compressed or expanded at constant temperature. Choose which of P₁, V₁, P₂ or V₂ you want, enter the other three, and it solves P₁V₁ = P₂V₂ and plots the isotherm — the curve every state of that gas sits on.
It suits chemistry and physics students, scuba divers thinking about how air in a lung or a balloon changes with depth, and anyone working with syringes, pistons or compressed-gas cylinders. Because the law is a ratio, you can use any pressure unit (atm, kPa, bar, mmHg, psi) and any volume unit, as long as both states use the same ones.
Boyle's law assumes an ideal gas, a closed system (no gas added or lost) and constant temperature. Real gases deviate at high pressures or near condensation, and fast compression heats a gas, so give it time to return to the starting temperature.
With the default inputs, the answer is 4. Change any value above to recalculate instantly.
How to use the boyle's law calculator
- 1Choose which quantity you want to find.
- 2Select the pressure and volume units (use the same units for both states).
- 3Enter the three known values.
- 4Read the answer and see where both states sit on the pressure–volume curve.
Formula and method
Boyle's law says that for a fixed mass of ideal gas at constant temperature, pressure and volume are inversely proportional: their product P × V stays constant. Doubling the pressure halves the volume, and halving the pressure doubles it.
To solve, the calculator multiplies the known pair (P and V of one state) and divides by the known value of the other state. Because only ratios matter, any pressure or volume unit works provided both states use the same unit. It follows from the ideal gas law PV = nRT with n and T held fixed.
- P₁, V₁
- Initial pressure and volume
- P₂, V₂
- Final pressure and volume
Worked examples
Compressing a gas
10 L of gas at 1 atm is squeezed to 2.5 atm. V₂ = 1 × 10 ÷ 2.5 = 4 L — 40% of the starting volume.
Syringe pressure
Pushing a sealed 60 mL syringe of air at 101.3 kPa down to 20 mL gives P₂ = 101.3 × 60 ÷ 20 = 303.9 kPa, three times the starting pressure.
Balloon rising to lower pressure
A 3.2 L balloon at 760 mmHg rises to where pressure is 540 mmHg. Its volume becomes 760 × 3.2 ÷ 540 ≈ 4.50 L, assuming the temperature does not change.
Frequently asked questions
What is Boyle's law?+
Boyle's law states that at constant temperature, the pressure of a fixed amount of gas is inversely proportional to its volume: P₁V₁ = P₂V₂. It was published by Robert Boyle in 1662.
Do I need to convert units for Boyle's law?+
No conversion is needed as long as both states use the same units. The answer comes out in whatever pressure or volume unit you used for the known values.
Why does Boyle's law require constant temperature?+
Temperature also changes pressure and volume (Charles’s and Gay-Lussac’s laws). If temperature varies, use the combined gas law P₁V₁/T₁ = P₂V₂/T₂ instead.
What are real-life examples of Boyle's law?+
Breathing (the diaphragm enlarges the lungs, lowering pressure so air flows in), syringes, bicycle pumps, and scuba diving, where air in the lungs compresses as depth and water pressure increase.
When does Boyle's law fail?+
It is exact only for an ideal gas. At very high pressures or low temperatures, molecular volume and attractions matter, and the van der Waals equation or other real-gas models are more accurate.