πŸ’¨ Boyle's Law Calculator

P₁V₁ = Pβ‚‚Vβ‚‚ at constant temperature. Solve for any variable.

β€”

How to Use This Calculator

Select the variable you want to find, enter the three known values, and click Calculate. Boyle's Law applies only when temperature and the amount of gas stay constant. You can use any unit for pressure and volume, as long as you use the same unit on both sides.

1

Choose what you are solving for: Vβ‚‚ (final volume), Pβ‚‚ (final pressure), V₁ (initial volume), or P₁ (initial pressure).

2

Enter the three known values. For example, if a gas starts at P₁ = 1 atm and V₁ = 10 L, and the pressure doubles to Pβ‚‚ = 2 atm, enter those three numbers.

3

Use the same pressure unit for P₁ and Pβ‚‚ (both atm, or both kPa, or both mmHg). Same rule for V₁ and Vβ‚‚.

4

Click Calculate. For the example above, Vβ‚‚ = (1 Γ— 10) / 2 = 5 L. The gas compressed to half its original volume.

Boyle's Law Formula

P₁V₁ = Pβ‚‚Vβ‚‚ (constant T and n) Vβ‚‚ = P₁V₁ / Pβ‚‚ Pβ‚‚ = P₁V₁ / Vβ‚‚

Boyle's Law states that at constant temperature, pressure and volume are inversely proportional. If you double the pressure on a gas, its volume is cut in half. If you triple the volume, the pressure drops to one-third. This makes intuitive sense: squeezing gas into a smaller space forces the molecules to collide with the walls more often, raising the pressure. P₁ and V₁ are the initial conditions, Pβ‚‚ and Vβ‚‚ are the final conditions after the change.

Worked Examples

P₁=1 atm, V₁=10 L, Pβ‚‚=2 atm: find Vβ‚‚5.00 L
P₁=4 atm, V₁=3 L, Vβ‚‚=6 L: find Pβ‚‚2.00 atm
P₁=101.3 kPa, V₁=22.4 L, Pβ‚‚=202.6 kPa: find Vβ‚‚11.20 L
Pβ‚‚=0.5 atm, V₁=8 L, Vβ‚‚=16 L: find P₁1.00 atm

Where This Calculation Comes Up

Boyle's Law comes up in any situation where a gas is compressed or expanded at roughly constant temperature. In the lab, you use it when you need to transfer gas from a large container to a small one and need to predict the resulting pressure, or when you pull a syringe back to expand the volume and observe the pressure drop. It also appears in problems where you calculate the pressure inside a gas-collecting tube at different depths.

In medicine, the mechanics of breathing rely directly on Boyle's Law. When your diaphragm contracts, the chest cavity volume increases, pressure inside the lungs drops below atmospheric pressure, and air flows in. Exhaling reverses this: volume decreases, pressure rises, air flows out. Scuba diving introduces a more dramatic version: at 10 metres depth the pressure roughly doubles, which means a lung full of air at the surface would compress to half the volume if you held your breath while descending. This is why divers are trained never to hold their breath during ascent.

Frequently Asked Questions

What is Boyle's Law?

Boyle's Law states that at constant temperature, the pressure and volume of a gas are inversely proportional: P₁V₁ = Pβ‚‚Vβ‚‚.

Why does pressure increase when volume decreases?

Compressing a gas into a smaller volume means molecules hit the walls more frequently, increasing pressure.

What units can I use?

Any consistent pressure units (atm, Pa, kPa, mmHg) and volume units (L, mL, mΒ³) β€” just keep both sides the same.

Does Boyle's Law apply to all gases?

It applies well to ideal gases and real gases at low to moderate pressures. At high pressures, deviations occur.

How does this relate to the ideal gas law?

Boyle's Law is a special case of PV=nRT where n and T are constant, giving P₁V₁ = Pβ‚‚Vβ‚‚ = nRT = constant.