Boyle's law states that at constant temperature and fixed amount of gas, pressure and volume are inversely proportional: P₁V₁ = P₂V₂. Doubling the pressure halves the volume.

Who discovered Boyle's law?

Robert Boyle published the result in 1662 from his experiments with a J-shaped glass tube containing mercury. Edme Mariotte independently confirmed the law in 1676.

What is an isothermal process?

An isothermal process is one in which temperature is held constant. Boyle's law describes gas behaviour during an isothermal compression or expansion.

Why must temperature be constant?

Heating or cooling a gas changes both pressure and volume independently of the P-V relationship Boyle's law describes. Keeping T fixed isolates the P-V dependency.

How does Boyle's law differ from Charles' law?

Boyle's law is isothermal: pressure and volume change at constant T. Charles' law is isobaric: volume and temperature change at constant P.

Does Boyle's law apply to real gases?

Yes, closely, for air, nitrogen, and oxygen at moderate pressure and room temperature. At very high pressure, real gas molecules take up enough of their own volume that the product PV is no longer perfectly constant, and the Van der Waals equation gives a more accurate result.

Boyle's Law Calculator

Solve P₁V₁ = P₂V₂, Boyle's law for an isothermal process. Enter any three values and the fourth is computed instantly.

Boyle's Law Calculator

P₁V₁ = P₂V₂ (constant T). Enter 3 values.

P₁

V₁

P₂

V₂ (solving for this)

V₂

1 L

V₂ = P₁V₁/P₂ = 1 L

Boyle's Law and the Isothermal Process

Boyle's law, P₁V₁ = P₂V₂, describes the inverse relationship between the pressure and volume of a fixed amount of gas held at constant temperature. Compress the gas to half its volume and its pressure doubles. Expand it to twice its volume and the pressure halves. The product PV remains constant throughout, which is the defining signature of an isothermal process.

Robert Boyle published this finding in 1662 after careful experiments with mercury in a J-tube, trapping a fixed column of air and measuring how its length changed as he added mercury to raise the pressure on it. The law is the historical and conceptual companion to Charles' law. Together they split general gas behaviour into a pressure-volume response and a volume-temperature response.

Kinetic molecular theory explains why the relationship is inverse rather than direct. Gas pressure comes from molecules colliding with the walls of their container. Squeeze the same number of molecules into a smaller volume and they strike the walls more often per second, so pressure rises. Temperature stays fixed, so the average speed of the molecules does not change; only the frequency of collisions does.

Boyle's Law Formula and Symbols

Symbol	Meaning	Unit
P₁	Initial pressure	Pa, kPa, atm, psi
V₁	Initial volume	L, mL, m³, ft³
P₂	Final pressure	Pa, kPa, atm, psi
V₂	Final volume	L, mL, m³, ft³

The four rearrangements of P₁V₁ = P₂V₂:

P₂ = P₁V₁ / V₂
V₂ = P₁V₁ / P₂
P₁ = P₂V₂ / V₁
V₁ = P₂V₂ / P₁

Worked Example 1: Syringe Compression

A syringe contains 50 mL of air at 1.0 atm. The plunger is pushed until the volume is 20 mL at the same temperature. What is the new pressure? P₂ = P₁V₁/V₂ = (1.0 × 50)/20 = 2.5 atm. The volume shrank by a factor of 2.5 (from 50 mL to 20 mL), and the pressure rose by that same factor.

Worked Example 2: Scuba Diving

A diver's lungs hold 6.0 L of air at 1.0 atm at the surface. Descending to where the pressure is 3.0 atm, the lungs would compress to V₂ = P₁V₁/P₂ = (1.0 × 6.0)/3.0 = 2.0 L if the diver held their breath. This is the reason divers must always exhale steadily on ascent: the reverse expansion, from 2.0 L back to 6.0 L, can rupture lung tissue if the air is not allowed to escape.

Worked Example 3: Bicycle Pump

A bicycle pump barrel holds 400 mL of air at 1.0 atm before the stroke begins. Pushing the handle down compresses the air to 100 mL just before it flows into the tyre valve. What is the pressure inside the pump at that point? P₂ = P₁V₁/V₂ = (1.0 × 400)/100 = 4.0 atm. This is why a pump feels harder to push the further the stroke goes: the trapped air's pressure keeps climbing as its volume shrinks.

Boyle's vs Charles' Law: When to Use Which

Use Boyle's law when temperature is constant and you need to relate pressure and volume. Use Charles' law when pressure is constant and you need to relate volume and temperature. When both change, use the combined gas law or the isothermal process calculator for work and energy details.