Last updated: 2026-07-01

What Boyle's law describes

Boyle's law captures one of the earliest quantitative discoveries about gases: at a fixed temperature, the pressure of a trapped gas rises as its volume falls, and vice versa. Compress a sample into a smaller space and the molecules strike the walls more often, so pressure climbs. Let it expand and the pressure eases. Robert Boyle established this inverse relationship in 1662, and it remains a cornerstone of introductory chemistry and physics.

The formula

For a fixed amount of gas held at constant temperature, the product of pressure and volume stays the same:

$$P_1 V_1 = P_2 V_2$$

Rearranging isolates whichever quantity is unknown:

$$P_2 = \frac{P_1 V_1}{V_2}, \qquad V_2 = \frac{P_1 V_1}{P_2}$$

Symbol	Quantity	Unit
P₁	Initial pressure	kPa (or atm, bar, mmHg)
V₁	Initial volume	L (or mL)
P₂	Final pressure	kPa (or atm, bar, mmHg)
V₂	Final volume	L (or mL)

Because the law is a ratio, the two pressures merely need to share a unit, and likewise the two volumes. Temperature and the amount of gas never appear — they are held constant, so they cancel.

Worked example

A gas occupies 2.0 L at 101.325 kPa. It is compressed at constant temperature until its volume is 1.0 L. What is the new pressure?

1. Identify the knowns: P₁ = 101.325 kPa, V₁ = 2.0 L, V₂ = 1.0 L.
2. Rearrange for the unknown: P₂ = P₁V₁ ÷ V₂.
3. Substitute: P₂ = (101.325 × 2.0) ÷ 1.0 = 202.65 kPa.

Halving the volume doubles the pressure, exactly as the inverse relationship predicts.

The inverse relationship in practice

Because pressure and volume multiply to a constant, plotting one against the other traces a hyperbola: as volume approaches zero the pressure grows without bound, and as volume grows large the pressure tends toward zero. This behaviour explains everyday observations — a syringe grows harder to push as the plunger advances, and a bubble rising through water swells as the surrounding pressure drops.

Volume (L)	Pressure (kPa)	P × V (kPa·L)
2.0	101.325	202.65
1.0	202.65	202.65
0.5	405.30	202.65
4.0	50.66	202.65

The final column stays constant, which is the signature of Boyle's law.

When the simple form breaks down

Boyle's law assumes ideal behaviour and a strictly constant temperature. Near a gas's condensation point, or at very high pressure, intermolecular forces and the finite size of molecules cause measurable deviations, and a real-gas model such as the van der Waals equation gives a closer estimate. If the temperature also changes during the process, the pressure-volume product no longer holds fixed, and the combined gas law is the right tool.

Related calculations

Boyle's law is one branch of the combined gas law, alongside Charles's law (constant pressure) and Gay-Lussac's law (constant volume). When you need an absolute quantity such as the number of moles rather than a comparison between two states, the ideal gas law PV = nRT is the starting point, and the molar volume of a gas links a measured volume back to an amount in moles.

Frequently Asked Questions (FAQ)

What is Boyle's law?

Boyle's law states that, for a fixed amount of gas held at constant temperature, pressure and volume are inversely proportional: P₁V₁ = P₂V₂. Squeezing a gas into half the volume doubles its pressure, and letting it expand to twice the volume halves the pressure. Given any three of the four values, the fourth follows directly from the equation.

Which units can I use in Boyle's law?

Because the law is a ratio, the two pressures only need to share the same unit, and the two volumes only need to share the same unit — they cancel. This calculator lets you enter pressure in kilopascals, atmospheres, bar, or millimetres of mercury, and volume in litres or millilitres, converting internally so the result is consistent.

How does Boyle's law relate to the combined gas law?

Boyle's law is the special case of the combined gas law (P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂) in which temperature does not change. When T₁ = T₂ the temperature terms cancel and the expression reduces to P₁V₁ = P₂V₂. If temperature also changes during the process, use the combined gas law instead.

Why must temperature stay constant for Boyle's law?

The simple inverse relationship holds only when temperature (and the amount of gas) is fixed. Heating a gas adds energy that changes pressure and volume independently of the Boyle relationship, so P₁V₁ = P₂V₂ would no longer balance. A process at constant temperature is called isothermal, and Boyle's law describes exactly that case.