Boyle's Law describes how a fixed amount of gas behaves when you change its volume at constant temperature: the pressure and volume are inversely proportional, so their product never changes — P₁V₁ = P₂V₂. Compress the gas into half the space and the pressure doubles; let it expand to twice the volume and the pressure halves. It is the constant-temperature special case of the ideal gas law and the most intuitive of the gas laws, governing everything from a bicycle pump to the breath in your lungs.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Boyle's Law as the isothermal case of PV = nRT.
The Boyle's Law equations
The product P × V is a constant for the gas as long as temperature and the amount of gas stay fixed. To find any one of the four quantities, set the two products equal and divide. Because pressure appears on both sides — and volume on both sides — the units cancel in pairs, so you can work in atm and litres, kPa and millilitres, or any consistent pair without converting to SI.
Worked example — compressing a gas
Scenario: A 2-litre sample of gas at 1 atm is compressed to 1 litre at the same temperature. What is the new pressure?
Halving the volume doubles the pressure to 2 atm — the product P × V stays at 2 atm·L throughout. Push the compression further to 0.5 L and the pressure climbs to 4 atm; expand back out to 4 L and it would fall to 0.5 atm. The inverse relationship is exact at constant temperature, which is why the same 2 atm·L appears in every row.
Frequently Asked Questions
At constant temperature, gas pressure and volume are inversely proportional: P₁V₁ = P₂V₂. Half the volume, double the pressure.
P₂ = P₁·V₁/V₂. e.g. 1 atm × 2 L ÷ 1 L = 2 atm. New volume is V₂ = P₁·V₁/P₂.
Yes — Boyle's Law is the isothermal case. If T changes, use P₁V₁/T₁ = P₂V₂/T₂ or PV = nRT.
Any consistent units — atm/kPa/psi for pressure, L/mL for volume. They cancel, so no SI needed.
Same molecules in less space hit the walls more often per area. Half the volume ≈ double the collisions = double pressure.