Solve P₁V₁ = P₂V₂ instantly. Enter any three values and the calculator fills in the fourth, at constant temperature.
Computed from the other three values.
Final Pressure
P₂ = 3 atm
P₂ = P₁V₁ / V₂ = (1 atm × 60 mL) / 20 mL = 3 atm
Boyle’s law states that the pressure of a fixed mass of gas is inversely proportional to its volume when temperature is held constant. In equation form: P ∝ 1/V, or equivalently PV = constant. For two states of the same gas at constant temperature, this gives the two-point form P₁V₁ = P₂V₂.
Definition
Boyle’s law states that the pressure and volume of a fixed mass of gas are inversely proportional when temperature is held constant: squeeze the volume down and the pressure rises to match, in exact proportion.
The law is named after Robert Boyle, who published it in 1662 after a series of experiments compressing air in a J-shaped glass tube. It was one of the first quantitative gas laws established, and it remains the textbook example of an isothermal process — a change that happens at constant temperature. If you want the full breakdown of the work done during that kind of compression or expansion, the isothermal process calculator picks up exactly where this page leaves off.
Boyle’s law is a special case of the Ideal Gas Law, PV = nRT: when the amount of gas n and temperature T are both fixed, the right-hand side is a constant, leaving PV = constant on the left — Boyle’s law exactly.
The formula P₁V₁ = P₂V₂ works in any consistent unit system — pressure can be entered in kilopascals, atmospheres, millimetres of mercury, or pounds per square inch, and volume in litres, millilitres, cubic metres, or cubic feet. Unlike the Charles' law homepage, there's no requirement to convert to a specific absolute scale first, since pressure and volume don't have the same "must be absolute" constraint that temperature does. If your two volumes were measured in different units, run them through the volume converter first so the ratio is easy to sanity-check by eye.
Rearranged for whichever value is unknown: P₂ = P₁V₁ / V₂, P₁ = P₂V₂ / V₁, V₂ = P₁V₁ / P₂, and V₁ = P₂V₂ / P₁. The calculator above picks the right rearrangement automatically based on which field you leave blank.
| Symbol | Meaning | Unit |
|---|---|---|
| P₁ | Initial pressure | kPa, atm, mmHg, psi |
| V₁ | Initial volume | L, mL, m³, ft³ |
| P₂ | Final pressure | kPa, atm, mmHg, psi |
| V₂ | Final volume | L, mL, m³, ft³ |
Example 1
A sealed syringe holds V₁ = 60 mL of air at P₁ = 1 atm. The plunger is pushed in until the volume drops to V₂ = 20 mL, with temperature unchanged. Find the new pressure.
Tripling the pressure for a third of the volume is exactly the inverse relationship Boyle’s law predicts.
Example 2
A diver's lungs hold V₁ = 2.5 L of air at the surface, where pressure is P₁ = 1 atm. Descending to a depth where pressure is P₂ = 2.5 atm, what volume would that same air occupy if it weren't replenished by breathing?
This is precisely why divers are trained never to hold their breath while ascending or descending: the volume change is real and can injure the lungs.
Boyle’s law holds temperature and the amount of gas constant and relates pressure to volume. It's the mirror image of Charles’ law, which holds pressure constant and relates volume to temperature instead — one page is the isothermal case, the other is the isobaric case, and together with Gay-Lussac's law they form the three building blocks of the combined gas law.
If your scenario changes pressure, volume, and temperature all at once, Boyle's law alone won't cover it — use the combined gas law calculator instead, which merges all three single-variable laws into one solver.
Boyle’s law states that the pressure of a fixed mass of gas is inversely proportional to its volume when temperature is held constant: as volume decreases, pressure increases, and vice versa.
P₁V₁ = P₂V₂, where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume of the same gas at the same temperature.
Use P₂ = P₁V₁ / V₂. No temperature conversion is needed here, unlike Charles’ law — Boyle’s law only involves pressure and volume.
Boyle’s law describes pressure and volume at constant temperature (an isothermal process). Charles’ law describes volume and temperature at constant pressure (an isobaric process). Use the Charles law calculator when temperature is the variable that changes.
Closely, at moderate pressure and temperature — air and other common gases follow it well enough for practical calculations. It becomes less accurate at very high pressure, where the Van der Waals equation gives a more precise result.
Volume is cut exactly in half, as long as temperature and the amount of gas stay constant. This inverse relationship is the defining feature of Boyle’s law.
Yes — together with Gay-Lussac’s law they form the combined gas law, P₁V₁/T₁ = P₂V₂/T₂, which lets pressure, volume, and temperature all change at once.
Need a different variable held constant, or want to convert your inputs first? These companion tools cover the rest of the gas law family.