Boyle's Law Calculator – Gas Pressure and Volume
Use Boyle's Law (P₁V₁ = P₂V₂) to calculate unknown gas pressure or volume at constant temperature instantly.
Enter any three of the four values — initial pressure, initial volume, final pressure, and final volume — to solve for the missing quantity.
Boyle's Law Calculator – Gas Pressure and Volume
Use Boyle's Law (P₁V₁ = P₂V₂) to calculate unknown gas pressure or volume at constant temperature instantly.
About Boyle's Law and this calculator
Boyle's Law, formulated by Robert Boyle in 1662, is one of the foundational gas laws of physical chemistry. It states that at constant temperature, the pressure of a fixed quantity of gas is inversely proportional to its volume. In mathematical form, P₁V₁ = P₂V₂, where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume after an isothermal (constant-temperature) change.
The law arises from the kinetic theory of gases. Gas molecules in a container exert pressure by colliding with the walls. If the volume decreases while temperature — and therefore average molecular speed — stays constant, molecules hit the walls more often per unit time, increasing the pressure. Doubling the pressure requires halving the volume; tripling the pressure requires reducing the volume to one-third. This perfect inverse relationship holds exactly for ideal gases and approximately for real gases when the pressure is not too high and the temperature is well above the liquefaction point.
Boyle's Law is a special case of the combined gas law (P₁V₁/T₁ = P₂V₂/T₂) when T is constant, and both are special cases of the ideal gas law PV = nRT. While the ideal gas law requires knowing the amount of gas in moles, Boyle's Law is valuable precisely because it does not: as long as the amount of gas and the temperature remain constant, any two states of the gas satisfy P₁V₁ = P₂V₂ regardless of the gas identity or quantity.
Practical applications are widespread. Scuba divers must understand that a tank of compressed air at 200 atm and 10 L would expand to 2000 L at 1 atm, which is why air must be breathed on demand rather than allowed to expand freely into the lungs. Syringes, bicycle pumps, piston engines, and lung mechanics all demonstrate Boyle's Law in everyday life. In analytical chemistry, gas chromatography and vacuum systems rely on accurate pressure-volume relationships for flow calculations.
This calculator lets you solve for any one of the four variables — P₁, V₁, P₂, or V₂ — given the other three. Pressure and volume can be entered in any consistent unit; the result will be in the same units as the given quantities. The optional temperature field is informational only and does not affect the Boyle's Law calculation, which assumes temperature is constant throughout.
Boyle's Law examples
Three scenarios demonstrating the pressure-volume relationship at constant temperature.
| tool.boyles-law-calculator.examples.colInput | Unknown | Context |
|---|---|---|
| P₁ = 1.0 atm, V₁ = 2.0 L, V₂ = 1.0 L | P₂ = 2.0 atm | Compressing gas to half its volume doubles the pressure. Classic piston compression demonstration. |
| P₁ = 3.0 atm, V₁ = 1.0 L, V₂ = 3.0 L | P₂ = 1.0 atm | Expanding gas to three times its volume reduces pressure to one-third. Gas cylinder release scenario. |
| P₁ = 2.0 atm, V₁ = 1.5 L, P₂ = 4.0 atm | V₂ = 0.75 L | Doubling the pressure halves the volume. Useful for sizing a compression chamber. |
| P₁ = 200 atm, V₁ = 10.0 L, P₂ = 1.0 atm | V₂ = 2000 L | Scuba tank at depth: compressed air at 200 atm expands enormously at surface pressure. |
How to use the Boyle's Law calculator
- Select which variable you want to solve for: Final Pressure, Final Volume, Initial Pressure, or Initial Volume.
- Enter the three known values — initial pressure (P₁), initial volume (V₁), and the known final quantity — in any consistent units.
- Optionally enter the temperature to annotate your calculation; it does not change the result.
- Click Calculate. The missing value appears immediately along with a verification that P₁V₁ = P₂V₂.
- Click Reset to clear all fields and choose a new solve-for variable.
Boyle's Law FAQ
What does Boyle's Law state?
Boyle's Law states that for a fixed amount of gas at constant temperature, pressure and volume are inversely proportional: P₁V₁ = P₂V₂. When volume decreases, pressure increases proportionally, and vice versa. The law was established experimentally by Robert Boyle in 1662 and later derived from the kinetic theory of gases.
What units should I use for pressure and volume?
Any consistent pressure unit works (atm, Pa, kPa, mmHg, psi, bar) as long as both P₁ and P₂ use the same unit. Likewise for volume (L, mL, m³, cm³). The law is a ratio relationship so the unit cancels, and the answer comes out in the same unit as the input.
Does Boyle's Law apply to real gases?
Boyle's Law is exact only for ideal gases. Real gases deviate at high pressures (where intermolecular forces become significant) and low temperatures (near the gas's condensation point). For common gases at moderate pressures and temperatures well above their boiling points, Boyle's Law is an excellent approximation. The van der Waals equation provides a more accurate model for non-ideal behaviour.
Why must temperature remain constant for Boyle's Law?
At a given temperature, the average kinetic energy of the gas molecules is fixed. If temperature changed, molecular speeds would change, altering the collision frequency independently of volume. To isolate the pure pressure-volume relationship, temperature must be held constant — this is called an isothermal process. If temperature also changes, you need the combined gas law.
How is Boyle's Law related to the ideal gas law?
The ideal gas law is PV = nRT, where n is the number of moles and R is the universal gas constant. Boyle's Law is simply the ideal gas law with n, R, and T held constant. Rearranging gives PV = constant, or equivalently P₁V₁ = P₂V₂. The ideal gas law is more general because it allows temperature and amount to vary.
What are real-world applications of Boyle's Law?
Boyle's Law governs the mechanics of syringes, bicycle pumps, internal combustion engines, and scuba diving regulators. It also explains why a sealed bag of chips puffs up at altitude, why a breath taken at depth from a scuba tank must be exhaled as the diver ascends, and how gas chromatography systems calculate flow rates. Respiratory physiology relies on it to describe how the diaphragm creates the pressure differential that inflates the lungs.