Enter any three of P₁ (initial pressure), V₁ (initial volume), P₂ (final pressure), and V₂ (final volume) — the Boyle's Law Calculator solves for the missing variable using P₁V₁ = P₂V₂. Choose which value to solve for, select your preferred pressure and volume units, and get the result for any isothermal gas process.
Calculated Result
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Solved Variable
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P₁V₁ Product (in base units)
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P₂V₂ Product (in base units)
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Boyle's Law states that the absolute pressure of a fixed amount of gas is inversely proportional to its volume, provided the temperature and mass remain constant. Mathematically this is expressed as P₁V₁ = P₂V₂. When pressure increases, volume decreases proportionally, and vice versa.
Select which variable you want to solve for from the 'Solve For' dropdown, then enter values for the other three variables along with their units. The calculator will automatically apply the formula P₁V₁ = P₂V₂ and display the unknown result with unit conversions handled internally.
Boyle's Law applies specifically when temperature is held constant — this condition is called isothermal (from the Greek 'iso' meaning equal and 'thermal' meaning heat). Because the temperature doesn't change, the product P×V stays constant throughout the process, which is the core principle of Boyle's Law.
If the initial pressure is 1 atm and the volume is halved, then by Boyle's Law: P₂ = P₁V₁ / V₂ = (1 × V₁) / (0.5 × V₁) = 2 atm. Halving the volume doubles the pressure, which perfectly illustrates the inverse relationship described by Boyle's Law.
Boyle's Law has many practical applications including the operation of syringes, bicycle pumps, and scuba diving equipment. It also explains why balloons expand at higher altitudes (lower atmospheric pressure), how lungs inflate and deflate, and is used in designing pneumatic systems and compressors.
At cruising altitude (~10,000 m), atmospheric pressure drops from ~1 atm at sea level to roughly 0.26 atm. A balloon with initial volume of 1000 cm³ at 1 atm would expand to approximately V₂ = (1 × 1000) / 0.26 ≈ 3846 cm³ — nearly four times its original volume, assuming constant temperature.
Boyle's Law is strictly accurate for ideal gases — theoretical gases where molecules have no volume and no intermolecular forces. Real gases approximate ideal behavior well at low pressures and high temperatures, but deviate significantly at high pressures or near the condensation point. For precise real-gas calculations, the van der Waals equation is more appropriate.
This calculator supports pressure units including atm, kPa, mmHg (torr), Pa, bar, and psi. For volume, it accepts litres (L), millilitres (mL), cubic centimetres (cm³), and cubic metres (m³). All values are converted to a consistent base unit (atm and L) internally before applying the Boyle's Law formula.