Boyle's Law Calculator
Boyle's Law states that for a fixed amount of gas at constant temperature, pressure and volume are inversely proportional — doubling the pressure halves the volume. This calculator solves for the final volume when you know the initial pressure-volume pair and the new pressure.
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Formula
P₁V₁ = P₂V₂ → V₂ = P₁V₁ / P₂
P₁ and V₁ are the initial pressure and volume. P₂ is the new pressure, and V₂ is the resulting volume. The product P × V equals a constant for a fixed amount of ideal gas at constant temperature. Pressure and volume can be in any consistent units — atm and liters are used here — as long as both pressures share the same unit and both volumes share the same unit.
How to use the Boyle's Law Calculator
- 1
Enter your initial pressure (p₁)
Value should be in atm.
- 2
Enter your initial volume (v₁)
Value should be in L.
- 3
Enter your final pressure (p₂)
Value should be in atm.
- 4
Read your results instantly
Results update in real time as you type.
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Robert Boyle and the spring of air
Robert Boyle formulated this law in 1662 after conducting experiments with a J-shaped tube sealed at one end and filled with mercury. He discovered that when he increased the pressure on a trapped column of air by adding mercury, the volume decreased in direct proportion, and the product of pressure times volume remained constant. Boyle described air as having a 'spring' — a tendency to resist compression and expand when released. This was one of the first quantitative studies of gas behavior and laid the groundwork for the kinetic molecular theory of gases, which would not be fully developed for another two centuries.
Real-world applications of Boyle's Law
Boyle's Law explains why scuba divers must never hold their breath while ascending — as pressure decreases with depth, the air in the lungs expands and can cause a pneumothorax (lung overexpansion injury). It explains why vacuum packaging preserves food by reducing oxygen partial pressure. In respiratory physiology, inhalation occurs because the diaphragm increases lung volume, lowering pressure inside the chest below atmospheric, causing air to flow in. In industrial settings, gas cylinders store enormous amounts of gas at high pressure in small volumes, and valve regulators apply Boyle's Law to deliver gas at a safe working pressure. The law also governs the function of syringes, bicycle pumps, and pneumatic systems.
Tips & Insights
Temperature must remain constant
Boyle's Law applies only at constant temperature. If temperature changes simultaneously, you need the Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂) instead.
Use consistent pressure units
P₁ and P₂ must be in the same units (both atm, both kPa, both mmHg, etc.). The units cancel in the ratio, so the result is valid regardless of which pressure unit you choose.
Increasing pressure always decreases volume
For an ideal gas at constant temperature, the inverse relationship is strict: if P₂ > P₁, then V₂ < V₁. If your answer shows a volume increase with a pressure increase, check your inputs.
Worked Examples
Compressing a gas from 1 to 4 atm
Final volume = 2.5 L — quadrupling the pressure quarters the volume, as predicted by the inverse relationship.
Expanding gas as pressure drops
Final volume = 6.0 L — releasing pressure from 3 atm to 1 atm triples the volume of the gas.
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Frequently Asked Questions
Does Boyle's Law apply to real gases?
Boyle's Law is exact only for ideal gases. Real gases deviate at high pressures and low temperatures where intermolecular forces and molecular volume become significant. For moderate conditions, the ideal approximation is accurate.
What units can I use for pressure?
Any pressure unit works — atm, kPa, mmHg, psi, bar — as long as P₁ and P₂ are in the same unit. The units cancel when computing the ratio.
What is constant during a Boyle's Law process?
Temperature and the amount of gas (number of moles) are both constant. Only pressure and volume change, and their product P×V remains constant.
How does Boyle's Law relate to Charles's Law?
Boyle's Law fixes temperature and relates P and V. Charles's Law fixes pressure and relates V and T. Together with Gay-Lussac's Law, they combine into the Combined Gas Law and ultimately the Ideal Gas Law PV = nRT.
Why does a sealed syringe get harder to push as you compress it?
As you push the plunger, you decrease the volume of the trapped air. By Boyle's Law, pressure must increase proportionally. The increased gas pressure resists further compression, requiring more force.
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