Boyle's Law CalculatorCalculator
Calculate pressure and volume changes for an ideal gas at constant temperature using Boyle's Law: P1 · V1 = P2 · V2.
Isothermal Gas States
Isothermal State Transition
Boyle's Law Calculator - Isothermal Gas Pressure & Volume: Free Boyle. Solve physics equations with formulas and instant scientific calculation. Fast, browser-based, and free. 100% free and private browser utility.
How to Use the Boyle's Law Calculator
Define Initial State (P1 & V1)
Enter initial gas pressure in atmospheres and initial gas volume in Liters.
Leave One Final Unknown Blank
Enter either final pressure P2 or final volume V2, leaving the other empty.
Inspect Calculated Final State
Read the derived parameter alongside pressure in Pascals and psi.
Examine Compression Work
Review the isothermal compression factor and mechanical PV boundary work in Joules.
Physics Principles & Thermodynamics Guide
Boyle's Law (also called the Boyle-Mariotte Law), formulated by Anglo-Irish natural philosopher Robert Boyle in 1662 and independently confirmed by French physicist Edme Mariotte in 1676, describes the inversely proportional relationship between the absolute pressure and volume of a gas when temperature remains strictly constant (an isothermal process).
Mathematically, Boyle's Law states that the product of pressure and volume is constant: P · V = k. Consequently, for a gas transitioning between two thermodynamic equilibrium states at the same temperature: P1 · V1 = P2 · V2. If the volume of a container is halved, gas molecules collide with the container walls twice as frequently, directly doubling the exerted pressure.
Boyle's Law is of paramount importance in scuba diving physiology and hyperbaric medicine. For every 10 meters (33 feet) of descent in sea water, ambient hydrostatic pressure increases by exactly 1 atmosphere. At a depth of 20 meters (3 atm ambient pressure), the volume of a flexible air bubble or a diver's lungs is compressed to exactly one-third of its sea-level volume.
This inverse relationship explains the extreme danger of holding one's breath while scuba ascending: as ambient water pressure drops from 3 atm back to 1 atm, trapped lung air expands threefold (V2 = 3 · V1), causing fatal pulmonary barotrauma unless the diver exhales continuously.
Key Scientific Advantages
Scuba Diving Safety Physics
Models air volume compression and lung expansion risks during ascent.
Syringe & Pneumatic Sizing
Calculates pressure spikes in piston pumps, syringes, and air compressors.
Exact Inverse Proportionality
Implements closed-form P1V1 = P2V2 equations with multi-unit conversions.
Isothermal Boundary Work
Computes thermodynamic PV work done during isothermal gas compression (nRT ln(V2/V1)).
Real-Time State Modeling
Instantly view pressure spikes as volume sliders are adjusted.
Private Mechanical Calculations
Proprietary pneumatic piston designs remain 100% private in your browser.
Frequently Asked Questions
Both the absolute temperature of the gas and the mass (number of moles) of the gas must remain strictly constant throughout the compression or expansion process.
When volume is halved, gas molecules have half the distance to travel between wall collisions. Doubling the collision frequency per unit surface area doubles the macroscopic pressure.
At sea level, atmospheric pressure is 1 atm. Every 10 meters of water adds roughly 1 atm of hydrostatic pressure. At 10 meters depth, total ambient pressure is 2 atm (cutting air volume in half).
Boyle's Law is an idealization. Real gases deviate slightly at very high pressures (hundreds of atmospheres) or near condensation temperatures where intermolecular forces become significant.
When your diaphragm contracts downward, it expands your thoracic lung volume. According to Boyle's Law, this volume expansion drops internal lung pressure below atmospheric pressure, causing air to rush inward.