BoylesLaw Gas Law Calculator

Boyle's Law states that at constant temperature, the pressure of a given mass of gas is inversely proportional to its volume. In equation form: P₁V₁ = P₂V₂. If you double the volume, the pressure halves. If you compress the gas to one-third of its original volume, the pressure triples. The product PV is a constant for a given sample of gas at constant temperature.

Robert Boyle published this relationship in 1662 in the second edition of his book New Experiments Physico-Mechanical Touching the Spring of the Air. He used a J-shaped glass tube sealed at the short end, partially filled with mercury. By pouring more mercury into the open end, he trapped air in the sealed end and observed that doubling the pressure halved the volume. The experiment was suggested and likely built by his assistant Robert Hooke.

The law was independently discovered by Edme Mariotte in France in 1676, which is why it is sometimes called the Boyle-Mariotte law in continental Europe. Mariotte noted the additional condition that temperature must remain constant, a detail Boyle had implicitly assumed but not stated.

At the molecular level, Boyle's Law follows directly from kinetic theory. Gas pressure results from molecules striking the container walls. Reducing the volume while keeping temperature constant means the same number of molecules are confined to a smaller space. They strike the walls more frequently because they have less distance to travel between collisions. The force per unit area — pressure — increases in exact proportion to the frequency of collisions, which is inversely proportional to volume.

This explanation requires that the molecules themselves have negligible volume and that collisions are perfectly elastic, conditions that hold for ideal gases. For real gases, deviations appear at high pressure when the volume occupied by the molecules themselves becomes a significant fraction of the container volume. The van der Waals equation corrects for this.

Select which variable to solve for: P₁, V₁, P₂, or V₂. The calculator disables the field you are solving for. Enter values for the other three with their units. The result updates instantly with full step-by-step working. Each step shows the unit conversions, the formula substitution, the arithmetic, and the final conversion to your chosen output unit.

The calculator handles all common pressure units (atm, bar, kPa, Pa, torr, mmHg, psi) and volume units (L, mL, m³, cm³). Because the formula is a ratio, any consistent set of units works as long as you use the same unit for both pressure values and the same unit for both volume values. For example, if P₁ is in kPa and P₂ is in atm, the calculator converts both to atm before computing.

Example 1: Compressing a gas. A gas occupies 5.00 L at 1.00 atm. If the volume is reduced to 2.50 L at constant temperature, what is the new pressure? P₂ = P₁V₁/V₂ = (1.00 × 5.00) / 2.50 = 2.00 atm. Halving the volume doubles the pressure, exactly as Boyle's Law predicts.

Example 2: Expanding against a piston. A cylinder contains gas at 3.50 atm and occupies 0.850 L. If the piston is released and the gas expands to a final pressure of 1.00 atm at constant temperature, what is the final volume? V₂ = P₁V₁/P₂ = (3.50 × 0.850) / 1.00 = 2.98 L.

Example 3: Scuba tank discharge. A scuba tank at 204 atm has an internal volume of 11.1 L. When the diver breathes the air at the surface (1.00 atm, constant temperature), what volume of air is available? V₂ = (204 × 11.1) / 1.00 = 2,260 L. This is why a tank that looks small contains enough air for roughly an hour underwater.

Example 4: Force and syringe. A syringe contains 10.0 mL of air at 1.00 atm. The plunger is depressed to 2.00 mL at constant temperature. What is the final pressure? P₂ = (1.00 × 10.0) / 2.00 = 5.00 atm. This is the principle behind every piston compressor.

Breathing operates on Boyle's Law. When the diaphragm contracts, the chest cavity volume increases, pressure inside the lungs drops below atmospheric pressure, and air flows in. When the diaphragm relaxes, the volume decreases, pressure rises above atmospheric, and air flows out. A mechanical ventilator uses the same principle: increase the container volume to draw gas in, decrease it to push gas out.

Aerosol cans and spray paint rely on Boyle's Law for their operation. A propellant gas is compressed into the can at high pressure. When the valve opens, the pressure drops and the propellant expands, carrying the product out with it. This is also why aerosol cans carry warnings about high temperature: heating increases the internal pressure, and if the pressure exceeds the can's burst strength, the can ruptures.

Syringes, bicycle pumps, air compressors, hydraulic systems, and vacuum cleaners all demonstrate Boyle's Law in operation. Any device that compresses or expands a gas at roughly constant temperature exhibits the inverse pressure-volume relationship.

Plotting pressure against volume for a fixed amount of gas at constant temperature produces a hyperbola. Each isotherm — a curve of constant temperature — has the shape P = k/V. At higher temperatures, the curve shifts outward because the same volume contains higher pressure. A set of isotherms on a PV diagram, called a Boyle's Law plot, is one of the most recognizable graphs in physical chemistry.

The area under the curve from V₁ to V₂ represents the work done by the gas during isothermal expansion. For an ideal gas, that work equals nRT × ln(V₂/V₁). This is the foundation of isothermal processes in thermodynamics.

Boyle's Law holds exactly only for an ideal gas. For real gases: at very high pressure, the product PV is not constant but shows a minimum and then rises, due to intermolecular forces at moderate pressure and the finite volume of molecules at high pressure. Carbon dioxide at 0 °C deviates by about 2 percent at 10 atm and 8 percent at 50 atm. Helium, the most ideal real gas, deviates by less than 0.1 percent at 10 atm.

What is Boyle's Law in simple terms? At constant temperature, squeezing a gas into a smaller volume increases its pressure. The pressure and volume are inversely related: double the pressure, halve the volume.

Who discovered Boyle's Law? Robert Boyle, an Anglo-Irish natural philosopher, published it in 1662 with experimental assistance from Robert Hooke. Edme Mariotte independently discovered it in France in 1676.

What are the units for Boyle's Law? Any consistent pressure and volume units work because it is a ratio. Both pressures must share the same unit, and both volumes must share the same unit. This calculator handles unit conversion automatically.

What is a real-life example of Boyle's Law? Breathing: your diaphragm increases chest volume, lowering lung pressure below atmospheric, and air flows in. Exhaling reverses the process. Syringes and bicycle pumps work on the same principle.

Why is temperature important? Boyle's Law requires constant temperature. If the gas heats up during compression, the pressure rises more than the law predicts. This is why a bicycle pump gets warm when you use it.