Boyle's Law Calculator - Gas Pressure
Apply Boyle's Law to calculate pressure-volume relationships in gases. Enter two variables to find the third instantly. Perfect for chemistry and physics.
Formula
P₁V₁ = P₂V₂
Initial Pressure × Initial Volume = Final Pressure × Final Volume.
Worked Examples
Example 1: Compressing Gas in a Sealed Syringe
Problem:A sealed syringe holds 10.0 L of air at 1.00 atm. The plunger is pushed slowly until the pressure reads 2.00 atm absolute. Temperature stays constant. What is the new volume?
Solution:Boyle's law: P1 x V1 = P2 x V2 Rearrange: V2 = P1 x V1 / P2 V2 = 1.00 atm x 10.0 L / 2.00 atm V2 = 10.0 / 2.00 = 5.00 L Check: the pressure ratio is 2, so the volume must fall by a factor of 2.
Result:V2 = 5.00 L (half the original volume)
Example 2: Scuba Bubble Rising From 30 Metres
Problem:A 6.0 L bubble of air is released at 30 m depth in sea water, where absolute pressure is about 4.0 atm. How large is it at the surface at 1.0 atm, assuming the temperature does not change?
Solution:Absolute pressure at depth = 1.0 atm surface + 3.0 atm water (about 1 atm per 10 m) = 4.0 atm V2 = P1 x V1 / P2 V2 = 4.0 atm x 6.0 L / 1.0 atm V2 = 24 L The bubble expands fourfold, the same factor by which pressure drops.
Result:V2 = 24 L (a fourfold expansion on ascent)
Example 3: Using Absolute Pressure, Not Gauge Pressure
Problem:A tyre gauge reads 30.0 psi with 12.0 L of air inside. The air is transferred to a rigid tank at a gauge pressure of 75.0 psi. What volume does it occupy? Sea-level atmospheric pressure is 14.7 psi.
Solution:Convert both readings to absolute pressure first: P1 = 30.0 + 14.7 = 44.7 psia P2 = 75.0 + 14.7 = 89.7 psia V2 = P1 x V1 / P2 = 44.7 x 12.0 / 89.7 V2 = 536.4 / 89.7 = 5.98 L Using the gauge numbers instead would give 30 x 12 / 75 = 4.80 L, a 20 percent error.
Result:V2 = 5.98 L (gauge-pressure shortcut would give 4.80 L)
Frequently Asked Questions
What does Boyle's law say about gas pressure and volume?
Boyle's law states that for a fixed amount of gas held at constant temperature, absolute pressure and volume are inversely proportional, so their product stays constant: P1V1 = P2V2. Double the pressure on a sealed sample and its volume halves; halve the pressure and the volume doubles. The law follows directly from the ideal gas law PV = nRT once n, R and T are all held fixed.
Why must Boyle's law use absolute pressure instead of gauge pressure?
The relationship P1V1 = P2V2 is only linear in pressure measured from a true zero. A tyre gauge reads the amount by which pressure exceeds the surrounding atmosphere, so a gauge reading of 30 psi is really about 44.7 psi absolute at sea level. Feeding gauge numbers into the formula makes the pressure ratio wrong and the calculated volume badly wrong. Add 14.7 psi, or 101.325 kPa, before you calculate.
How do I rearrange P1V1 = P2V2 to solve for the final volume?
Divide both sides by the final pressure: V2 = P1 x V1 / P2. That is exactly what Boyle's Law Calculator - Gas Pressure does. To find a final pressure instead, use P2 = P1 x V1 / V2. Because the answer depends only on the pressure ratio P1/P2, the arithmetic is unaffected by which pressure unit you choose, provided both pressures are on the same absolute scale.
Do the pressure and volume units have to match on both sides?
Yes, within each pair. Both pressures must share one absolute unit (atm, kPa, bar or psia) and both volumes must share one volume unit (litres, millilitres or cubic metres). You do not need to convert between the two pairs, because the units cancel inside each ratio. Mixing atm with kPa, or litres with millilitres, is the single most common source of wrong answers in gas law problems.
What happens if the gas temperature changes while it is compressed?
Boyle's law no longer applies on its own, because it assumes isothermal conditions. Rapid compression is closer to adiabatic: the gas warms as work is done on it, and the final pressure ends up higher than P1V1/V2 predicts. This is why a bicycle pump barrel gets hot. For a process where temperature also changes, use the combined gas law P1V1/T1 = P2V2/T2 with absolute temperatures in kelvin.
Why does a plot of pressure against volume give a hyperbola?
Because the product PV is constant, P equals a constant divided by V, which is the equation of a rectangular hyperbola. Each curve of constant temperature is called an isotherm, and higher temperatures push the curve further from the origin. Plotting P against 1/V instead gives a straight line through the origin, and that straight-line test is the standard laboratory check for whether a gas is behaving ideally.
When do real gases stop obeying Boyle's law?
At high pressure and near the condensation point. The ideal model assumes molecules occupy no volume and do not attract one another. At high pressure the finite molecular volume makes the gas harder to compress than predicted, while near condensation intermolecular attraction makes it easier. Deviations are summarised by the compressibility factor Z = PV/nRT, which equals 1 for an ideal gas and departs from 1 for real ones.
How does Boyle's law explain breathing and a syringe?
Both work by changing volume to change pressure. When the diaphragm contracts, the chest cavity expands, lung volume rises, the pressure inside falls below atmospheric, and air flows in. Pulling a syringe plunger back increases the barrel volume and lowers the internal pressure, so fluid is pushed in by the outside pressure. Pushing the plunger reverses both steps and expels the contents.
What is the difference between Boyle's law and the combined gas law?
Boyle's law is the special case of the combined gas law in which temperature is held constant. The combined form, P1V1/T1 = P2V2/T2, also folds in Charles's law for volume against temperature and Gay-Lussac's law for pressure against temperature. If your problem changes only pressure and volume, Boyle's law is sufficient; if temperature moves as well, use the combined form with kelvin temperatures.
Why does a diver's air volume change with depth under Boyle's law?
Water adds roughly one atmosphere of pressure for every 10 metres of depth, so absolute pressure at 30 metres is about 4 atm. A 6 litre bubble released there expands to about 24 litres at the surface, where pressure is 1 atm. This is why divers are trained never to hold their breath while ascending: the trapped gas in the lungs expands by the same factor and can rupture lung tissue.