Boyle's Law Calculator

Multiply the starting pressure by the starting volume, then divide by whichever final value you know. P1 x V1 = P2 x V2, so V2 = P1 x V1 / P2. With 1 atm, 10 L and a final pressure of 2.5 atm, V2 = 1 × 10 / 2.5 = 4 L. Use absolute pressure and keep the temperature constant.

V2 = P1 x V1 / P2. The new volume is the old volume multiplied by the ratio of the old pressure to the new one. If the pressure triples, V2 is a third of V1. Starting from 6 L at 1 atm and rising to 3 atm, V2 = 1 × 6 / 3 = 2 L.

V1 = P2 x V2 / P1. Use it when the final state is known and the starting volume is not. For a final state of 250 kPa and 2 L, with a start of 100 kPa, V1 = 250 × 2 / 100 = 5 L. Choose V1 in the Solve for list and enter the other three values.

Rearrange to P2 = P1 x V1 / V2, or P1 = P2 x V2 / V1. A gas at 760 mmHg in 500 mL squeezed into 125 mL ends at 760 × 500 / 125 = 3,040 mmHg, which is 4 atm. The pressure rises by the same factor that the volume falls.

A syringe holds 20 mL of air at 1 atm. Pushing the plunger until the volume is 5 mL gives P2 = 1 × 20 / 5 = 4 atm, assuming the temperature stays the same. The pressure rises fourfold because the volume is a quarter of what it was. The calculator gives the same result in any unit.

Write P1 x V1 = P2 x V2. Convert the pressures to one absolute unit and the volumes to one unit. Identify the unknown and rearrange the formula to isolate it. Substitute, calculate, and check that the sign makes sense: a higher pressure should give a smaller volume. The calculator follows exactly these steps.

For a fixed amount of gas at a constant temperature, pressure and volume are inversely proportional: squeeze the gas to half the volume and the pressure doubles. Robert Boyle published the relationship in 1662. The product of pressure and volume stays the same, which is why the graph of P against V is a curve.

The temperature and the amount of gas. If gas leaks out or heat is added, the product P x V changes, and Boyle's law no longer applies on its own. When the temperature changes as well, use the combined gas law, P1V1/T1 = P2V2/T2, with the temperatures in kelvin.

Boyle's law needs absolute pressure. A gauge shows the pressure above the atmosphere, so add about 1 atm. A tyre at 32 psi gauge is 46.7 psi absolute. Set the Pressure type to gauge and the calculator adds the atmosphere for you, then subtracts it from any pressure it solves.

Pressure can be atm, kPa, bar, mmHg, psi or Pa, and volume can be litres, millilitres or cubic metres. Both pressures share one unit and both volumes share one unit, so the answer comes back in the units you chose. Any pair of units gives the same physical result.

You do not need to install anything. This calculator runs in the browser on a phone, tablet or computer, and it updates as you type. Choose what to solve for, enter three values with their units, and the fourth appears. It works without an account or a download.

Charles's law says volume is proportional to kelvin temperature at constant pressure, V1/T1 = V2/T2. A gas of 10 L at 300 K reaches 11.67 L at 350 K. Boyle's law covers a pressure change at constant temperature, and the two combine into the combined gas law.

Gas pressure comes from molecules hitting the walls. Halve the volume and the same molecules hit the walls twice as often, so the pressure doubles, provided the temperature, and so the average speed of the molecules, is unchanged. That is why the product P x V stays the same.

Pressure plotted against volume is a curve that falls steeply and then flattens, called a hyperbola. A plot of pressure against 1/V is a straight line through the origin. With P x V = 10 atm L, the point (2 L, 5.0 atm) and (5 L, 2.0 atm) both lie on the same curve.

Moving the plunger changes the volume, so the pressure of the trapped air changes the opposite way. Pushing in raises the pressure, pulling out lowers it. The effect is largest for small trapped volumes. In a real pump the air also warms when compressed quickly, so the result is an approximation.

Pressure falls as depth falls, so the bubble expands. In seawater the pressure drops by about 1 atm for every 10 m. A bubble that is 10 L at 30 m grows to 20.0 L at 10 m and 39.8 L at the surface, if its temperature is constant. This is for physics practice only.

The volume doubles, at constant temperature. From 1 L at 101.325 kPa, dropping to 50.6625 kPa gives 2 L. A pressure cut to a quarter makes the volume four times larger. The expansion table lists several pressures and the volume each one gives.

It is a special case. The ideal gas law, PV = nRT, includes the amount of gas and the temperature. Hold n and T fixed and PV is a constant, which is Boyle's law. Real gases follow Boyle's law closely near normal pressure and temperature, and drift away at high pressure.

It becomes less accurate at high pressure, at low temperature close to condensation, and for gases with strong attractions between molecules. Rapid compression also warms the gas, which breaks the constant temperature condition. Treat results from very large pressure changes as rough estimates and follow equipment ratings.

The calculation is an estimate for education and planning. Compressing or storing gas is hazardous. Use containers rated for the pressure, follow the manufacturer's instructions and safety data sheets, and have a qualified person check any pressure system. Never rely on a web calculator for safety limits.