Boyle's law calculator

Boyle's law says that for a fixed amount of gas at constant temperature, pressure and volume are inversely proportional: P₁V₁ = P₂V₂. Halve the volume and the pressure doubles. Squeeze 60 mL of air at 100 kPa into 20 mL and the pressure becomes 100 × 60 ÷ 20 = 300 kPa. This Boyle's law calculator is part of our Gas Laws Calculator: it finds the new pressure or the new volume in whatever units you use, with the working and a pressure-volume graph.

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Gas Laws Calculator

Apply Boyle's law, Charles's law and the ideal gas equation

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How to use the Boyle's law calculator

1. Open the Gas Laws Calculator and choose Boyle on the top row of Calculate.
2. Choose P₂ to find the new pressure, or V₂ to find the new volume.
3. Pick your units below the inputs. Pressure can be Pa, kPa, MPa, bar, atm, mmHg or psi, and volume mm³, cm³, mL, L or m³. Both pressures use the same unit, and so do both volumes.
4. Type the three values you know. Common values on a pressure box fills in atmospheric pressure, 101,325 Pa.
5. Read the answer in SI units (Pa or m³) with Also equal to listing it in the other units, the working, and the value of PV, which stays the same. The graph plots pressure against volume through your point.

There is no P₁ or V₁ button, and you don't need one. The law is symmetrical, so call the state you know "1" and the state you want "2". To find a starting volume from a final one, type the final values as state 1.

Boyle's law formula

Rearranged, P₂ = P₁V₁ ÷ V₂ and V₂ = P₁V₁ ÷ P₂. It holds only while the temperature and the amount of gas stay the same, and it is most accurate for gases at ordinary pressures, where they behave close to an ideal gas.

Why it happens: the gas particles are always hitting the walls of the container. Squash the gas into half the volume and the same number of particles, moving at the same speed because the temperature hasn't changed, hit each part of the wall twice as often. The pressure doubles.

Boyle's law graph

Here x is the volume in mL and y is the pressure in kPa, for the syringe in Example 1. The curve is a hyperbola: pressure never reaches zero, and doubling the volume halves the pressure. Plot P against 1/V instead and you get a straight line through the origin.

Worked examples you can check in the calculator

Example 1: squeezing a syringe

You block the end of a 60 mL syringe full of air at 100 kPa and press until the air takes up 20 mL. Done gently, the air stays at room temperature. Choose P₂, set the pressure unit to kPa and the volume unit to mL, and type 100, 60 and 20.

The calculator gives 300,000 Pa, which is 300 kPa. The volume went to a third, so the pressure tripled.

Example 2: a bubble rising from a diver

A diver 30 m down in the sea breathes out a 2.0 cm³ bubble. The water and the air above it put a total pressure of 402,982 Pa on the bubble there (the pressure calculator guide works this out with P = ρgh plus the atmosphere). What is its volume at the surface, at 101,325 Pa? Choose V₂, set the volume unit to cm³, and type 402982, 2 and 101325.

The bubble grows to almost four times its size, if the water temperature stays the same on the way up. This is why divers must never hold their breath as they rise.

Example 3: a gas cylinder

A 50 L cylinder holds gas at 200 bar. What volume would the gas fill at 1 bar, at the same temperature? Choose V₂, set the pressure unit to bar and the volume unit to L, and type 200, 50 and 1: V₂ = 200 × 50 ÷ 1 = 10,000 L, which the calculator shows as 10 m³.

Example 4: in psi

A bike pump holds 0.5 L of air at 14.7 psi. The handle is pushed down until the air takes up 0.1 L, without letting any out. Set the pressure unit to psi: P₂ = 14.7 × 0.5 ÷ 0.1 = 73.5 psi. The calculator gives 506,764 Pa, and 73.50 psi in the Also equal to list.

When the temperature changes too

Boyle's law needs a constant temperature. If the temperature changes as well, use the combined gas law, P₁V₁/T₁ = P₂V₂/T₂, with temperatures in kelvin; the Combined topic in the same calculator does it, and the combined gas law calculator guide explains it. To link pressure and volume to the amount of gas, use PV = nRT: see the ideal gas law calculator guide.

Common mistakes

• Mixing units. Both pressures must be in the same unit and both volumes in the same unit. The calculator converts for you if you set them.
• Expecting pressure to rise with volume. It is inverse: more volume, less pressure. Check your answer goes the right way.
• Using it when the temperature changes. Fast compression heats a gas. Use the combined gas law then.
• Gauge pressure instead of absolute pressure. Boyle's law needs the total pressure. A tyre (tire) gauge reads pressure above the atmosphere, so add 101 kPa (14.7 psi) first.
• Letting gas escape. The amount of gas must stay fixed.

Read next

Physics · Thermal physics and matterCombined gas law calculator: P1V1/T1 = P2V2/T2Solve the combined gas law P1V1/T1 = P2V2/T2 for pressure, volume or temperature, with Celsius converted to kelvin for you and worked examples.