Quick Answer

A gas at 2 atm in a 10 L container compressed to 5 L reaches 4 atm. Doubling the volume of a gas at 1 atm drops the pressure to 0.5 atm.

Solve For Initial Pressure (P₁) Initial Volume (V₁) Final Pressure (P₂) Final Volume (V₂)

Initial Volume (L)

Final Pressure (atm)

Final Volume (L)

Common Examples

Input	Result
P₁ = 2 atm, V₁ = 10 L, V₂ = 5 L	P₂ = 4 atm
P₁ = 1 atm, V₁ = 22.4 L, P₂ = 2 atm	V₂ = 11.2 L
V₁ = 5 L, P₂ = 3 atm, V₂ = 10 L	P₁ = 6 atm
P₁ = 4 atm, P₂ = 1 atm, V₂ = 20 L	V₁ = 5 L
P₁ = 1 atm, V₁ = 1 L, P₂ = 0.5 atm	V₂ = 2 L

How It Works

Boyle’s Law

P₁V₁ = P₂V₂

Where:

• P₁ = initial pressure (atm)
• V₁ = initial volume (L)
• P₂ = final pressure (atm)
• V₂ = final volume (L)

Temperature must remain constant throughout. This is the key constraint: Boyle’s law applies only to isothermal (constant-temperature) processes.

Rearranged forms:

• Initial Pressure: P₁ = P₂V₂ / V₁
• Initial Volume: V₁ = P₂V₂ / P₁
• Final Pressure: P₂ = P₁V₁ / V₂
• Final Volume: V₂ = P₁V₁ / P₂

Background

Robert Boyle published this relationship in 1662, making it one of the earliest quantitative laws in chemistry. The law describes the inverse relationship between pressure and volume: when you compress a gas (decrease volume), its pressure increases proportionally, and vice versa. Plot pressure against the reciprocal of volume and you get a straight line through the origin.

Boyle’s law is one of the three classical gas laws. Charles’s Law describes the volume-temperature relationship at constant pressure, and Gay-Lussac’s Law describes the pressure-temperature relationship at constant volume. Together with Avogadro’s law, these combine into the ideal gas law: PV = nRT.

Worked example

A bicycle pump contains air at 1 atm and 500 mL. The piston compresses the air to 125 mL. What is the resulting pressure (assuming no air escapes and temperature stays constant)?

P₂ = P₁V₁ / V₂ = (1 atm x 500 mL) / 125 mL = 4 atm

Compressing the air to one quarter of its original volume quadruples the pressure to 4 atm.

Limitations

Boyle’s law applies to ideal gases. Real gases deviate at very high pressures (where molecular volume becomes significant) and near condensation points (where intermolecular attractions matter). For most chemistry and physics problems at standard conditions, the deviation is small enough to ignore.

Related Calculators

Ideal Gas Law Calculator

Calculate pressure, volume, moles, or temperature using the ideal gas law PV = nRT.

Charles's Law Calculator

Calculate volume or temperature changes using Charles's law V₁/T₁ = V₂/T₂ at constant pressure.

Frequently Asked Questions

Does Boyle's law work for all gases?

Boyle's law works well for gases that behave ideally: low pressure, high temperature, and weak intermolecular forces. Common gases like nitrogen, oxygen, and helium follow it closely at standard conditions. Gases with strong intermolecular forces (like water vapor or carbon dioxide at high pressure) show measurable deviations. For precise work at extreme conditions, the van der Waals equation gives better results.

What happens at extremely high pressures?

At very high pressures, real gases compress less than Boyle's law predicts. Gas molecules occupy a non-negligible volume themselves, so the available space decreases more slowly than the ideal model assumes. Additionally, intermolecular repulsive forces become significant. At pressures of hundreds of atmospheres, corrections from real-gas equations are necessary for accurate results.

How is Boyle's law used in everyday life?

Boyle's law explains many familiar phenomena. Scuba diving regulators use it to deliver air at ambient pressure as depth (and surrounding pressure) increases. Syringes work by expanding volume to draw in fluid and compressing volume to expel it. Breathing itself relies on the same principle: the diaphragm expands lung volume to drop pressure below atmospheric, drawing air in, then contracts to raise pressure and push air out.

What units should I use?

This calculator uses atmospheres (atm) for pressure and liters (L) for volume, but Boyle's law works with any consistent pressure and volume units. The pressure and volume units do not need to match between the initial and final states, but each side of the equation must use the same units internally. Common pressure units: 1 atm = 101.325 kPa = 760 mmHg = 14.696 psi.

What is the relationship between Boyle's law and the ideal gas law?

Boyle's law is a special case of the ideal gas law (PV = nRT) where temperature and moles are held constant. If n and T are fixed, then nRT is a constant, so PV = constant, which gives P₁V₁ = P₂V₂. The ideal gas law is the more general equation; Boyle's law, Charles's Law, and Gay-Lussac's Law are each derived from it by holding two of the four variables constant.

Learn More

How Boyle's law explains gas behavior

Boyle's law explained: P₁V₁ = P₂V₂ with worked examples, real-world applications in scuba diving and syringes, limitations, and connection to the ideal gas law.