What is Boyle's Law?
Boyle's law (also known as the Boyle–Mariotte law) describes the relationship between the pressure and volume of a gas at constant temperature. It states that the absolute pressure of a gas is inversely proportional to its volume when temperature and the amount of gas remain constant.
Boyle's Law Formula
The mathematical expression of Boyle's law is:
p₁ × V₁ = p₂ × V₂
Where:
- p₁ — initial (absolute) pressure of the gas
- V₁ — initial volume of the gas
- p₂ — final pressure of the gas
- V₂ — final volume of the gas
This calculator lets you solve for any one of these four parameters — simply enter the three known values and select which one to find.
Supported Units
Pressure
- Pa (Pascal) — SI base unit
- kPa (Kilopascal) — 1 kPa = 1,000 Pa
- MPa (Megapascal) — 1 MPa = 1,000,000 Pa
- atm (Standard atmosphere) — 1 atm ≈ 101,325 Pa
- bar — 1 bar = 100,000 Pa
- mmHg (Millimeter of mercury / Torr) — 1 mmHg ≈ 133.322 Pa
- psi (Pound-force per square inch, US/imperial) — 1 psi ≈ 6,894.76 Pa
Volume
- L (Liter) — most common in chemistry
- mL (Milliliter) — 1 mL = 0.001 L
- m³ (Cubic meter) — SI unit, 1 m³ = 1,000 L
- cm³ (Cubic centimeter) — 1 cm³ = 0.001 L
- ft³ (Cubic foot, US/imperial) — 1 ft³ ≈ 28.317 L
- in³ (Cubic inch, US/imperial) — 1 in³ ≈ 0.0164 L
- gal (US gallon) — 1 gal ≈ 3.785 L
Boyle's Law Examples
Example 1 — Finding the final pressure
A gas occupies 2 L at 100 kPa. The container is compressed to 1 L at constant temperature. What is the new pressure?
p₂ = p₁ × V₁ / V₂ = 100 kPa × 2 L / 1 L = 200 kPa
Example 2 — Finding the final volume
A gas is at 2.5 atm and occupies 6 L. It is decompressed isothermally to 0.2 atm. What is the new volume?
V₂ = p₁ × V₁ / p₂ = 2.5 atm × 6 L / 0.2 atm = 75 L
Where is Boyle's Law Applied?
- Breathing — When your diaphragm expands your lung volume, pressure drops below atmospheric, drawing air in. Exhaling reverses this process.
- Syringes — Pulling the plunger increases the accessible volume, decreasing pressure and causing suction of fluid.
- Carnot heat engine — Two of the four thermodynamic steps in a Carnot cycle are isothermal (Boyle's law) processes.
- Scuba diving — Compressed air in tanks expands as a diver ascends. Understanding Boyle's law is critical for safe diving.
- Bicycle pumps & tires — Pumping air into a tire compresses the gas, increasing the pressure.
Other Thermodynamic Gas Laws
- Charles's Law — Volume is proportional to temperature at constant pressure (isobaric process).
- Gay-Lussac's Law — Pressure is proportional to temperature at constant volume (isochoric process).
- Combined Gas Law — Combines Boyle's, Charles's, and Gay-Lussac's laws: (p₁V₁)/T₁ = (p₂V₂)/T₂.
- Ideal Gas Law — pV = nRT, the universal equation of state for an ideal gas.
FAQs
Does Boyle's law apply to real gases?
Boyle's law is strictly valid for ideal gases. Real gases obey it closely at low pressures and high temperatures, where intermolecular forces are negligible. At very high pressures or low temperatures, deviations appear.
What does "isothermal" mean?
Isothermal means the temperature stays constant throughout the process. Boyle's law describes isothermal compression and expansion of gases.
Is pressure inversely proportional to volume?
Yes. According to Boyle's law, if you double the volume of a gas at constant temperature, the pressure is halved, and vice versa. The product p × V remains constant.