What Is Boyle's Law and How Is It Calculated?
Boyle's law states that for a fixed amount of gas at constant temperature, pressure and volume are inversely proportional: when the volume of the gas decreases, its pressure increases by the same factor. The relationship was published by Robert Boyle in 1662.
The Boyle's law formula is: P₁ × V₁ = P₂ × V₂, where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume. Rearranged, V₂ = (P₁ × V₁) ÷ P₂ and P₂ = (P₁ × V₁) ÷ V₂. Any consistent pressure and volume units work.
Standard atmospheric pressure is defined by the International Bureau of Weights and Measures as exactly 101,325 Pa (1 atm), which equals 14.696 psi or 760 mmHg. Doubling the pressure on a gas at constant temperature halves its volume.
How to Use This Boyle's Law Calculator
- Solve for: Choose which of the four values (P₁, V₁, P₂, V₂) to calculate.
- Units: Pick pressure (atm, kPa, Pa, bar, psi, mmHg) and volume (L, mL, m³, US gal) units. Values are converted internally, so the answer comes back in the units you chose.
- Known values: Enter the other three values. Pressure must be absolute, not gauge.
The law applies equally in metric and imperial units. Remember that gauge pressure (as shown on tyre and scuba gauges) excludes the roughly 14.7 psi or 101.3 kPa of atmospheric pressure, so add it before using the calculator.
Boyle's Law Example Values
| Pressure change | Volume change | Example |
|---|---|---|
| ×2 | ÷2 | 1 atm, 4 L → 2 atm, 2 L |
| ×4 | ÷4 | 1 atm, 4 L → 4 atm, 1 L |
| ÷2 | ×2 | 2 atm, 3 L → 1 atm, 6 L |
Frequently Asked Questions About Boyle's Law
What is the formula for Boyle's law?
The formula for Boyle's law is P₁V₁ = P₂V₂, meaning the product of pressure and volume stays constant for a fixed amount of gas at constant temperature. To find the final volume, use V₂ = P₁V₁ ÷ P₂.
What is the difference between Boyle's law and Charles's law?
Boyle's law relates pressure and volume at constant temperature (inverse relationship), while Charles's law relates volume and absolute temperature at constant pressure (direct relationship). Both are special cases of the ideal gas law, PV = nRT.
When does Boyle's law not apply?
Boyle's law assumes an ideal gas with constant temperature and a fixed amount of gas. It becomes less accurate at very high pressures or very low temperatures, where gas molecules attract each other and occupy significant volume, and it fails if gas leaks or the temperature changes.
Do I use gauge or absolute pressure?
Use absolute pressure. Gauge pressure measures the pressure above the surrounding atmosphere, so add about 101.325 kPa (14.696 psi) to a gauge reading before applying P₁V₁ = P₂V₂.