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📋 Boyle's Law Reference P₁V₁ = P₂V₂ (constant T, n)
Formula & Rearrangements
P₁V₁ = P₂V₂
P₂ = P₁V₁ / V₂ Final pressure
V₂ = P₁V₁ / P₂ Final volume
P₁ = P₂V₂ / V₁ Initial pressure
V₁ = P₂V₂ / P₁ Initial volume
Key Assumptions
TemperatureConstant (isothermal)
Amount of gasFixed (closed system)
Gas behaviorIdeal gas
Pressure & VolumeInversely proportional
P ∝ 1/V (at constant T and n)
Common Units
Pressureatm, kPa, mmHg, bar, PSI
VolumeL, mL, m³, ft³
1 atm101.325 kPa
1 atm760 mmHg
1 atm14.696 PSI
Use consistent units for P and V
Note: Boyle's Law was published by Robert Boyle in 1662. It is valid for ideal gases at constant temperature and fixed amount of gas. For processes where temperature also changes, use the Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂).
📌 Boyle's Law: P₁V₁ = P₂V₂  |  At constant T and n, P ∝ 1/V

What Is Boyle's Law?

Boyle's Law is a fundamental gas law that describes the inverse relationship between the pressure and volume of a gas when temperature and the amount of gas are held constant. It was first published by Robert Boyle in 1662.

The mathematical expression of Boyle's Law is:

P₁V₁ = P₂V₂

where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume.

This means that if you increase the pressure on a gas, its volume decreases proportionally, and vice versa , as long as the temperature and the amount of gas remain constant.

How to Use This Calculator

1. Select which variable to solve for , P₁, V₁, P₂, or V₂.

2. Enter the other three values in the input fields. The field for the unknown variable will be automatically disabled.

3. Click "Calculate" , the calculator will display the result, show the step-by-step calculation, and indicate whether the pressure or volume increased or decreased.

4. Use consistent units , pressure units (P₁ and P₂) must match, and volume units (V₁ and V₂) must match. The calculator does not convert between units.

Example Problems

Example 1: A gas has an initial pressure of 1.00 atm and an initial volume of 2.50 L. It is compressed to a final volume of 1.00 L. What is the final pressure?

P₁ = 1.00 atm, V₁ = 2.50 L, V₂ = 1.00 L

P₂ = (P₁V₁) / V₂ = (1.00 × 2.50) / 1.00

P₂ = 2.50 atm

Example 2: A gas at 760 mmHg and 500 mL expands to a final pressure of 380 mmHg. What is the final volume?

P₁ = 760 mmHg, V₁ = 500 mL, P₂ = 380 mmHg

V₂ = (P₁V₁) / P₂ = (760 × 500) / 380

V₂ = 1000 mL (1.00 L)

Why Use This Calculator?

  • Instant results: Get accurate Boyle's Law calculations in real-time.
  • Step-by-step breakdown: See exactly how the calculation is performed.
  • Flexible variable selection: Solve for any of the four variables.
  • Free & private: No registration, no data storage , all calculations are done in your browser.

❓ Boyle's Law Calculator FAQ

What is Boyle's Law?

Boyle's Law states that for a fixed amount of gas at constant temperature, pressure and volume are inversely proportional: P₁V₁ = P₂V₂.

What are the assumptions of Boyle's Law?

Boyle's Law assumes constant temperature (isothermal process), fixed amount of gas (closed system), and ideal gas behavior. For real gases at high pressure or near liquefaction, deviations may occur.

What units can I use with this calculator?

This calculator supports any pressure units (atm, kPa, mmHg, bar, PSI) and any volume units (L, mL, m³, ft³), as long as you use consistent units for P₁/P₂ and V₁/V₂.

How do I solve for P₂?

Using the formula P₂ = P₁V₁ / V₂. Select "P₂" as the unknown variable and enter P₁, V₁, and V₂.

How do I solve for V₂?

Using the formula V₂ = P₁V₁ / P₂. Select "V₂" as the unknown variable and enter P₁, V₁, and P₂.

What is the difference between Boyle's Law and the Combined Gas Law?

Boyle's Law (P₁V₁ = P₂V₂) applies when temperature is constant. The Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂) applies when temperature also changes.

When was Boyle's Law discovered?

Boyle's Law was published by Robert Boyle in 1662 in his work "New Experiments Physico-Mechanicall, Touching the Spring of the Air."

How accurate is this calculator?

This calculator provides exact results for Boyle's Law calculations. Accuracy depends on the precision of the input values. You can adjust the decimal precision in the output.

Is this calculator free?

Yes, this calculator is completely free to use. No registration or personal data storage is required. All calculations run locally in your browser.

What are some real-world applications of Boyle's Law?

Boyle's Law is used in scuba diving (lung volume changes with depth), syringe demonstrations, vacuum systems, pneumatic air springs, and medical applications like breathing mechanics.