Boyle’s Law describes how a gas’s pressure and volume change together at constant temperature. Use the Boyle’s Law Calculator to compute the missing value—final pressure or final volume—based on your initial conditions. This is the standard relationship for ideal gases in sealed systems.
Boyle’s Law in Plain Terms
Boyle’s Law applies when a gas is kept at a constant temperature and the amount of gas stays the same. Under those conditions, the product of pressure and volume remains constant. In other words, squeezing the gas raises pressure, and letting it expand lowers pressure.
The core relationship
The law is written as:
P₁V₁ = P₂V₂
- P₁ = initial pressure
- V₁ = initial volume
- P₂ = final pressure
- V₂ = final volume
Variables, Units, and What “Constant Temperature” Means
Boyle’s Law is an idealized model. It works best for gases that behave close to ideal and when temperature changes are small. If temperature changes significantly, you must use a different gas law (like Charles’s Law or the Combined Gas Law).
Compatible units
You can use different pressure and volume units as long as each quantity is converted consistently inside the calculation. The calculator handles common unit conversions for you, so you can focus on the physics.
- Pressure units: atm, kPa, bar, psi
- Volume units: L, mL, cm³
How to Use Boyle’s Law Calculator
The calculator computes one missing value from three known inputs using P₁V₁ = P₂V₂. Choose what you want to find, enter your initial and (if needed) final quantities, and select units.
Common calculation paths
- Find final pressure (P₂): enter P₁, V₁, and V₂
- Find final volume (V₂): enter P₁, V₁, and P₂
Formulas used
Rearrange the core equation to solve for the unknown:
| Find | Rearranged formula |
|---|---|
| P₂ | P₂ = (P₁ × V₁) / V₂ |
| V₂ | V₂ = (P₁ × V₁) / P₂ |
Worked Examples (Real-World Use Cases)
Example 1: A sealed syringe
Suppose a syringe contains gas at 1.0 atm with a volume of 50 mL. You push the plunger so the volume becomes 25 mL. At constant temperature, what is the new pressure?
Because volume halves, pressure doubles. Boyle’s Law gives:
P₂ = (1.0 atm × 50 mL) / 25 mL = 2.0 atm
This matches the intuitive result: the gas occupies half the space, so it exerts twice the pressure.
Example 2: Tire pressure changes during expansion
Imagine a small compressed-air tank where pressure is 6.0 bar and volume is 2.5 L. If the tank is expanded (or the gas is transferred into a larger container) to 5.0 L while temperature stays nearly constant, what is the final pressure?
Use Boyle’s Law:
P₂ = (6.0 bar × 2.5 L) / 5.0 L = 3.0 bar
The pressure drops by half when the volume doubles.
Common Mistakes to Avoid
- Mixing incompatible units: Pressure and volume must be converted consistently. The calculator does this automatically.
- Using zero or negative values: Pressure and volume must be positive real numbers. Zero volume (or zero pressure) breaks the model.
- Ignoring temperature changes: Boyle’s Law assumes constant temperature. If temperature changes, use the correct gas law.
Frequently Asked Questions
What is Boyle’s Law used for?
Boyle’s Law is used to predict how the pressure and volume of a gas change when temperature stays constant. It applies to sealed or fixed-mass gas systems like syringes, compressed-air setups, and many lab demonstrations where heating or cooling is minimal.
How do you calculate final pressure with Boyle’s Law?
To calculate final pressure, use P₂ = (P₁ × V₁) / V₂. Enter your initial pressure P₁ and initial volume V₁, then provide the new volume V₂. Keep temperature constant and use consistent pressure and volume units.
How do you calculate final volume with Boyle’s Law?
To calculate final volume, use V₂ = (P₁ × V₁) / P₂. Provide the initial pressure P₁ and initial volume V₁, then enter the final pressure P₂. The result gives the volume at the new pressure under constant temperature.
Does Boyle’s Law work for real gases?
Boyle’s Law works best for ideal gases at moderate pressures and temperatures where gas behavior is close to ideal. At very high pressures or very low temperatures, real-gas effects can cause deviations, so experimental data may differ from the prediction.
Why does pressure increase when volume decreases?
When you compress a gas, you reduce the space available for molecules. With constant temperature, molecules move with similar average energy, so they collide with container walls more often. More frequent collisions mean higher pressure.