🔬 Boyle's Law Calculator

Boyle's Law, formulated by the Anglo-Irish chemist Robert Boyle in 1662, describes the inverse relationship between the pressure and volume of a fixed amount of gas at constant temperature. Mathematically, it states that the product of pressure and volume is constant: P₁ × V₁ = P₂ × V₂. When you squeeze a balloon and it shrinks, or when a syringe draws in liquid as you pull the plunger, you are watching Boyle's Law in action.

This calculator is designed for chemistry students, scuba divers, engineers, weather scientists, and anyone who works with gas systems. Simply enter any three of the four values—initial pressure (P₁), initial volume (V₁), final pressure (P₂), and final volume (V₂)—and the calculator instantly returns the fourth. You can use any pressure unit (atm, kPa, psi, mmHg, bar) and any volume unit (L, mL, m³, ft³) as long as P₁ and P₂ share the same unit and V₁ and V₂ share the same unit.

The calculator applies the relation P₁ × V₁ = P₂ × V₂. If you know P₁, V₁, and P₂, it solves for V₂ = (P₁ × V₁) / P₂. If you know P₁, V₁, and V₂, it solves for P₂ = (P₁ × V₁) / V₂. The same logic covers the remaining two cases.

The table below shows how pressure changes when the volume of a gas sample is varied, assuming an initial pressure of 1 atm and initial volume of 1 L:

Notice that P × V always equals 1.00 atm·L—this constant product is the hallmark of Boyle's Law. The same principle governs deep-sea diving (as a diver descends, water pressure compresses the air in their lungs) and aerosol cans (compressed gas expands forcefully when released).

1. Enter any three of the four values: P₁, V₁, P₂, and V₂.
2. Leave the fourth field blank—that is what will be calculated.
3. Click the Calculate button.
4. Review the result for the unknown value.
5. Verify that pressure and volume units are consistent (P₁/P₂ same unit, V₁/V₂ same unit).

What units should I use for Boyle's Law?

Pressure and volume can be in any unit, as long as P₁ and P₂ share the same unit (e.g. both atm) and V₁ and V₂ share the same unit (e.g. both L). Common choices: pressure in atm, kPa, psi, mmHg, or bar; volume in L, mL, or m³.

Does Boyle's Law assume constant temperature?

Yes. Boyle's Law applies only when temperature is held constant. If temperature also changes, you need the Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂) instead.

Can I use this for real gases?

Boyle's Law is exact for ideal gases. Real gases (oxygen, nitrogen, CO₂) follow it closely at moderate pressures and temperatures, but deviate at very high pressures or near condensation points where intermolecular forces become significant.

What happens if I enter all four values?

When all four fields are filled, the calculator verifies whether P₁V₁ = P₂V₂ and displays the product for each state, so you can check if the data is consistent with Boyle's Law.

How is Boyle's Law used in everyday life?

Syringes (pulling the plunger increases volume, decreasing pressure and drawing fluid in), bicycle pumps (compressing air increases its pressure), breathing (your diaphragm expands your chest volume, lowering pressure so air flows in), and scuba diving (lung volume shrinks under water pressure) all follow Boyle's Law.

Why does my result show infinity or zero?

If the denominator (P₂ when solving for V₂, or V₂ when solving for P₂) is zero, the result is undefined. A zero final pressure or volume is physically impossible for a gas sample, so check your inputs.

Always use consistent units: P₁ and P₂ must be in the same unit (both in atm, or both in kPa), and V₁ and V₂ must be in the same unit. Boyle's Law assumes an ideal gas at constant temperature with a fixed amount of gas (no leaks, no reactions). Real gases deviate slightly at very high pressures or very low temperatures. For scuba diving calculations, remember that pressure increases by roughly 1 atm for every 10 m of depth—a volume of air in your lungs at the surface will be half that size at 10 m depth. You can also use this calculator to check your combined gas law or ideal gas results.