Boyle's Law Calculator

This Boyle's law calculator calculates how the pressure and volume of a gas behave when temperature is constant. Enter any three of the four values - initial pressure, initial volume, final pressure, and final volume - and leave the field blank for the value you want to calculate.

The calculation tool will then figure out the result. You can freely mix units, so for example you can enter the pressure in atmospheres and read the result in kilopascals.

What is Boyle's Law?

Boyle's law states that at a constant temperature, the pressure and volume of an ideal gas are inversely proportional to one another. When a gas is compressed into a smaller space, its pressure increases, and when it expands, its pressure decreases. Pressure and volume always change in opposite directions by the same factor.

In 1662 Robert Boyle studied the reaction of compressed air to different pressures and described this relationship, one of the earliest known gas laws, which later became part of the ideal gas equation.

How to use this calculator:

Select and enter the three known values. Use the units that are most convenient for the problem with each value. Leave the fourth field blank.

If you enter three values the calculator will immediately fill in the blank fields with corresponding results and display the final pressure as the main result. The pressure ratio and volume ratio are also shown. To calculate for a different unknown value simply erase the unwanted fields and leave one field blank. There is no need to select a mode since leaving a field blank tells the calculator which quantity to solve for.

Boyle's law formula:

Boyle's law is usually expressed as a product that remains constant for two states of the same gas.

In this equation P₁ and V₁ are the initial pressure and volume respectively, while P₂ and V₂ represent the final pressure and volume respectively. By rearranging this equation we can obtain formulas for each of these variables individually. This is the method used in the calculator tool.

In this relationship the product of P and V is constant. This value depends only on temperature and amount of gas, both of which are held constant in Boyle's Law.

Example calculation

A sample of oxygen has a volume of 500 milliliters and a pressure of 400 kilopascals. It is transferred to a container with a volume of 1.5 liters while the temperature remains constant. What will be the new pressure?

Starting with the Boyle's Law equation, solve for final pressure. The initial volume is 0.5 liters, so your formula should look like this:

Since the gas expands to three times its original volume, the pressure will drop to about one-third of the initial value. In a calculator, you can input 400 kPa, 500 mL and 1.5 L, and the final pressure will be directly displayed as 133.3 kPa.

Variations of Boyle's Law:

This table shows the same equations in four different forms for each of the four possible missing quantities.

Application of Boyle's Law.

The relationship between pressure and volume, which change in opposite directions, is easy to observe in everyday life. Try covering the tip of a bicycle pump with your thumb and pushing down on the handle. As the air gets compressed into a smaller space, it becomes increasingly difficult to push down.

Breathing is also based on the same principle. When the diaphragm expands, it reduces pressure inside the lungs and air is drawn into them. A syringe draws liquid by increasing the volume behind the plunger, reducing the pressure there. Divers must also be aware of Boyle's law as a breath of air deep underwater can expand dangerously when they rise to the surface.

Assumptions and limitations

Boyle's law assumes that the gas behaves as an ideal gas, with temperature remaining constant and amount of gas being equal. As real gases often follow this law under normal pressure and temperature conditions, it is very useful for textbook problems and rough engineering estimates.

At extremely high pressures or very low temperatures, the size of molecules and the forces between them can no longer be ignored, leading to deviations from this law. Under such conditions, models for real gases like the Van der Waals equation can be used to more accurately describe behavior.

Tips for a correct solution.

Please ensure that both pressure values are absolute pressures and not gauge pressures. This is because Boyle's Law considers the actual pressure of a gas. Although the calculator does conversions internally, you do not need to manually adjust the units in each field but it is advisable to check the results for accuracy. As volume decreases, pressure should increase proportionally.