# Boyle’s law calculator

Calculate the final pressure and final volume of an isothermal reaction of a gas using this boyle’s law calculator. Enter both the initial pressure, and initial volume, as well as the final volume or pressure to calculate the unknown value.

As you’ll see in the section below, boyle’s law is the relation ship between the change of pressure and volume of a gas in iso-thermal reactions. Only 3 of the 4 parameters need to be known to calculate the missing parameter. The combination of which parameters are known does not matter, so you can use this calculator in many ways.

## Boyle’s Law Formula

The formula for boyle’s law is as follows:

p₁ * V₁ = p₂ * V₂

• Where p1 and p2 are initial and final pressures
• V1 and V2 are initial and final volumes
• The reaction is iso-thermal

This formula is derived from the ideal gas law equation of pV = nRT. Since the change in temperatures and moles are the same in this reaction, that side of the equation can be canceled out

As mentioned previously, You can manipulate the equation above to calculate for any parameter, not just the final volume as this calculator displays. For instance, if you want to calculator for the initial volume given the initial pressure, final volume and final pressure, manipulate the equation as follows:

V₁ = p₂ * V₂ / p₁

You can do that in any combination, so as long as you have three of the known variables, you should be able to calculate the last variable easily.

## How to Calculate Boyle’s Law

The following example will go over how to calculate an unknown pressure or volume of a gas using boyle’s law.

1. First, we must determine the missing variable we want to solve for. For this example we are going to be searching for the initial volume.
2. Next, we need to re-arrange the formula to solve for our miss variable. Luckily, we have already done this above under the formula section so, V₁ = p₂ * V₂ / p₁ .
3. The next step is determining or measure the known variables. this is typically done empirically, but could as be done mathematically using other formulas like the ideal gas law formula. For this example we will assume P2= 20 Pa, P1= 10 Pa, and V2 = 5 m^3.
4. Finally, enter all of the information into the calculator or formula above and we find that V1 = 10 m^3.
5. The last step is to analyze your results.