Boyle's Law Calculator
Calculate pressure or volume using Boyle's law (constant temperature).
About Boyle's Law Calculator
Boyle's law: at constant temperature, pressure and volume are inversely proportional. Doubling pressure halves volume.
$$P_1V_1 = P_2V_2$$
How to use this calculator
- Enter the known values for initial pressure and volume, plus the final value you know.
- Choose the unknown, either pressure or volume.
- Use the calculator to solve using \(P_1V_1 = P_2V_2\).
- Check that your units match, for example pressure in \(\text{atm}\), \(\text{kPa}\), or \(\text{mmHg}\), and volume in \(\text{L}\) or \(\text{mL}\).
The formula explained
Boyle's law computes the pressure and volume of a gas when temperature is constant. The product \(P_1V_1\) stays equal to \(P_2V_2\), so you can solve for the missing pressure or volume.
- \(P_1\) = initial pressure
- \(V_1\) = initial volume
- \(P_2\) = final pressure
- \(V_2\) = final volume
Step by step method
- Start with \(P_1V_1 = P_2V_2\).
- If you need pressure, rearrange to \(P_2 = \frac{P_1V_1}{V_2}\). If you need volume, rearrange to \(V_2 = \frac{P_1V_1}{P_2}\).
- Substitute the known values and compute the result with matching units.
Worked example
Problem. A gas has an initial pressure of \(2.0\\,\text{atm}\) and an initial volume of \(3.0\\,\text{L}\). If the volume changes to \(1.5\\,\text{L}\) at constant temperature, what is the new pressure?
- Use \(P_1V_1 = P_2V_2\).
- Solve for \(P_2\): \(P_2 = \frac{P_1V_1}{V_2} = \frac{(2.0)(3.0)}{1.5}\).
- Compute \(P_2 = 4.0\\,\text{atm}\).
Answer. \(4.0\\,\text{atm}\)
Tips and common mistakes
- Make sure temperature stays constant, because Boyle's law only works under that condition.
- Keep pressure units the same on both sides and volume units the same on both sides before calculating.
Frequently asked questions
How do I use a Boyle's law calculator to find the missing pressure or volume?+
Enter the known values for the two states, then leave the one unknown field blank. The calculator uses the relationship P1V1 = P2V2 to solve for the missing pressure or volume when temperature stays constant.
What does P1V1 = P2V2 mean in Boyle's law?+
It means that for a fixed amount of gas at constant temperature, pressure and volume change in opposite directions so their product stays the same. If volume goes down, pressure goes up, and if volume goes up, pressure goes down.
What units can I use for pressure and volume?+
Use any consistent units for pressure, such as atm, kPa, mmHg, or psi, and any consistent units for volume, such as L or mL. The key is to keep the units the same on both sides of the equation for pressure and for volume.
What happens if the temperature is not constant?+
Boyle's law does not apply directly if temperature changes, because the pressure volume relationship also depends on temperature. In that case, you need a different gas law, often the combined gas law or the ideal gas law.
How do I interpret a Boyle's law example with compression of a gas?+
If a gas is compressed from 4.0 L to 2.0 L at constant temperature, the volume is cut in half, so the pressure must double. For example, if the initial pressure is 100 kPa, the final pressure would be 200 kPa.
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