Boyle's Law Calculator
Solve for the unknown pressure or volume of an ideal gas at constant temperature. Enter three known variables into Boyle's Law to find the fourth.
Result
V2 = 5
Initial state P1=1, V1=10 gives final state P2=2, V2=5
Quick Answer
A Boyle's Law calculator uses the equation P1 × V1 = P2 × V2 to find missing gas parameters. If you have 5 liters of gas at 1 atmosphere (atm) of pressure, and you compress it to 2.5 liters without changing the temperature, the new pressure doubles to 2 atm (5 × 1 = P2 × 2.5). The calculator lets you select which variable is unknown, input the other three, and automatically balances the equation.
What Boyle's Law Is and How the Equation Actually Works
Boyle's Law states that the absolute pressure and volume of a given mass of confined gas are inversely proportional, provided the temperature remains constant within a closed system. As volume decreases, pressure increases proportionally, and vice versa. The calculator uses this inverse relationship to predict how a gas will behave when compressed or expanded.
The Boyle's Law Equation Fully Explained: P1V1 = P2V2
P1 × V1 = P2 × V2
- P1 × V1 = P2 × V2
- P1: initial pressure
- V1: initial volume
- P2: final pressure
- V2: final volume
How To Solve for Missing Gas Variables Step By Step
Inputs
- Solve for: choose which of the four variables is unknown from the dropdown
- P1 / V1: the starting state of the gas
- P2 / V2: the ending state of the gas
Steps
- Select the variable you want to calculate (P1, V1, P2, or V2) from the dropdown.
- Enter the value for your initial pressure (P1).
- Enter the value for your initial volume (V1).
- Enter the known value for your final state (P2 or V2).
- Read the calculated result for the missing variable.
Boyle's Law Worked Example: Compressing Air in a Syringe
Compressing 50 mL of air at 14.7 psi down to 20 mL at constant temperature.
- Set up equation: P1 × V1 = P2 × V2 → 14.7 × 50 = P2 × 20.
- Multiply initial values: 735 = P2 × 20.
- Isolate P2: P2 = 735 / 20 = 36.75 psi.
The final pressure inside the syringe is 36.75 psi.
When to Use This Formula and Its Primary Limitations
Use this calculator for chemistry homework, predicting scuba tank pressure dynamics, calculating pneumatic cylinder forces, or estimating manual bicycle pump output. It is highly accurate for common gases under everyday conditions.
Assumptions
- Temperature of the gas remains constant (isothermal process).
- Amount of gas (moles) remains constant in a sealed system.
- The gas behaves ideally.
Limitations
- Does not work accurately at extremely high pressures.
- Does not work accurately at extremely low temperatures near condensation.
- Rapid compression generates heat (adiabatic process), violating constant temperature unless allowed to cool.
In Practice
When applying this calculator to practical engineering, remember that pressure gauges read "gauge pressure" (pressure above atmospheric pressure), not absolute pressure. Boyle's Law only works with absolute pressure. If your tire gauge reads 30 psi, the absolute pressure is actually 44.7 psi (30 psi gauge + 14.7 psi atmospheric pressure). Always convert gauge readings to absolute pressure before entering them.
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Frequently Asked Questions: Boyle's Law Calculator
Why does Boyle's Law require constant temperature?
If temperature changes, the kinetic energy of the gas molecules changes. Heating a gas makes molecules move faster and hit container walls harder, increasing pressure even if volume stays constant (Gay-Lussac's Law).
Must I convert my units to standard SI units?
No. The equation P1 × V1 = P2 × V2 is a proportional relationship. As long as the unit for P1 matches P2, and V1 matches V2, the math works in any units.
Who discovered Boyle's Law?
Named after chemist and physicist Robert Boyle (published 1662). In continental Europe, it is sometimes called the Boyle-Mariotte law after Edme Mariotte who independently discovered it in 1679.
What is the difference between Boyle's Law and Charles's Law?
Boyle's Law describes the inverse relationship between pressure and volume at constant temperature. Charles's Law describes the direct relationship between volume and temperature at constant pressure.
Why is Boyle's Law an inverse relationship?
It is inverse because as one variable increases, the other must decrease to keep the product P × V constant.
Sources
Last updated: . Reviewed for accuracy against the formula shown above.