Solve Boyle's law P₁V₁ = P₂V₂ for any one missing pressure or volume. Choose your pressure and volume units, tick the gauge box for tire or tank readings, and get the answer with step-by-step working, the pressure–volume curve and the isothermal work.
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Solve for
Initial state (1)
Final state (2)
Enter your values to see the result.
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How to use the Boyle's Law Calculator
Choose what to solve for: P₁, V₁, P₂ or V₂.
Select the units for pressure and volume.
Tick gauge pressure if your numbers come from a tire, tank or compressor gauge.
Enter the three known values.
Press Solve to see the answer, the steps and the pressure–volume curve.
Boyle's law formula and rearrangements
Unknown
Formula
Example
Final volume V₂
V₂ = P₁V₁ ÷ P₂
1 atm × 10 L ÷ 2.5 atm = 4 L
Final pressure P₂
P₂ = P₁V₁ ÷ V₂
101.3 kPa × 60 mL ÷ 20 mL = 304 kPa
Initial volume V₁
V₁ = P₂V₂ ÷ P₁
2 bar × 3 L ÷ 1 bar = 6 L
Initial pressure P₁
P₁ = P₂V₂ ÷ V₁
760 mmHg × 1 L ÷ 2 L = 380 mmHg
The graph of pressure against volume at a constant temperature is a hyperbola called an isotherm: every point on it has the same product P·V. The work done by the gas as it moves along the isotherm is W = P₁V₁ · ln(V₂ ÷ V₁), using absolute pressure in pascals and volume in cubic meters to get joules.
Pressure units
1 atm = 101.325 kPa = 1.01325 bar = 14.696 psi = 760 mmHg = 760 Torr = 29.92 inHg. Gauge pressure = absolute pressure − atmospheric pressure, so a tire at 32 psi gauge holds about 46.7 psi absolute.
Tips
Let the gas return to its starting temperature before measuring; quick compression warms it and pushes the pressure above the Boyle's law value.
Boyle's law says that for a fixed amount of gas at constant temperature, pressure and volume are inversely proportional: P₁V₁ = P₂V₂. If you halve the volume, the pressure doubles. It was published by Robert Boyle in 1662.
How do I solve for final volume with Boyle's law?
Rearrange to V₂ = P₁V₁ ÷ P₂. For example, 10 L of gas at 1 atm compressed to 2.5 atm takes up 10 × 1 ÷ 2.5 = 4 L, as long as the temperature returns to its starting value.
Do I have to convert units for Boyle's law?
No, as long as both pressures use the same unit and both volumes use the same unit, because the units cancel. The calculator also shows the answer in other common units.
Can I use gauge pressure in Boyle's law?
Not directly. Boyle's law needs absolute pressure. Gauge readings are relative to the atmosphere, so add about 14.7 psi or 101.3 kPa first. Tick the gauge option and the calculator does this for you and converts the answer back to gauge.
What are real-life examples of Boyle's law?
A syringe that is hard to push when blocked, a balloon that grows as it rises into thinner air, ears popping on a plane, a diver's lungs and the air in a scuba tank, which expands to many times its volume at the surface.
When does Boyle's law not work?
It assumes constant temperature, a fixed amount of gas and ideal behavior. Fast compression heats the gas, gas may leak, and real gases deviate at high pressure or near condensation. For changing temperature, use the combined gas law.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.