Boyle's Law Calculator (P₁V₁ = P₂V₂)
By Santaji GadepatilinUpdated October 27, 2026
At constant temperature, the pressure of a gas is inversely proportional to its volume — squeeze it to half the volume and its pressure doubles. Boyle's law explains syringes, breathing and gas compression.
Final volume (L) vs Final pressure (absolute) (kPa) — other inputs held at your current values.
How to use the Boyle’s law calculator
Enter any three of the initial and final pressure and volume. The fourth is calculated. Temperature and the amount of gas must stay constant.
Boyle’s law formula
P₁ V₁ = P₂ V₂
Worked example
10 L of gas at 100 kPa is compressed to 250 kPa:
V₂ = 100 × 10 ÷ 250 = 4 L
Pressure–volume table
Starting at 100 kPa and 10 L, at constant temperature:
| Pressure | Volume |
|---|---|
| 50 kPa | 20.00 L |
| 100 kPa | 10.00 L |
| 150 kPa | 6.67 L |
| 200 kPa | 5.00 L |
| 300 kPa | 3.33 L |
| 500 kPa | 2.00 L |
| 1000 kPa | 1.00 L |
Double the pressure and the volume halves; the product P × V stays at 1,000 kPa·L.
Everyday examples
- Syringes: pulling the plunger increases volume, lowering pressure, so liquid is drawn in.
- Breathing: your diaphragm enlarges the chest, lowering lung pressure so air flows in.
- Bicycle pumps: pushing the handle compresses air until its pressure exceeds the tyre’s.
- Aerosol cans: gas expands as it leaves the higher-pressure can.
Why temperature must be constant
Compressing a gas quickly heats it (think of a bicycle pump getting warm). Boyle’s law applies to slow changes where heat can escape, keeping the temperature steady. If temperature changes too, use the combined gas law.
Gauge vs absolute pressure
Always use absolute pressure. A tyre gauge reading of 200 kPa is about 301 kPa absolute at sea level. Using gauge pressure gives wrong answers.
Diving example
At 10 m depth, the absolute pressure is about 2 atm, so a lungful of air from the surface shrinks to half its volume — which is why divers must never hold their breath while ascending.
Frequently asked questions
What is Boyle's law?
At constant temperature, the pressure of a fixed amount of gas is inversely proportional to its volume — P₁V₁ = P₂V₂.
Do I need absolute pressure?
Yes. Add atmospheric pressure (about 101.3 kPa) to gauge readings.
Where is Boyle's law seen in daily life?
Syringes, bicycle pumps, scuba diving (air spaces shrink with depth) and air compressors.
What is Boyle’s law?
At constant temperature, the pressure of a fixed amount of gas is inversely proportional to its volume: P₁V₁ = P₂V₂.
Who discovered Boyle’s law?
Robert Boyle published it in 1662, based on experiments with air trapped in a J-shaped tube.