Case 1
- Initial pressure p₁
- 100
- Initial volume V₁
- 2
- Final volume V₂
- 1
200.00
Open with these valuesBoyle's Law Calculator
200.00unit of p₁
Result: 200.00 unit of p₁At constant temperature, pressure times volume stays the same: halve the volume and the pressure doubles. Enter the starting pressure and volume plus the final volume; the answer comes back in whatever pressure unit you started with, because the law is a pure ratio.
Worked examples
Case 2
- Initial pressure p₁
- 101.325
- Initial volume V₁
- 10
- Final volume V₂
- 5
202.65
Open with these valuesCase 3
- Initial pressure p₁
- 50
- Initial volume V₁
- 4
- Final volume V₂
- 8
25.00
Open with these valuesHow it's calculated
p₂ = p₁ × V₁ ÷ V₂
- StepEnter the starting pressure in any unit you like.
- StepEnter the starting volume and the final volume in the same volume unit.
- ResultRead the final pressure in the unit you used for the first one.
What this number means
The units cancel, so choose your own
Both volumes go in the same unit, and the final pressure arrives in the unit of the first one. That is why the reference rows mix kPa (101.325), torr (760) and bare numbers without any trouble.
Constant temperature, constant amount of gas
Boyle's law holds only while neither of those changes. Warm the gas during the squeeze or let some escape and the product p × V no longer stays put.
Pressure and volume are inversely proportional
Their product is what stays the same: 100 × 2 and 200 × 1 are both 200. Doubling the volume from 4 to 8 therefore pushes 50 down to 25.
Commonly misread
The gauge reads 2 bar, so p₁ is 2.
Gauge pressure is measured against the surrounding air. Add the atmospheric pressure first, or the ratio no longer holds.
V₁ entered in litres and V₂ in cubic metres.
The two volumes need one shared unit, because only their ratio is used. Mixed units put the answer out by a factor of a thousand.
The gas heats up while it is being compressed.
Then Boyle's law no longer carries on its own. The combined gas law adds the temperature ratio.
Reference table
| p₁, V₁, V₂ | Volume change | Final pressure p₂ |
|---|---|---|
| 1, 1, 1 | unchanged | 1.00 |
| 2, 6, 3 | halved | 4.00 |
| 50, 4, 8 | doubled | 25.00 |
| 100, 2, 1 | halved | 200.00 |
| 101.325, 10, 5 | halved | 202.65 |
| 760, 0.5, 0.25 | halved | 1520.00 |
Questions
What is Boyle's law?
For a fixed amount of gas at constant temperature, pressure and volume are inversely proportional. Their product p times V stays the same, so p₁V₁ equals p₂V₂.
Which units should I use?
Any, as long as you are consistent. Both volumes in the same unit and the answer arrives in whatever unit the first pressure used, whether that is bar, pascal or torr.
Must the pressure be absolute?
Yes. Gauge pressure is measured against the surrounding air and would break the proportionality; add the atmospheric pressure first if your gauge reads zero in open air.
What if the temperature changes too?
Then Boyle's law no longer applies on its own. Use the combined gas law, which carries the temperature ratio alongside the pressure and volume.
Sources and last check
Information, not professional advice.