P₁V₁ = P₂V₂ | Calculate Pressure or Volume of a Gas | Chemistry & Physics Tool
Result
--
📝 Step-by-step solution
Select what to calculate and enter values
💡 P in atm, kPa, mmHg, or Pa | V in L or mL | Use consistent units on both sides
📖 What is Boyle's Law?
Boyle's Law states that the pressure of a fixed amount of gas at constant temperature
is inversely proportional to its volume. In other words, when you compress a gas, its pressure increases,
and when you expand it, its pressure decreases — as long as the temperature stays constant.
It's one of the three fundamental gas laws (along with Charles's Law and Gay-Lussac's Law) and is a special
case of the Ideal Gas Law (PV = nRT) when temperature and number of moles are constant.
The law is named after Irish chemist Robert Boyle, who published it in 1662.
Formula: P₂ = (P₁ × V₁) / V₂ Calculation: P₂ = (1 × 5) / 2 = 2.5 atm Result: When the gas is compressed from 5 L to 2 L, the pressure rises from 1 atm to 2.5 atm.
💡 Note: As volume decreases, pressure increases — that's why compressed gas cylinders are so dangerous.
📊 Common Pressure Units
1 atm = 101.325 kPa = 760 mmHg = 14.696 psi
1 kPa = 1000 Pa
1 bar = 100,000 Pa = 0.9869 atm
1 mmHg (torr) = 133.322 Pa
💡 Real-World Applications
Scuba Diving: As a diver descends, water pressure increases and air in the lungs compresses (Boyle's Law).
Syringes: Pulling the plunger increases volume and lowers pressure, drawing fluid in.
Breathing: The diaphragm expands the chest cavity, lowering pressure so air flows in.
Compressed Gas Cylinders: High-pressure gas in small volumes — a direct application of P₁V₁ = P₂V₂.
Weather Balloons: As balloons rise, atmospheric pressure drops and the gas inside expands.
⚠️ Limitations & Assumptions
📌 Important Notes
Assumes constant temperature — if temperature changes, Boyle's Law does not apply alone.
Assumes constant amount of gas — no gas is added or removed.
Works best for ideal gases — real gases deviate at high pressures or low temperatures.
Units must be consistent — pressure in the same unit on both sides, and volume in the same unit on both sides.
Does not account for phase changes — if the gas condenses, the law breaks down.
Results are theoretical estimates — real systems have small deviations.
📚 References & Sources
Authoritative Sources
OpenStax — Chemistry 2e, Chapter 9: Gases
NIST — Ideal Gas Law and Thermophysical Properties
Khan Academy — Boyle's Law and Gas Laws
CRC Handbook of Chemistry and Physics
Brown, LeMay, Bursten — Chemistry: The Central Science
❓ Frequently Asked Questions
What is the relationship between pressure and volume in Boyle's Law?
Pressure and volume are inversely proportional at constant temperature. When one increases,
the other decreases by the same factor. Their product (P × V) remains constant.
What units should I use for pressure and volume?
You can use any consistent units — atm, kPa, mmHg, or Pa for pressure, and L, mL, or m³ for volume.
Just make sure the same unit is used on both sides of the equation.
Can I use this for a gas where temperature changes?
No — Boyle's Law assumes constant temperature. If temperature changes, use the Combined Gas Law:
(P₁V₁)/T₁ = (P₂V₂)/T₂.
Why does Boyle's Law fail at high pressures?
At high pressures, gas molecules are close together, and intermolecular forces become significant.
The gas no longer behaves ideally, so Boyle's Law becomes less accurate.
Who discovered Boyle's Law?
The law is named after Robert Boyle, an Irish chemist who published it in 1662.
He also worked with Robert Hooke to experimentally verify the relationship.
This Boyle's Law Calculator is provided for informational and educational purposes only.
Results are based on the ideal gas assumption and constant temperature. Real gases may deviate from ideal behavior,
especially at high pressures or low temperatures. Always verify critical calculations with authoritative sources
or a qualified professional.