Boyle's Law Calculator

Boyle's law states that at constant temperature, pressure and volume are inversely proportional. Double the pressure, halve the volume. P₁V₁ = P₂V₂ for any ideal gas at constant T.

💨 Gas Laws📐 P₁V₁ = P₂V₂🌡️ Constant Temperature

Initial Pressure P₁

Initial Volume V₁

Final Volume V₂

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Boyle's Law	—	P₁V₁ = P₂V₂	—
Final Pressure	P₂	P₁V₁/V₂	Pa or atm
Final Volume	V₂	P₁V₁/P₂	L or mL
Relationship	—	P ∝ 1/V (at constant T,n)	—
Standard Pressure	1 atm	= 101,325 Pa = 760 mmHg = 14.7 psi	—

Step-by-Step Examples

Example 1

Compression

Gas at 1.00 atm, 5.00 L is compressed to 2.50 L. Find P₂.

P₂ = P₁V₁/V₂ = (1.00×5.00)/2.50
P₂ = 2.00 atm

✓ 2.00 atm (pressure doubled, volume halved)

Example 2

Expansion

Gas at 3.00 atm, 2.00 L expands to 1.00 atm. Find V₂.

V₂ = P₁V₁/P₂ = (3.00×2.00)/1.00
V₂ = 6.00 L

✓ 6.00 L (pressure drops to 1/3, volume triples

Example 3

Piston Compression

Oxygen at 760 mmHg, 10.0 L compressed to 5.50 L.

P₂ = 760×10.0/5.50 = 1382 mmHg
= 1382/760 = 1.82 atm

✓ P₂ = 1382 mmHg = 1.82 atm

Real-World Applications

🚨

Scuba Diving

At 10 m depth, pressure = 2 atm. Lungs compress to half volume. Critical safety knowledge.

🚔

Pistons & Engines

Engine compression strokes use Boyle's law; higher compression ratio gives more power.

🛢️

Pumps

Bicycle pumps, air compressors, and syringes all operate on Boyle's law.

🔬

Lab Gas Handling

Gas collection and transfer use Boyle's law to calculate amounts at different pressures.

Common Mistakes to Avoid

⚠️

Temperature must be constant

Boyle's law only applies at constant temperature. If T changes, use Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂.

⚠️

Consistent pressure units

P₁ and P₂ must be in the same units (both atm, both Pa, etc.). Same for volume.

⚠️

Ideal gas assumption

Boyle's law is exact only for ideal gases. Real gases deviate at very high pressures or low temperatures.

Frequently Asked Questions

Who discovered Boyle's law? ▾

Robert Boyle in 1662, based on experiments with a J-shaped tube sealed with mercury. He was the first to publish the inverse P-V relationship quantitatively.

Why are pressure and volume inversely proportional? ▾

Fewer molecules hit the walls each second when volume is larger (at same T). Pressure = force/area = molecule collision rate × force per collision. At larger V, collision rate drops.

What is an isothermal process? ▾

A process at constant temperature. Boyle's law applies to isothermal processes. In PV diagrams, isotherms are hyperbolas (PV = constant).

Does Boyle's law apply to liquids? ▾

No. Liquids are nearly incompressible. Boyle's law applies only to gases (ideal gas behavior).

What is the product PV for an ideal gas? ▾

PV = nRT (ideal gas law). At constant T and n, PV = constant = nRT. This is the mathematical statement of Boyle's law.

Related Chemistry Calculators

Formula Explorer connections

Interpretation: This relationship connects pressure, volume, temperature, amount or phase composition for gases and volatile mixtures. Assumption: Use absolute temperature and compatible pressure-volume units. Ideal behavior weakens at high pressure, low temperature, strong intermolecular attraction or near phase change.

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