Boyle's Law Calculator

Last updated: April 5, 2026

The Boyle's Law Calculator applies P₁V₁ = P₂V₂ at constant temperature. Enter any three of the four variables — P₁, V₁, P₂, or V₂ — to solve for the fourth. Covers chemistry, scuba diving, respiratory physiology, and pneumatic engineering applications.

Calculator

Solve For

Initial Pressure (P₁)Pa

Initial Volume (V₁)L

Final Pressure (P₂)Pa

Final Volume (V₂)L

Results

Calculated Value

Result Type: Pressure

Result Type: Volume

Initial Pressure-Volume Product

1,013,250

Pa·L

Final Pressure-Volume Product from Inputs

1,013,250

Pa·L

Final Pressure-Volume Product with Calculated Value

1,013,250

Pa·L

Volume Ratio (V₂/V₁)

0.5

Pressure Ratio (P₂/P₁)

Consistency Ratio ((P₂V₂)/(P₁V₁))

Results

Calculated Value

Result Type: Pressure

Result Type: Volume

Initial Pressure-Volume Product

1,013,250

Pa·L

Final Pressure-Volume Product from Inputs

1,013,250

Pa·L

Final Pressure-Volume Product with Calculated Value

1,013,250

Pa·L

Volume Ratio (V₂/V₁)

0.5

Pressure Ratio (P₂/P₁)

Consistency Ratio ((P₂V₂)/(P₁V₁))

Boyle's Law states that for a fixed amount of an ideal gas at constant temperature, pressure and volume are inversely proportional — double the pressure and the volume halves. This relationship governs everything from how your lungs work when you breathe to why scuba divers must never hold their breath while ascending. The Boyle's Law calculator solves for any unknown variable in the relationship P₁V₁ = P₂V₂.

Boyle's Law Formula

P₁V₁ = P₂V₂ (at constant temperature and fixed amount of gas)

Or equivalently: PV = constant (k)

To solve for any variable: V₂ = P₁V₁/P₂; P₂ = P₁V₁/V₂; V₁ = P₂V₂/P₁; P₁ = P₂V₂/V₁

Example: a gas at 2 atm occupying 3 L is compressed to 1 L at constant temperature. What is the new pressure? P₂ = P₁V₁/V₂ = (2 × 3)/1 = 6 atm. Use this online calculator for any Boyle's Law problem. The Charles's Law calculator and combined gas law calculator cover temperature-dependent gas law problems.

Pressure and Volume Units Reference

The calculator accepts any pressure unit (they must match in numerator and denominator, or be explicitly converted):

1 atm = 101,325 Pa = 101.325 kPa = 760 mmHg (Torr) = 14.696 psi
1 bar = 100,000 Pa = 0.9869 atm
Pressure at sea level: 1 atm; at 10 m underwater: 2 atm (absolute)

Volume units: L (liters), mL, m³, ft³, gallons. Ensure consistent units within each calculation.

Real-World Applications of Boyle's Law

Breathing: when your diaphragm contracts and lung volume increases, pressure drops below atmospheric, drawing air in (Boyle's Law in action with every breath)
Scuba diving: a breath of air at 20 m depth (3 atm absolute) will triple in volume upon ascent to the surface (1 atm) — holding your breath while ascending causes lung rupture
Syringes: pulling the plunger back increases volume and decreases pressure, drawing liquid into the syringe
Tire pressure: reducing tire volume by pressing increases internal pressure
Bicycle pumps: compressing air in the pump barrel increases pressure to overcome tire pressure

The ideal gas law calculator and gas law calculators complete the thermodynamics toolkit.

Visual Analysis

How It Works

Enter three of four variables: P₁ (initial pressure), V₁ (initial volume), P₂ (final pressure), V₂ (final volume). Ensure pressure units match and volume units match (or select from the unit dropdown for automatic conversion). Solve: P₂ = P₁V₁/V₂; or V₂ = P₁V₁/P₂; etc. Temperature must remain constant for Boyle's Law to apply.

Understanding Your Results

If you double the pressure on a gas, the volume halves — and vice versa. The P₁V₁ and P₂V₂ products should be equal; any mismatch means the temperature or amount of gas changed. A compression ratio below 1 indicates the gas was compressed; above 1 means it expanded.

Worked Examples

Compressing Gas to Half Volume

Inputs

solve forP2

P1101325

V110

V25

Results

result202650

result unitPa

compression ratio0.5

Halving the volume from 10 L to 5 L at constant temperature doubles the pressure from 101325 Pa to 202650 Pa (1 atm → 2 atm).

Scuba Tank Expansion

Inputs

solve forV2

P120265000

V10.012

P2101325

Results

result2400

result unitL

A 12-liter scuba tank at 200 atm contains gas that would expand to about 2400 liters at surface pressure (1 atm).

Frequently Asked Questions

Boyle's Law states that for a fixed amount of an ideal gas at constant temperature, pressure and volume are inversely proportional: PV = constant, or P₁V₁ = P₂V₂. Conditions for Boyle's Law to apply: constant temperature (isothermal process); fixed amount of gas (no gas is added or removed); the gas behaves approximately ideally (low pressure, not near the condensation point). Real gases deviate from Boyle's Law at high pressures (where intermolecular forces become significant) and near their critical temperature. At moderate pressures and temperatures well above the boiling point of the gas, Boyle's Law is an excellent approximation. It was discovered by Robert Boyle in 1662 through experiments with mercury manometers and trapped air columns — one of the earliest quantitative gas law studies.

Using P₁V₁ = P₂V₂, solve for the unknown variable by cross-multiplication. Finding P₂: P₂ = (P₁ × V₁) / V₂. Finding V₂: V₂ = (P₁ × V₁) / P₂. Finding P₁: P₁ = (P₂ × V₂) / V₁. Finding V₁: V₁ = (P₂ × V₂) / P₁. Worked example: A 4 L sample of gas at 1.5 atm is compressed at constant temperature until the pressure is 3 atm. Find the new volume. V₂ = (P₁ × V₁) / P₂ = (1.5 × 4) / 3 = 2 L. Sanity check: pressure doubled (1.5 → 3 atm), so volume should halve (4 → 2 L) — consistent with inverse proportionality. Always check units: both pressure values must be in the same unit; both volume values must be in the same unit.

Breathing is a perfect demonstration of Boyle's Law in action. Inhalation: the diaphragm contracts downward and the external intercostal muscles expand the rib cage — this increases lung volume. By Boyle's Law (P₁V₁ = P₂V₂), as lung volume increases, pressure inside the lungs decreases below atmospheric pressure (approximately 1–3 mmHg below). This pressure gradient drives air from the atmosphere into the lungs. Exhalation: the diaphragm relaxes and lung volume decreases — pressure inside rises above atmospheric, pushing air out. The entire respiratory cycle is driven by pressure changes resulting from volume changes — a direct application of Boyle's Law. Normal breathing uses only about 0.5 L of a total lung capacity of approximately 6 L.

Boyle's Law is a matter of life and death in scuba diving. At depth, water pressure is greater: at 10 m (33 ft), absolute pressure is 2 atm (1 atm water + 1 atm atmospheric); at 20 m, 3 atm; at 30 m, 4 atm. A scuba regulator delivers air at ambient pressure — a breath of air at 30 m fills your lungs at 4 atm. If you hold that breath and ascend to the surface (1 atm), the air in your lungs expands to 4× the original volume by Boyle's Law. Lungs cannot expand that much — the result is pulmonary barotrauma (lung rupture), arterial gas embolism, or death. This is why the cardinal rule of scuba diving is: never hold your breath. Ascending from even 2–3 meters while holding your breath can cause serious injury.

Absolute pressure is total pressure including atmospheric pressure. Gauge pressure is pressure above (or below) atmospheric pressure — what a typical pressure gauge reads. For Boyle's Law, you must use absolute pressure. At sea level: 0 psi gauge = 14.7 psi absolute (atmospheric). A car tire at 32 psi gauge = 32 + 14.7 = 46.7 psi absolute. In scuba: at 10 m depth, gauge pressure = 14.7 psi (1 atm from water); absolute pressure = 14.7 + 14.7 = 29.4 psi = 2 atm. Always convert gauge pressure to absolute (add 1 atm or 14.7 psi or 101.325 kPa) before applying Boyle's Law. Using gauge pressure directly in P₁V₁ = P₂V₂ gives incorrect answers when one of the pressures is near zero or atmospheric.

Boyle's Law describes the pressure-volume relationship at constant temperature: P ∝ 1/V (inverse proportionality). Charles's Law describes the volume-temperature relationship at constant pressure: V ∝ T (direct proportionality, in Kelvin). Boyle's Law is an isothermal process (constant T); Charles's Law is an isobaric process (constant P). Combined: the Ideal Gas Law PV = nRT combines both, plus accounting for the amount of gas (n moles). Practical difference: Boyle's Law governs gas compression and expansion in sealed systems at constant temperature (tire inflation, syringes, diving); Charles's Law governs how gas expands when heated at constant pressure (hot air balloons, why bread rises in an oven, why tire pressure increases after driving).

Sources & Methodology

Boyle, R. (1662). New Experiments Physico-Mechanical. Atkins, P., de Paula, J. (2014). Atkins' Physical Chemistry, 10th ed. Nave, R. (2023). HyperPhysics: Boyle's Law. Georgia State University.

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How It Works

Worked Examples

Compressing Gas to Half Volume

Inputs

solve forP2

P1101325

V110

V25

Results

result202650

result unitPa

compression ratio0.5

Halving the volume from 10 L to 5 L at constant temperature doubles the pressure from 101325 Pa to 202650 Pa (1 atm → 2 atm).

Scuba Tank Expansion

Inputs

solve forV2

P120265000

V10.012

P2101325

Results

result2400

result unitL

A 12-liter scuba tank at 200 atm contains gas that would expand to about 2400 liters at surface pressure (1 atm).

Frequently Asked Questions