About

Boyle's Law describes the inverse relationship between pressure (P) and volume (V) of a confined ideal gas at constant temperature. Formally: P₁V₁ = P₂V₂. Miscalculating gas expansion in sealed containers leads to equipment rupture, failed experiments, or incorrect dosing in respiratory medicine. This calculator solves for any unknown variable given the other three, with unit conversion across 7 pressure units and 6 volume units. The law assumes ideal gas behavior and breaks down at high pressures (above ~10 atm for most gases) or near condensation points where intermolecular forces become significant.

Formulas

Boyle's Law states that for a fixed amount of ideal gas at constant temperature, the product of pressure and volume remains constant:

P₁ ⋅ V₁ = P₂ ⋅ V₂

Solving for each variable:

P₂ = P₁ ⋅ V₁V₂

V₂ = P₁ ⋅ V₁P₂

P₁ = P₂ ⋅ V₂V₁

V₁ = P₂ ⋅ V₂P₁

Where P₁ = initial pressure, V₁ = initial volume, P₂ = final pressure, V₂ = final volume. All values must be positive. Temperature and amount of gas (n) are held constant. The relationship is hyperbolic: as P increases, V decreases proportionally, and vice versa.

Reference Data

Gas	Ideal Behavior Range	Critical Pressure atm	Critical Temp K	Molar Mass g/mol	Common Application
Helium (He)	Nearly all conditions	2.26	5.19	4.003	Balloons, cryogenics
Hydrogen (H₂)	< 100 atm	12.8	33.2	2.016	Fuel cells, synthesis
Nitrogen (N₂)	< 50 atm	33.5	126.2	28.014	Inert atmosphere
Oxygen (O₂)	< 40 atm	50.4	154.6	31.998	Medical, welding
Argon (Ar)	< 40 atm	48.7	150.9	39.948	Welding shielding
Neon (Ne)	< 80 atm	26.9	44.4	20.180	Signage, lasers
Carbon Dioxide (CO₂)	< 10 atm	72.9	304.2	44.009	Carbonation, fire suppression
Methane (CH₄)	< 20 atm	45.8	190.6	16.043	Natural gas, fuel
Ammonia (NH₃)	< 5 atm	111.3	405.5	17.031	Refrigeration, fertilizer
Water Vapor (H₂O)	< 2 atm	217.7	647.1	18.015	Steam engines
Sulfur Dioxide (SO₂)	< 5 atm	77.7	430.8	64.066	Preservative, refrigerant
Chlorine (Cl₂)	< 5 atm	76.1	417.2	70.906	Water treatment
Propane (C₃H₈)	< 8 atm	42.5	369.8	44.096	Heating fuel, LPG
Ethane (C₂H₆)	< 10 atm	48.2	305.3	30.069	Petrochemical feedstock
Xenon (Xe)	< 20 atm	58.4	289.7	131.293	Anesthesia, ion propulsion

Frequently Asked Questions

Boyle's Law assumes ideal gas behavior. It deviates significantly above approximately 10 atm for most real gases (earlier for polar molecules like NH₃ or H₂O vapor). At high pressures, intermolecular forces and molecular volume become non-negligible. For such conditions, use the van der Waals equation: (P + aV²)(V − b) = RT.

Boyle's Law is derived from the ideal gas law PV = nRT by holding n, R, and T constant. If temperature changes during compression or expansion, you need the combined gas law: P₁V₁T₁ = P₂V₂T₂. In practice, rapid compression heats gas (adiabatic process), so slow isothermal processes or temperature-controlled systems are necessary.

All conversions reference 1 atm as the base. Key equivalences: 1 atm = 101325 Pa = 101.325 kPa = 760 mmHg = 1.01325 bar = 14.696 psi = 760 Torr. The calculator internally converts all inputs to atm, performs the Boyle's Law calculation, then converts the result back to your selected output unit.

Yes. Dalton's Law of partial pressures states that each component of a mixture obeys the gas laws independently. The total pressure P is the sum of partial pressures. Boyle's Law applies to the total pressure and total volume of the mixture, provided all components behave ideally and temperature remains constant. This is routinely used in diving gas calculations and ventilator settings.

Pressure and volume must be strictly positive in classical thermodynamics. Zero volume implies infinite pressure (a physical impossibility), and zero pressure implies infinite volume. The calculator validates all inputs and rejects non-positive values with an error notification. Negative values have no physical meaning in this context.

At sea level (1 atm), air in a diver's lungs occupies its normal volume. At 10 m depth (2 atm), that volume halves. At 30 m (4 atm), it is one quarter. Ascending without exhaling causes lung over-expansion (pulmonary barotrauma). Boyle's Law directly predicts the volume change: V₂ = V₁ × (P₁ ÷ P₂).