About

The Combined Gas Law merges Boyle's, Charles's, and Gay-Lussac's laws into a single relation: P₁ ⋅ V₁T₁ = P₂ ⋅ V₂T₂. It governs the behavior of a fixed mass of gas when amount of substance (n) remains constant. Miscalculating state transitions leads to incorrect sizing of pressure vessels, faulty HVAC designs, or dangerous conditions in sealed systems. Temperature must always be in absolute units (Kelvin); using Celsius or Fahrenheit directly in the formula produces nonsense outputs and is the single most common error in gas-law problems.

This calculator converts all inputs to SI base units (Pa, m³, K) before solving, then converts the result back to your chosen unit. It assumes an ideal gas approximation, which breaks down at pressures above roughly 10 MPa or temperatures near the substance's condensation point. For real-gas corrections, apply the van der Waals equation instead.

Formulas

The Combined Gas Law relates two states of a fixed quantity of ideal gas:

P₁ ⋅ V₁T₁ = P₂ ⋅ V₂T₂

Solving for each variable:

P₂ = P₁ ⋅ V₁ ⋅ T₂T₁ ⋅ V₂

V₂ = P₁ ⋅ V₁ ⋅ T₂T₁ ⋅ P₂

T₂ = P₂ ⋅ V₂ ⋅ T₁P₁ ⋅ V₁

Temperature conversions to Kelvin:

T_K = T_°C + 273.15

T_K = T_°F − 321.8 + 273.15

Where P = pressure, V = volume, T = absolute temperature (Kelvin). Subscript 1 denotes the initial state, subscript 2 denotes the final state. The equation assumes constant amount of gas (n) and ideal behavior.

Reference Data

Gas Law	Relation	Held Constant	Equation
Boyle's Law	P ∝ 1V	T, n	P₁V₁ = P₂V₂
Charles's Law	V ∝ T	P, n	V₁T₁ = V₂T₂
Gay-Lussac's Law	P ∝ T	V, n	P₁T₁ = P₂T₂
Combined Gas Law	PV/T = k	n	P₁V₁T₁ = P₂V₂T₂
Ideal Gas Law	PV = nRT	-	PV = nRT
Common Pressure Conversions
1 atm	101,325 Pa	760 mmHg	14.696 psi
1 bar	100,000 Pa	750.062 mmHg	14.504 psi
Common Volume Conversions
1 m³	1,000 L	1,000,000 mL	35.3147 ft³
1 gal (US)	3.78541 L	3,785.41 mL	0.13368 ft³
Temperature Reference Points
Absolute Zero	0 K	−273.15 °C	−459.67 °F
Water Freezing	273.15 K	0 °C	32 °F
Water Boiling	373.15 K	100 °C	212 °F
STP (IUPAC)	273.15 K	100 kPa	22.711 L/mol
NTP (Old)	293.15 K	101.325 kPa	24.04 L/mol
Gas Constant R
8.31446	J/(mol⋅K)	SI standard value
0.08206	L⋅atm/(mol⋅K)	Commonly used in chemistry
1.98720	cal/(mol⋅K)	Calorie-based systems
62.3637	L⋅mmHg/(mol⋅K)	Mercury-gauge applications

Frequently Asked Questions

The Combined Gas Law is derived from proportionality relationships (V ∝ T). These proportionalities only hold on an absolute scale where 0 represents zero molecular kinetic energy. Using Celsius would place zero at an arbitrary point (water's freezing), producing mathematically meaningless ratios. For example, halving 100 °C to 50 °C does not halve the thermal energy. The calculator automatically converts all temperature inputs to Kelvin before solving.

The equation assumes ideal gas behavior: no intermolecular forces and negligible molecular volume. This breaks down above roughly 10 MPa or near the gas's condensation temperature. For example, CO₂ at 31.1 °C and 7.38 MPa (its critical point) cannot be modeled accurately. Use the van der Waals equation or Peng-Robinson EOS for real-gas corrections in those regimes.

No. The Combined Gas Law holds n (moles of gas) constant. If gas leaks out or is added, you need the full Ideal Gas Law: PV = nRT, applied separately to each state. Compare the computed n values to quantify the change.

The formula requires absolute pressure. Gauge pressure reads zero at atmospheric conditions, so you must add atmospheric pressure: P_abs = P_gauge + P_atm. At sea level, P_atm ≈ 101.325 kPa (14.696 psi). Forgetting this conversion is a common source of factor-of-two errors in pressure vessel calculations.

It applies to gas mixtures provided the mixture behaves ideally as a whole. By Dalton's law, each component contributes a partial pressure p_i = x_i ⋅ P_total. The combined law governs the total P, V, T of the mixture. Non-ideal mixing (e.g., polar molecules) introduces errors.

STP (IUPAC, since 1982) is 273.15 K and 100 kPa, giving a molar volume of 22.711 L/mol. The older NTP standard uses 293.15 K (20 °C) and 101.325 kPa. Many engineering references still cite the pre-1982 STP of 273.15 K at 101.325 kPa (22.414 L/mol). Always verify which convention your data source uses.