What is the combined gas law formula?

The combined gas law formula is P₁V₁/T₁ = P₂V₂/T₂, where P is pressure, V is volume, and T is temperature in absolute units (Kelvin). It relates the initial state (P₁, V₁, T₁) to the final state (P₂, V₂, T₂) of a fixed amount of ideal gas.

How do I calculate the combined gas law?

Enter five of the six variables (P₁, V₁, T₁, P₂, V₂, T₂) and select which variable to solve for. The calculator rearranges P₁V₁/T₁ = P₂V₂/T₂ automatically. For example, to find V₂: V₂ = P₁V₁T₂ / (P₂T₁). Always convert temperatures to Kelvin before solving.

Why must temperature be in Kelvin for gas law calculations?

Gas law equations require absolute temperature because they are based on the kinetic theory of gases, where temperature is proportional to average molecular kinetic energy. At 0 K (absolute zero) molecules have minimum energy. Celsius and Fahrenheit have arbitrary zero points that would make the ratios meaningless. Convert using K = °C + 273.15.

What is the difference between the combined gas law and the ideal gas law?

The combined gas law (P₁V₁/T₁ = P₂V₂/T₂) compares the same gas in two states and does not need the number of moles or the gas constant R. The ideal gas law (PV = nRT) calculates absolute values using moles (n) and the universal gas constant (R = 8.314 J/mol·K). Use the combined law when comparing before/after states; use the ideal gas law when you know or need the amount of gas.

How do I calculate P₂ in the combined gas law?

Rearrange the formula to P₂ = P₁V₁T₂ / (V₂T₁). For example, if a gas at 1 atm, 10 L, and 300 K is compressed to 5 L at 350 K: P₂ = (1 × 10 × 350) / (5 × 300) = 3500 / 1500 = 2.33 atm.

How do I calculate T₂ in the combined gas law?

Rearrange to T₂ = P₂V₂T₁ / (P₁V₁). For example, if 2 L of gas at 1 atm and 300 K is compressed to 1 L at 3 atm: T₂ = (3 × 1 × 300) / (1 × 2) = 900 / 2 = 450 K (176.85 °C).

What are the special cases of the combined gas law?

When one variable is constant, the combined gas law reduces to: (1) Boyle's Law (constant T): P₁V₁ = P₂V₂, (2) Charles' Law (constant P): V₁/T₁ = V₂/T₂, and (3) Gay-Lussac's Law (constant V): P₁/T₁ = P₂/T₂. This calculator auto-detects these cases and highlights them.

Can the combined gas law be used with real gases?

The combined gas law assumes ideal gas behavior and works well for most gases at moderate temperatures and pressures. At very high pressures (above ~10 atm) or very low temperatures (near condensation), real gases deviate significantly. For more accuracy in those conditions, use the van der Waals equation.

How does a scuba tank demonstrate the combined gas law?

At the surface, air is at 1 atm. At 30 meters depth, pressure is about 4 atm. If the water is cooler than the surface, both pressure and temperature change. Using P₁V₁/T₁ = P₂V₂/T₂, you can calculate that the volume of air from a 12 L tank at 25 °C (298 K) would compress to roughly 2.85 L at 4 atm and 10 °C (283 K).

What units can I use with this calculator?

This calculator supports 7 pressure units (atm, kPa, Pa, bar, mmHg, psi, torr), 6 volume units (L, mL, m³, cm³, ft³, US gal), and 4 temperature units (K, °C, °F, °R). All unit conversions are handled automatically — you can mix different units for initial and final states.

Combined Gas Law Calculator

Solve for

Find final volume

Initial State

Pressure (P₁)

Volume (V₁)

Temperature (T₁)

Final State

Pressure (P₂)

Volume (V₂)

Temperature (T₂)

Preset Scenario

Final Volume (V₂)

10.00L

This is a special case of Gay-Lussac's Law!

Volume is constant → P₁/T₁ = P₂/T₂. Pressure and temperature are directly proportional.

All Values

P₁V₁/T₁ = P₂V₂/T₂ — all values in base units

Initial State

P₁

1.00atm

V₁

10.00L

T₁

273.15K

Final State

P₂

2.00atm

V₂

10.00L

T₂

546.30K

Step-by-Step Solution

Calculation walkthrough with your values

1.Formula: P₁V₁ / T₁ = P₂V₂ / T₂

2.Convert P₁: 1.0000 atm = 101325.00 Pa

3.Convert P₂: 2.0000 atm = 202650.00 Pa

4.Rearrange: V₂ = P₁V₁T₂ / (P₂T₁)

5.V₂ = 101325.00 × 10.0000 × 546.30 / (202650.00 × 273.15)

6.V₂ = 10.0000 L

Unit Conversions

Result expressed in all supported units

Volume

L10.000

mL10,000

m³0.010000

cm³10,000

ft³0.353147

gal (US)2.642

How to Calculate the Combined Gas Law

Core formula and rearrangements for every variable

The Combined Gas Law relates pressure, volume, and temperature of a fixed quantity of ideal gas across two states. It merges Boyle's, Charles', and Gay-Lussac's Laws into a single equation — no need to know the number of moles or the gas constant.

Combined Gas Law

P₁V₁ / T₁ = P₂V₂ / T₂

P = pressure · V = volume · T = absolute temperature (K)

Solve for P₁

P₁ = P₂V₂T₁ / (V₁T₂)

Initial pressure

Solve for V₁

V₁ = P₂V₂T₁ / (P₁T₂)

Initial volume

Solve for T₁

T₁ = P₁V₁T₂ / (P₂V₂)

Initial temperature

Solve for P₂

P₂ = P₁V₁T₂ / (V₂T₁)

Final pressure

Solve for V₂

V₂ = P₁V₁T₂ / (P₂T₁)

Final volume

Solve for T₂

T₂ = P₂V₂T₁ / (P₁V₁)

Final temperature

Example — Gas Compressed at Higher Temperature

P₁

Initial

atm

V₁

Initial

T₁

273.15

Initial

V₂ = ?

Solved!

With P₂ = 2 atm, T₂ = 546.3 K: V₂ = (1 × 10 × 546.3) / (2 × 273.15) = 10 L. The doubling of temperature offsets the doubling of pressure, so volume stays the same.

What Is the Combined Gas Law?

Understanding the unified gas relationship

The Combined Gas Law merges three foundational gas laws into one equation. It describes how pressure, volume, and temperature of a fixed amount of ideal gas are interrelated when any of these variables change between two states.

Unlike the Ideal Gas Law (PV = nRT), the combined gas law does not require knowing the amount of gas (moles) or the gas constant. It works by comparing the same gas sample in two different states: initial (P₁, V₁, T₁) and final (P₂, V₂, T₂).

Chemistry and physics students use this law to solve problems where two or more gas properties change simultaneously — for example, calculating how a weather balloon expands as it rises through the atmosphere where both pressure and temperature decrease.

Special Cases of the Combined Gas Law

When one variable is held constant, the law simplifies

Law	Constant	Simplified Formula	Relationship
Boyle's Law	Temperature	P₁V₁ = P₂V₂	P and V inversely proportional
Charles' Law	Pressure	V₁/T₁ = V₂/T₂	V and T directly proportional
Gay-Lussac's Law	Volume	P₁/T₁ = P₂/T₂	P and T directly proportional

This calculator automatically detects when your inputs match one of these special cases and displays a highlighted notification identifying the law.

Real-World Applications

Where the combined gas law applies in everyday life

Scuba diving

Air volume changes with depth pressure and water temperature

Weather balloons

Balloon expands as altitude pressure drops and temperature changes

Car tires

Tire pressure rises in summer heat at nearly constant volume

Aerosol cans

Warning labels based on pressure increase when heated

Aircraft cabins

Pressurization compensates for low external pressure at altitude

Syringes

Compressing gas in a syringe at constant temperature (Boyle's)

Common Mistakes to Avoid

Frequent errors in combined gas law calculations

Using Celsius or Fahrenheit directly

The combined gas law requires absolute temperature (Kelvin or Rankine). Using °C or °F will produce wrong results. Convert first: K = °C + 273.15.

Mismatched units between states

P₁ and P₂ must be in the same unit, as must V₁ and V₂. Mixing atm with kPa or liters with mL without converting will give incorrect answers.

Assuming gas quantity is fixed

The combined gas law only works when the amount of gas (moles) stays constant. If gas is added or removed, use the Ideal Gas Law (PV = nRT) instead.

Applying to extreme conditions

Real gases deviate from ideal behavior at very high pressures (>10 atm) or very low temperatures (near condensation). Use the van der Waals equation for accuracy in those cases.

Combined Gas Law vs. Ideal Gas Law

When to use each equation

Aspect	Combined Gas Law	Ideal Gas Law
Formula	P₁V₁/T₁ = P₂V₂/T₂	PV = nRT
Variables	P, V, T (two states)	P, V, n, T (one state)
Requires moles?	No	Yes
Gas constant?	Not needed	R = 8.314 J/mol·K
Best for	Before/after comparisons	Absolute calculations
Example	Balloon at two altitudes	Moles in a container

Frequently Asked Questions

Common questions about gas law calculations

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Last updated Apr 29, 2026

Combined Gas Law Calculator

All Values

Step-by-Step Solution

Unit Conversions

How to Calculate the Combined Gas Law

What Is the Combined Gas Law?

Special Cases of the Combined Gas Law

Real-World Applications

Common Mistakes to Avoid

Combined Gas Law vs. Ideal Gas Law

Frequently Asked Questions

Embed Combined Gas Law Calculator

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