Combined Gas Law Calculator

Calculate pressure, volume, and temperature changes using the combined gas law P1V1/T1 = P2V2/T2.

Solve for

P₁ (atm) (atm)

V₁ (L) (L)

T₁ (K) (K)

P₂ (atm) (atm)

V₂ (L) (L)

T₂ (K) (K)

Please check your inputs and try again.

One Law, Several Names

The combined gas law is not a separate principle. It is PV = nRT rearranged for a fixed amount of gas compared between two states. Because n and R are constant, PV/T must be the same before and after.

P₁V₁/T₁ = P₂V₂/T₂

The named gas laws are all special cases of this, obtained by holding one variable constant so it cancels:

Law	Held constant	Reduces to	Statement
Boyle's	Temperature	P₁V₁ = P₂V₂	Volume falls as pressure rises
Charles's	Pressure	V₁/T₁ = V₂/T₂	Volume rises with temperature
Gay-Lussac's	Volume	P₁/T₁ = P₂/T₂	Pressure rises with temperature
Avogadro's	P and T	V₁/n₁ = V₂/n₂	Volume scales with amount

There is no need to memorise four separate relationships. Write the combined law, cancel whatever is constant, and the correct special case falls out.

Combined Law or Ideal Gas Law?

Situation	Use	Why
Same gas sample, two conditions	Combined law	n cancels; no need to know it
Absolute amount required	PV = nRT	Only this gives moles
Gas escapes or is added	PV = nRT	n changes, so the combined law is invalid
Density or molar mass needed	PV = nRT	Requires the amount explicitly

The decisive question is whether the amount of gas stays fixed. If a container leaks, or gas is generated by reaction, n changes and the combined law no longer applies — a point worth checking before reaching for it.

Temperature must always be absolute. This is not a convention but a physical necessity: Charles's law extrapolates to zero volume at 0 K, and using Celsius would predict negative volumes below freezing.

Worked Examples

Example 1: Gas compressed: P1=1atm, V1=2L, T1=300K, P2=2atm, T2=350K

V2=1×2×350/(300×2)

Result: V2=1.167 L

Combined law: both P and T changed

Example 2: Boyle's law only: T constant T1=T2=300K

V2=P1V1/P2 (T cancels)

Result: V2=1.0L at P2=2atm

Inverse pressure-volume relationship

Example 3: Gay-Lussac at constant volume

Sealed can at 1 atm, 293 K, heated to 400 K

Result: P₂ = 1 × 400/293 = 1.37 atm

Volume is fixed so it cancels, leaving P/T constant. This is why sealed containers are dangerous when heated — pressure rises in direct proportion.

Example 4: Charles's law

Balloon at 2.0 L and 300 K cooled to 200 K at constant pressure

Result: V₂ = 2.0 × 200/300 = 1.33 L

Cooling by a third of the absolute temperature shrinks the volume by a third — which is why balloons visibly contract in liquid nitrogen.

Example 5: When the combined law fails

Tyre inflated from 2 to 3 atm by adding air

Result: Combined law does not apply

The amount of gas changed, so n does not cancel. This requires PV = nRT at each state with different n values.

Common Mistakes

⚠️

Using Celsius instead of Kelvin

Every gas law requires absolute temperature. Using Celsius gives wrong answers, and below 0°C it produces physically impossible negative values.

⚠️

Applying the law when the amount of gas changes

P₁V₁/T₁ = P₂V₂/T₂ assumes n is constant. If gas leaks, dissolves or is produced, use PV = nRT at each state instead.

⚠️

Mixing pressure or volume units between states

The units cancel only if both states use the same ones. Comparing atm with kPa, or litres with millilitres, gives an answer wrong by the conversion factor.

⚠️

Memorising the named laws separately

Boyle, Charles and Gay-Lussac are all the combined law with one variable cancelled. Deriving them is more reliable than recalling which is which.

Frequently Asked Questions

Combined vs individual gas laws?

Boyle: P1V1=P2V2 (T constant). Charles: V1/T1=V2/T2 (P constant). Gay-Lussac: P1/T1=P2/T2 (V constant). Combined: P1V1/T1=P2V2/T2 (all three vary). All assume ideal gas.

When to use combined vs ideal gas law?

Combined: comparing initial and final states of same gas sample. Ideal (PV=nRT): when moles are known or needed. Both give same answer for state comparisons.

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

The combined law compares one fixed sample of gas between two states, so n cancels. The ideal gas law relates absolute quantities and is needed whenever the amount matters.

Do I need to memorise Boyle's and Charles's laws separately?

No. Both are the combined law with one variable held constant. Writing the combined law and cancelling is more reliable than recalling individual names.

Why must temperature be in kelvin?

Because gas volume is proportional to absolute temperature, extrapolating to zero at 0 K. Celsius has an arbitrary zero and would predict negative volumes below freezing.

When can I not use the combined gas law?

Whenever the amount of gas changes — leaks, dissolution, or gas produced by reaction. Use PV = nRT separately for each state instead.

Do the units need to match?

Pressure and volume units cancel provided both states use the same ones. Temperature must always be kelvin regardless.

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.

Boyle's Law Calculator →Charles's Law Calculator →Clausius-Clapeyron Calculator →Chemistry Formula Explorer →