Combined Gas Law

\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

Worked example: 1 L at 1 atm, 273.15 K → 0.5 atm, 546.3 K gives 4 L — press Try an example to run it live, then adjust anything.

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The gas laws →

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Combined Gas Law explained

The combined gas law merges Boyle's, Charles's, and Gay-Lussac's laws into a single statement: for a fixed amount of gas, PV/T is constant. A weather balloon shows all three variables moving at once. Launched with 2.0 m³ of helium at 101 kPa and 288 K, it rises to where the pressure is 30 kPa and the temperature 228 K; its new volume is V₂ = P₁V₁T₂ ÷ (P₂T₁) = 2.0 × 101 × 228 ÷ (30 × 288) ≈ 5.3 m³ — more than double.

Hold any one variable constant and the named laws drop out: fix T for Boyle's law, fix P for Charles's, fix V for Gay-Lussac's. Temperatures must be absolute — the ratio of 20 °C to 40 °C is not 1:2 but 293:313 — and Celsius or Fahrenheit inputs convert to kelvin automatically. Add Avogadro's insight about the amount of gas n and this law becomes the full ideal gas law, PV = nRT.

Combined Gas Law formula

\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

Where

$P_1$ = Initial pressure (kPa)
$V_1$ = Initial volume (L)
$T_1$ = Initial absolute temperature (°C)
$P_2$ = Final pressure (kPa)
$V_2$ = Final volume (L)
$T_2$ = Final absolute temperature (°C)

Missing one of these? Work it out first, then come back

Initial pressure — Boyle's Law, Gay-Lussac's Law
Initial volume — Boyle's Law, Charles's Law
Initial absolute temperature — Charles's Law, Gay-Lussac's Law
Final pressure — Boyle's Law, Gay-Lussac's Law
Final volume — Boyle's Law, Charles's Law
Final absolute temperature — Charles's Law, Gay-Lussac's Law

Part of this formula set

The gas laws

5 formulasBoyle, Charles, Gay-Lussac, the combined law and the ideal gas law — each holding one property fixed, and how they collapse into PV = nRT.