Combined Gas Law

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

P₁ =

V₁ =

T₁ =

P₂ =

V₂ =

T₂ =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

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

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

Where

$P_1$ = Initial pressure
$V_1$ = Initial volume
$T_1$ = Initial absolute temperature
$P_2$ = Final pressure
$V_2$ = Final volume
$T_2$ = Final absolute temperature

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.