Combined gas law calculator

The formula

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

Subscript 1 is the gas before a change, and subscript 2 is after. $P$ is pressure, $V$ volume and $T$ absolute temperature (kelvin).

Where it comes from

Start from the ideal gas law, $PV = nRT$, and divide both sides by $T$:

$$\frac{PV}{T} = nR$$

If no gas gets in or out, the amount $n$ stays the same, and $R$ is a constant. So $PV/T$ has the same value before and after any change. Setting the two states equal gives the combined gas law.

It also contains the three older gas laws as special cases:

• Boyle’s law (constant $T$): $P_1 V_1 = P_2 V_2$
• Charles’s law (constant $P$): $V_1 / T_1 = V_2 / T_2$
• Gay-Lussac’s law (constant $V$): $P_1 / T_1 = P_2 / T_2$

Worked example

2.00 L of gas at 1.00 atm and 25 °C is compressed to 2.50 atm and heated to 100 °C. First convert the temperatures to kelvin, 298.15 K and 373.15 K. Then solve for $V_2$:

$$V_2 = \frac{P_1 V_1 T_2}{P_2 T_1} = \frac{1.00 \times 2.00 \times 373.15}{2.50 \times 298.15} = 1.00\ \text{L}$$

Raising the pressure 2.5 times would shrink it to 0.80 L, but heating pushes it back out to about 1.00 L.

Watch out for

• Kelvin, always. Using °C gives wrong answers, and divides by zero at 0 °C. The calculator converts for you.
• Same units on both sides. Pressures and volumes cancel, so any unit works as long as both states use it. Temperature is the exception and must be absolute.
• Real gases drift from this at high pressure or near condensation.

Sources

• OpenStax, Chemistry 2e, section 9.2 "Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law"

Last checked November 11, 2026