Combined Gas Law Calculator

The Combined Gas Law brings together Boyle's Law and Charles's Law into a single equation that describes how a fixed amount of gas behaves when pressure, volume, and temperature all change at the same time. The formula is P1V1 divided by T1 equals P2V2 divided by T2, where the subscripts 1 and 2 refer to the initial and final states of the gas. Unlike the two simpler laws, which each hold one variable constant, the Combined Gas Law works for any change of state as long as the quantity of gas stays the same. You can use it to find any one of the six variables given the other five. The most common use is to find the final volume V2 after a gas has been compressed or expanded and also heated or cooled, but the equation can equally be rearranged to find any pressure or temperature. The only firm requirement is that temperatures must be in kelvin: convert from Celsius by adding 273.15. This calculator lets you choose which variable to solve for, enter the other five values, and get the result immediately. The supporting display shows the ratio P1V1/T1 and P2V2/T2 for verification that the law holds, along with the individual pressure, volume, and temperature ratios. Results are suitable for science coursework and introductory engineering calculations involving ideal gases.

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atm
L
K
atm
K
L
1.3333 L
solved variable
P1V1/T10.006667
P2V2/T20.006666
Pressure ratio P2/P12
Volume ratio V2/V10.6666

Temperature must be in kelvin (K = °C + 273.15). Assumes ideal gas behaviour and constant amount of gas.

How it works

The Combined Gas Law states P1V1/T1 = P2V2/T2. Rearranging for each variable: V2 = P1V1T2/(T1P2); P2 = P1V1T2/(T1V2); T2 = T1P2V2/(P1V1); V1 = P2V2T1/(T2P1); P1 = P2V2T1/(T2V1); T1 = T2P1V1/(P2V2). Select the variable you want to solve for and the calculator applies the correct form. The constant ratio P1V1/T1 = P2V2/T2 is displayed for verification.

Worked example

A gas starts at P1 = 1 atm, V1 = 2 L, T1 = 300 K. It is compressed to P2 = 2 atm and heated to T2 = 400 K. Using the Combined Gas Law: V2 = (1 × 2 × 400) / (300 × 2) = 800 / 600 = 1.333 L. P1V1/T1 = 2/300 = 0.006667 and P2V2/T2 = (2 × 1.333)/400 = 0.006667. These match the default values pre-filled above.

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Frequently asked questions

What is the Combined Gas Law?

The Combined Gas Law merges Boyle's Law and Charles's Law into a single equation: P1 times V1 divided by T1 equals P2 times V2 divided by T2. It describes how a fixed amount of ideal gas behaves when pressure, volume, and temperature all change simultaneously. Unlike Boyle's Law (which requires constant temperature) or Charles's Law (which requires constant pressure), the Combined Gas Law applies to any change of state where the amount of gas remains constant.

How do you solve for V2 using the Combined Gas Law?

Rearrange P1V1/T1 = P2V2/T2 to isolate V2: V2 = (P1 times V1 times T2) divided by (T1 times P2). Substitute your known values to find V2. For example, P1=1 atm, V1=2 L, T1=300 K, P2=2 atm, T2=400 K gives V2 = (1 times 2 times 400) / (300 times 2) = 800/600 = 1.333 L.

What is the difference between the Combined Gas Law and the Ideal Gas Law?

The Combined Gas Law compares two states of the same fixed amount of gas (P1V1/T1 = P2V2/T2) without needing to know the number of moles. The Ideal Gas Law (PV = nRT) includes the number of moles n and the gas constant R, making it more general: it can find the absolute state of a gas rather than just comparing two states. If the amount of gas changes between states, you need the Ideal Gas Law, not the Combined Gas Law.