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.
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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