Combined Gas Law Calculator (P1V1/T1 = P2V2/T2)
Choose which of the six values to find, then enter the other five. Temperatures are converted to kelvin internally, so Celsius works too.
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Formula
P1 × V1 ÷ T1 = P2 × V2 ÷ T2
- Temperatures must be absolute: K = °C + 273.15.
- Rearranged for each unknown, for example
V2 = P1 × V1 × T2 ÷ (T1 × P2)andT2 = T1 × P2 × V2 ÷ (P1 × V1). - Pressure and volume units cancel, as long as both states use the same unit. Conversions used: 1 atm = 101325 Pa, 1 bar = 100000 Pa, 1 mmHg = 101325 / 760 Pa, 1 L = 1000 mL = 0.001 m³.
- The amount of gas shown is
n = P × V ÷ (R × T)with R = 8.314462618 J/(mol K).
Worked example
A gas at 1 atm, 10 L and 273.15 K is compressed to 2 atm and heated to 400 K. Find the final volume.
- V2 = P1 × V1 × T2 ÷ (T1 × P2)
- V2 = 1 × 10 × 400 ÷ (273.15 × 2) = 4000 ÷ 546.3
- V2 = 7.322 L
Frequently asked questions
What is the combined gas law?
It joins Boyle's, Charles's and Gay-Lussac's laws into one: P1 × V1 ÷ T1 = P2 × V2 ÷ T2, for a fixed amount of gas. Temperature must be in kelvin. It lets you follow a gas as pressure, volume and temperature all change at once.
How do I solve for the final volume?
Rearrange to V2 = P1 × V1 × T2 ÷ (T1 × P2). A gas at 1 atm, 10 L and 273.15 K compressed to 2 atm and heated to 400 K gives V2 = 1 × 10 × 400 ÷ (273.15 × 2) = 7.322 L.
Do the pressure and volume units matter?
Only that each pair uses the same unit on both sides, because the units cancel in the ratio. Temperature is different: it must be absolute, so 20 °C is 293.15 K. This calculator converts for you.
When can I not use the combined gas law?
It assumes a fixed amount of gas, so it fails if gas leaks, reacts or is added. It also assumes ideal behaviour, which is a good approximation at low pressure and high temperature but not near condensation.
What is the difference between this and the ideal gas law?
The ideal gas law PV = nRT needs the amount of gas n. The combined gas law compares two states of the same gas, so n and R cancel. The calculator still reports the implied n, for example 0.9994 mol for 101325 Pa, 22.4 L and 273.15 K.