Combined Gas Law Calculator
The combined gas law ties together how a fixed amount of gas changes pressure, volume, and temperature between two states. Pick the unknown, enter the other five values in whatever units you like, and this calculator converts everything to SI, solves, and converts the answer back, showing every step.
Formula
Worked example
A 2 L gas at 1 atm and 25 °C (298.15 K) is compressed to 2 atm at 25 °C: V₂ = (1 × 2 × 298.15) ÷ (298.15 × 2) = 1 L. Pressure doubled, so volume halved.
What the combined gas law describes
The combined gas law merges Boyle’s law (pressure and volume), Charles’s law (volume and temperature), and Gay-Lussac’s law (pressure and temperature) into one relationship for a sealed, fixed amount of gas. It states that the quantity PV/T stays constant as the gas moves between any two states, so P₁V₁/T₁ must equal P₂V₂/T₂. Because the amount of gas never changes, you do not need to know the number of moles or the gas constant, only the before-and-after values of pressure, volume, and temperature.
Mixing units freely
This calculator lets every input carry its own unit. Pressure can be atmospheres, pascals, kilopascals, bar, millibar, millimetres of mercury, or psi. Volume can be litres, cubic metres, millilitres, cubic feet, cubic inches, or gallons. Temperature can be Celsius, Fahrenheit, or kelvin. Behind the scenes each value is converted to SI base units (pascals, cubic metres, kelvin), the algebra is performed there, and the answer is converted back into the unit of the matching known value so it reads naturally. That means you can enter P₁ in psi and P₂ in bar and still get a correct result, something most textbook calculators cannot do because they force a single fixed unit per quantity.
Why temperature must be absolute
Pressure and volume are absolute scales that start at zero, but the Celsius and Fahrenheit scales do not, so they cannot be used directly in a ratio. Doubling from 10 °C to 20 °C is not a doubling of thermal energy, whereas doubling from 283 K to 566 K genuinely is. This calculator therefore converts every Celsius or Fahrenheit temperature you enter into kelvin, performs the algebra in kelvin, and converts the answer back. Forgetting this conversion is the single most common mistake students make with the gas laws.
Reading the ratios and the constant
Alongside the solved value, the calculator reports the pressure, volume, and temperature ratios between the two states and the value of PV/T in SI joules per kelvin. The ratios make the physics intuitive: if you compress a gas so the volume ratio is 0.5 at constant temperature, you should see the pressure ratio land near 2.0, which is Boyle’s law in action. The PV/T constant is identical for both states by construction, so it is a quick sanity check that your five inputs describe one consistent gas process rather than two unrelated snapshots.
The gas laws that combine into one
| Law | Held constant | Relationship |
|---|---|---|
| Boyle’s law | Temperature | P₁V₁ = P₂V₂ |
| Charles’s law | Pressure | V₁/T₁ = V₂/T₂ |
| Gay-Lussac’s law | Volume | P₁/T₁ = P₂/T₂ |
| Combined gas law | Amount of gas | P₁V₁/T₁ = P₂V₂/T₂ |
Each named law is a special case where one quantity is held constant.
Frequently asked questions
Do I need the gas constant R or the number of moles?
No. The combined gas law applies to a fixed, sealed amount of gas, so the moles and the gas constant are identical on both sides and cancel out. You only supply the before-and-after pressure, volume, and temperature. If the amount of gas changes, use the ideal gas law PV = nRT instead.
Can I mix units, for example psi for one pressure and bar for the other?
Yes. Each input has its own unit selector. The calculator converts every value to SI base units (pascals, cubic metres, kelvin) before solving, so you can enter P₁ in psi and P₂ in bar, or V₁ in litres and V₂ in cubic feet, and still get a correct answer. The result is returned in the unit of the matching known value.
Why does the calculator convert temperatures to kelvin?
Gas-law ratios are only valid on an absolute scale that starts at zero. Celsius and Fahrenheit do not, so the tool converts your temperature to kelvin, runs the math, and converts any temperature answer back to the unit you chose. This gives correct physics without you doing the conversion by hand.
What do the pressure, volume, and temperature ratios tell me?
They show how each quantity scaled between the two states. Because PV/T is constant, the three ratios are linked: the pressure ratio times the volume ratio equals the temperature ratio. If they do not, one of your five inputs is inconsistent with the others.