Combined gas law calculator
Pick the law, choose what to find and enter the gas's first state and what you know of its second. Temperatures are converted to kelvin for the calculation, so you can type them in °C or °F. Pressure and volume can be in any unit, as long as both states use the same one.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Pick the law. Use the combined law when pressure, volume and temperature all change; choose Boyle’s, Charles’s or Gay-Lussac’s law when one of them stays constant.
- Choose what to find: P₂, V₂ or T₂.
- Enter the first state and the known values of the second, and pick the units.
- Combined: P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂, so V₂ = P₁V₁T₂ ÷ (T₁P₂), P₂ = P₁V₁T₂ ÷ (T₁V₂), T₂ = T₁P₂V₂ ÷ (P₁V₁).
- Boyle: P₁V₁ = P₂V₂. Charles: V₁ ÷ T₁ = V₂ ÷ T₂. Gay-Lussac: P₁ ÷ T₁ = P₂ ÷ T₂.
- T in kelvin: K = °C + 273.15.
Worked example
10 L of gas at 1 atm and 25 °C is compressed to 2 atm and heated to 100 °C. V₂ = 1 × 10 × 373.15 ÷ (298.15 × 2) = 6.2578 L, a change factor of 0.6258.
Charles’s law: the same 10 L warmed from 25 °C to 100 °C at constant pressure grows to 10 × 373.15 ÷ 298.15 = 12.5155 L.
Tips and common mistakes
- Same amount of gas. If gas leaks out or is added, use the ideal gas law with moles instead.
- Gauge pressure is not absolute. A tyre gauge reads pressure above the atmosphere; add about 1 atm (101.3 kPa, 14.7 psi) before using these laws.
- Real gases deviate at high pressures and near condensation.
Frequently asked questions
What is the combined gas law?
For a fixed amount of gas, P × V ÷ T stays the same, so P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂ with T in kelvin. It combines Boyle's, Charles's and Gay-Lussac's laws and follows from the ideal gas law PV = nRT with n constant.
What do Boyle's, Charles's and Gay-Lussac's laws say?
Boyle: at constant temperature P₁V₁ = P₂V₂, so squeezing a gas to half its volume doubles its pressure. Charles: at constant pressure V₁ ÷ T₁ = V₂ ÷ T₂, a gas expands as it warms. Gay-Lussac: at constant volume P₁ ÷ T₁ = P₂ ÷ T₂, a sealed can's pressure rises with temperature.
Why must the temperature be in kelvin?
The laws are proportions, and only the absolute scale starts at zero. Warming from 10 °C to 20 °C does not double the volume; in kelvin it is 283.15 K to 293.15 K, a 3.5 % rise. The calculator converts °C and °F for you.
Does the unit of pressure or volume matter?
No, as long as both states use the same unit, because the units cancel in the ratio. The answer comes out in the unit you chose.