Combined Gas Law
Find final pressure, volume, or temperature with the combined gas law. Includes algebra steps and consistent-unit guidance for gas-law problems. Free online calculator with formulas and step-by-step solutions.
Key formula
(P1V1)/T1 = (P2V2)/T2
How do you use the combined gas law?
For a fixed amount of gas, P₁V₁/T₁ = P₂V₂/T₂. Convert °C to K (add 273 or 273.15), keep P and V units consistent, then rearrange for the unknown: P₂ = P₁V₁T₂/(T₁V₂), V₂ = P₁V₁T₂/(T₁P₂), or T₂ = P₂V₂T₁/(P₁V₁).
About this tool
The combined gas law links two states of the same gas sample: P₁V₁/T₁ = P₂V₂/T₂. This page keeps the ratio visible so you can solve for final pressure, volume, or temperature without losing the Kelvin and unit checks that usually cost marks.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: find final pressure
A gas at 100 kPa, 2.0 L, and 300 K is heated to 360 K at 2.0 L (volume fixed). P₂ = (100)(2.0)(360) / ((300)(2.0)) = 120 kPa. Check: T rose by 20%, so P rose by 20%.
Example 2: convert °C first
Initial: 1.0 atm, 5.0 L, 27 °C. Final: 2.0 atm, T₂ = ? at 2.5 L. T₁ = 27 + 273 = 300 K. T₂ = (2.0)(2.5)(300) / ((1.0)(5.0)) = 300 K. Using 27 °C raw in the formula would be wrong.
Example 3: find final volume
P₁ = 200 kPa, V₁ = 3.0 L, T₁ = 250 K → P₂ = 100 kPa, T₂ = 250 K. V₂ = (200)(3.0)(250) / ((250)(100)) = 6.0 L. Halving pressure at fixed T doubles volume (Boyle’s law).
Frequently asked questions
What is the combined gas law formula?
P₁V₁/T₁ = P₂V₂/T₂ for a fixed amount of gas. It combines Boyle’s, Charles’s, and Gay-Lussac’s laws into one two-state relation. Temperatures must be absolute (kelvin).
Why must temperature be in kelvin?
Gas laws use absolute temperature. 0 °C is 273 K, not zero. Leaving Celsius in P₁V₁/T₁ = P₂V₂/T₂ breaks the ratio and often produces nonsense answers.
How do I convert °C to K for gas laws?
T(K) = T(°C) + 273 (many school papers) or + 273.15. Convert both T₁ and T₂ before substituting. Never mix °C on one side with K on the other.
When should I use the ideal gas law instead?
Use PV = nRT when moles (or mass via molar mass) change, or when you need an absolute state from P, V, n, and T rather than comparing two states of the same sample.
Do pressure and volume units have to be SI?
They must match across both states. kPa with litres is fine if both sides use the same pair. Mixing atm with kPa, or mL with L, without converting will skew the unknown.