Combined Gas Law Calculator
Solve the combined gas law P₁V₁/T₁ = P₂V₂/T₂ for any unknown. Enter five known values (pressure in Pa, volume in m³, temperature in K) to find the sixth.
How to use this tool
- Enter initial pressure p₁, initial volume v₁, initial temperature t₁, final pressure p₂, final volume v₂ and final temperature t₂ in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your final pressure p₂ and the full breakdown beneath it.
The combined gas law combines Boyle's and Charles's laws: P₁V₁/T₁ = P₂V₂/T₂. It describes how a fixed amount of gas changes when pressure, volume and temperature all vary. Always use Kelvin for temperature.
Formula
P1V1 ÷ T1 = P2V2 ÷ T2
Rearranged to solve for each unknown:
P2 = P1V1T2 ÷ (T1V2) | V2 = P1V1T2 ÷ (T1P2) | T2 = P2V2T1 ÷ (P1V1)
How it works
The combined gas law merges Boyle's Law (P ∝ 1/V at constant T), Charles's Law (V ∝ T at constant P), and Gay-Lussac's Law (P ∝ T at constant V) into one equation relating the initial and final states of a fixed amount of ideal gas. Enter five of the six variables (pressure in Pa, volume in m³, temperature in K) and set the unknown to zero to find it.
The law applies to ideal gases only; real gases deviate at high pressures and low temperatures. Temperatures must be in Kelvin (absolute scale) — using Celsius will produce incorrect results.
Worked example
Worked example — find final volume
- Initial state: P1 = 101,325 Pa, V1 = 0.001 m³, T1 = 273.15 K.
- Final state: P2 = 202,650 Pa (pressure doubled), T2 = 273.15 K (same temperature); V2 unknown.
- V2 = P1V1T2 ÷ (T1P2) = (101,325 × 0.001 × 273.15) ÷ (273.15 × 202,650).
- V2 = 101,325 ÷ 202,650 × 0.001 = 0.0005 m³.
Final volume V2 = 0.0005 m³ — doubling the pressure at constant temperature halves the volume (Boyle's Law).
Common mistakes to avoid
- Entering temperature in Celsius instead of Kelvin; the combined gas law requires absolute temperature, so 25 C must be entered as 298.15 K or the result will be grossly wrong.
- Assuming the combined gas law applies to real gases at high pressures or low temperatures; it is valid only for ideal gases far from condensation conditions.
- Forgetting that if one of the three variables is held constant, a simpler special-case law (Boyles, Charless, or Gay-Lussacs) applies and dividing by zero for the constant variable will produce an error.
Key terms
- Combined gas law
- An equation relating pressure, volume, and absolute temperature of a fixed amount of gas between two states: P1V1/T1 = P2V2/T2.
- Ideal gas
- A theoretical gas whose molecules occupy no volume and have no intermolecular forces; real gases approximate ideal behaviour at low pressure and high temperature.
- Kelvin (K)
- The absolute temperature scale; 0 K is absolute zero. Required by gas law equations because 0°C is not the absence of thermal energy.
- Boyle's Law
- At constant temperature, pressure and volume are inversely proportional: P1V1 = P2V2.
- Charles's Law
- At constant pressure, volume is directly proportional to absolute temperature: V1/T1 = V2/T2.
Frequently asked questions
- How is this different from the ideal gas law?
- The combined gas law relates two states of the same gas sample without needing to know the moles or R. The ideal gas law (PV=nRT) gives absolute values.
- What is Boyle's Law?
- Boyle's law is the special case where T is constant: P₁V₁ = P₂V₂.