Combined Gas Law Calculator
Pressure, volume and temperature all move at once — type five states of one gas sample and the sixth falls out of P₁V₁/T₁ = P₂V₂/T₂.
Combined Gas Law Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Fixed amount of gas — no leak between states
- Ideal behaviour; real gases drift near liquefaction
In short: A 30 L balloon leaves sea level at 1.000000 atm and 293.15 K and levels off where the pressure is 0.400000 atm and the cold is 250.15 K: the same sample now fills 63.998806 L. The lift doubled the room twice over — the pressure gave a 2.5 factor and the cold took a third of it back. Hold temperature instead and the same numbers reduce to Boyle’s squeeze: 30 L at 1 atm would need 75.000000 L at 0.4 atm.
Formula
P₁V₁/T₁ = P₂V₂/T₂ · solve any one of the six
Boyle, Charles and Gay-Lussac are the same ledger with one letter frozen; the combined law lets all three move at once between two states of a fixed sample. Amount is the unwritten constant — no gas leaks in or out between the two readings. Temperatures are Kelvin because the scale’s zero has to be the state where nothing moves.
Worked Example
- Type five of the six state boxes.
- Leave exactly one blank — the unknown.
- Check the Kelvin ledger: temperatures live on the absolute scale.
- Read the solved sixth box and the reduced law it implies.
Defaults: 1 atm, 30 L, 293.15 K → 0.4 atm, 250.15 K gives 63.998806 L. Drive the new volume to 64 instead and the new temperature solves to 250.154667 K.
Strengths & Limits Of This Model
Where this engine is strong
- Any one of six unknowns solved
- The reduced named law printed with your numbers
Where it stops
- No real-gas correction
- Kelvin only — no Celsius input
Practical Use Cases
Weather balloons
ascent bookkeeping
Compressed-gas transfer
cylinder to receiving tank
Teaching
the three named laws in one ledger
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Combined Gas Law Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why must the temperature be in Kelvin?
Because the law multiplies and divides by it. A Celsius zero is not a state where gas arithmetic stops — 0 °C is 273.15 K of molecular motion — so feeding the ledger a 20 where a 293.15 belongs corrupts every ratio. The guard refuses temperatures below 50 K and asks whether a Celsius number slipped in.
What if I fill all six boxes?
Then the law has nothing to solve: five states of one sample over-determine it. The page refuses rather than guess which box you meant to leave blank.
Can I use it for a leaking sample?
No — the ledger assumes the same amount of gas at both readings. A leak changes n, and the combined law does not carry n. Weigh the loss or switch to the ideal gas page, which solves for the count itself.
Which of the named laws hides inside a drive?
Freeze temperature and the ledger reduces to Boyle’s P₁V₁ = P₂V₂; freeze pressure and it is Charles’s V/T; freeze volume and it is Gay-Lussac’s P/T. The card prints the reduction with your own numbers so the connection is arithmetic, not decoration.
Why does a solved temperature below 50 K still print?
Because the arithmetic is honest even when the state is exotic — deep-cryogenic gases exist. The ledger prints the number and names the Celsius suspicion: a drive meant for room temperature reads 25 K only if 273.15 never got added.
Why does the card call 63.998806 the balloon answer?
Because the ledger multiplies three ratios: the pressure factor 1/0.4 gives 2.5, the temperature factor 250.15/293.15 gives back about 0.8533, and 30 L times 2.5 times 0.8533 lands at 63.998806. The card shows the same product from the ledger form P₁V₁T₂/(T₁P₂) so the arithmetic is one line, auditable at a glance.
What if the two states are identical?
Then every box agrees and the ledger is a mirror: solving any box returns the value already typed, and the reduced-law card prints the honest tautology. The page does not refuse a drive that goes nowhere — confirming that nothing changed is a real question when you suspect a leak or a bad gauge.
What breaks the law in the real world?
Liquefaction first: compress a gas near its boiling point and part of it condenses, dropping it out of the gas count. Then the idealisation of point particles itself. For air at room temperature and modest pressure the ledger holds to a percent or two.