Ideal Gas Law Calculator
PV = nRT with any three in hand: blank the box you do not know and the equation hands it back — R derived from exact constants, both STPs named.
Ideal Gas Law Calculator
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What this result does not account for
- Dilute-gas idealisation — no van der Waals terms
- One blank per solve; P in atm, V in L, T in K
In short: One mole at 273.15 K under 1 atm: V = nRT/P = 22.413970 L — the molar volume a generation of textbooks rounded to 22.4. The R behind it is no longer measured: R = kₘ·N_A = 1.380649e-23 × 6.02214076e23 = 8.314463 J/(mol·K), exact since the SI fixed both constants. At the current IUPAC STP of 100 kPa the same mole fills 22.710955 L — name your convention before you invoice it.
Formula
PV = nRT · R = kₘ·N_A = 8.314463 J/(mol·K) exact · V(1 atm, 273.15 K) = 22.413970 L per mol
The ideal gas law is the state equation for a gas of point particles: pressure times volume counts the mole-seconds of thermal motion, and any fourth quantity falls to a division once three are known. It is exact for the model, approximate for real gases — best when dilute, worst near condensation, silent below the boiling point it cannot see.
Worked Example
- Fill any three of P, V, n, T.
- Leave exactly one blank — the one to solve.
- Read the missing quantity.
- Read the STP card and name your convention.
Defaults: 1 atm, blank V, 1 mol, 273.15 K → 22.413970 L. Balloon card: double the Kelvin, double the volume (44.827939 L at 546.3 K).
Strengths & Limits Of This Model
Where this engine is strong
- Any fourth quantity from any three
- R derived from exact constants, both STPs named
Where it stops
- No real-gas corrections
- No vapour-pressure helper
Practical Use Cases
Gas collectors
moles from a captured volume
Reaction heads
headspace pressure checks
Teaching
the state equation, one blank at a time
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.
Ideal Gas Law Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why is R exact now, of all constants?
Because the current SI fixed BOTH of R’s parents: the Boltzmann constant kₘ and the Avogadro constant N_A are now defined numbers, and R is simply their product. A generation of careful measurement went into choosing those pins; since then R carries no uncertainty bar at all — 8.314463 J/(mol·K), full stop.
Why do 22.414 and 22.711 both get called molar volume?
Because STP changed: the old standard was 1 atm (101.325 kPa) and gives 22.414 L; the current IUPAC convention is 100 kPa and gives 22.711 L — about 1.3% apart. Textbooks and gas bills disagree because they picked different decades. The card prints both; commerce requires you to name yours.
Why must temperature be in Kelvin?
Because the law relates volume to ABSOLUTE thermal motion, and Celsius zero is just where water melts — not where motion stops. A −273.15 in the box would demand negative volume. Kelvin starts at the true floor; the gas-law pages refuse anything below it on principle.
When does the ideal model actually break?
When the point-particle assumption fails: high pressure (molecules crowd and feel each other), low temperature near condensation (attractions win), and anywhere near the gas’s boiling point. The corrections have names (van der Waals among them); this page prices the honest dilute limit and says so.
How do I get moles from a gas I captured over water?
Correct the pressure first — the collected gas is saturated with water vapour, so subtract the vapour pressure at the bath temperature from the total. Then P, V and T feed this page directly and n falls out. Forgetting the water correction is the classic first-lab error.
What does blanking a box mean physically?
That the state has one degree of freedom left: three coordinates fix the point, the fourth follows. Filling all four over-determines the state — if the numbers disagree, one of them is wrong, which is a useful experiment in itself but not this page’s arithmetic.
Where does the mole count come from for a reacting gas?
From the stoichiometry page — the balanced equation’s coefficients count moles directly, so gas volumes at shared P and T obey the same ratios. Avogadro’s original law is this equation wearing its historical hat.
How does gas density connect here?
Divide the solved state by the molar mass: density is PM/RT, which is the gas-density page’s entire world. Same equation, one multiplication further — this page counts moles, that one weighs them.