A tool to calculate the amount of air "just sufficient" to fully burn a hydrocarbon fuel CxHyOz. Change the carbon and hydrogen counts and the equivalence ratio phi to see the molar and mass air-fuel ratios, excess air and a rich/lean verdict update in real time.
Parameters
Carbon atoms x
Number of carbon atoms per fuel molecule (1 for CH₄, 8 for C₈H₁₈)
Hydrogen atoms y
Number of hydrogen atoms per fuel molecule (4 for CH₄, 18 for C₈H₁₈)
Oxygen atoms z in fuel
0 for plain hydrocarbons, 1 for methanol CH₃OH, 1 for ethanol
Fuel (orange) flows in from the left and air (blue) flows in from the top, mixing and burning in the chamber. The number of air and fuel particles is scaled to the actual A/F ratio; the bottom gauge places the stoichiometric line (φ=1) at the centre with rich and lean to each side.
Stoichiometric A/F (mass) vs carbon number x (CH₂ family)
Air is 21% O₂ + 79% N₂ by mole, so each mole of O₂ corresponds to 4.76 moles of air. The mass basis uses the mean molar mass of air (28.97 g/mol) and the fuel molar mass Mf.
The equivalence ratio φ is the inverse ratio of "actual A/F" to "stoichiometric A/F". φ=1 is stoichiometric, φ>1 is rich (fuel excess) and φ<1 is lean (air excess).
What is the stoichiometric air-fuel ratio?
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I often see "air-fuel ratio 14.7" in car books. What is that a ratio of, exactly? I get that it's air over fuel, but why such an odd number as 14.7?
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Good question. It means "14.7 kg of air + 1 kg of fuel" is exactly what you need to burn gasoline completely. We call that the stoichiometric, or theoretical, air-fuel ratio. The reason it's 14.7 is that burning one mole of gasoline (roughly C₈H₁₈, molar mass about 114) needs 12.5 moles of O₂, which means about 59.5 moles of air (4.76 × O₂). Convert that back into mass and you get 14.7. Plug CH₄ (methane) into the panel on the left and you'll see about 17.2 — that is the theoretical A/F for natural gas.
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I see! And what about "phi" — I see that too. How is it different from the A/F ratio? When I move the slider it labels things "rich" or "lean"...
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Phi is the equivalence ratio — a dimensionless number that tells you how many times richer the actual fuel/air ratio is than the stoichiometric one. φ=1 is exactly stoichiometric, φ=1.2 means "20% more fuel than stoichiometric (rich)" and φ=0.8 means "20% less fuel (lean)". The absolute A/F values are completely different for gasoline and natural gas, but phi gives you a single ruler that says "how far from stoichiometric" regardless of the fuel. Racers run φ ≈ 1.15 (rich), boiler people run φ ≈ 0.9 (lean) — they use phi every day.
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If rich gives more power and lean gives better fuel economy, you'd think you'd pick one — but I heard regular cars hold phi=1 strictly. Why not run rich for power?
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It's the three-way catalyst. That catalytic converter in your exhaust is the only device that can oxidise CO and HC while simultaneously reducing NOx — and the window where both reactions balance is a very narrow band around φ=1 (about ±1%). Go rich and unburned HC and CO leak through; go lean and NOx survives. So an O₂ sensor reads exhaust oxygen and the ECU trims the injector pulse width every few milliseconds, dithering around an average phi of 1. That is the heart of engine control. Diesels handle NOx with a different catalyst (SCR), so they're free to run lean all day.
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I also heard boilers run "slightly lean". Why not exactly phi=1?
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Because mixing isn't perfect. Inside the burner flame, combustion starts before air and fuel are fully blended at the molecular level. Any locally air-starved pocket spits out unburned CO and soot. To avoid that, industrial boilers routinely run with 10–20% more air than theory says — what we call "10–20% excess air", or φ ≈ 0.83–0.91. Too much and the flue gas just carries heat away, so the modern standard is an O₂ sensor in the flue trimming the air supply automatically. The same logic applies to your home water heater — it runs slightly lean too.
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Hydrogen engines are in the news. The theoretical A/F for hydrogen is 34.3 — what does that even mean?
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Hydrogen has a molar mass of only 2, so on a mass basis it looks like "a tiny bit of fuel needs a huge mass of air". It really does take 34.3 kg of air to burn 1 kg of H₂. On a molar basis though, H₂ + 0.5 O₂ → H₂O — only 0.5 mol of O₂ and 2.38 mol of air per mole of fuel. The large mass number is just the "hydrogen is too light" problem. In practice hydrogen engines run very lean, around φ ≈ 0.3–0.5. The trick is that hydrogen burns very fast and is stable even when lean, so you can engineer combustion that simply doesn't produce NOx in the first place. This is the cutting edge of combustion engineering in the decarbonisation era.
Frequently Asked Questions
The stoichiometric air-fuel ratio (theoretical AFR) is the amount of air just sufficient to burn a fuel completely, divided by the amount of fuel. When a hydrocarbon fuel CxHyOz burns completely, every carbon ends up as CO2 and every hydrogen as H2O. The moles of O2 needed are x + y/4 − z/2, and since air is about 21% O2 and 79% N2 by mole, the moles of air are 4.76 times that. On a mass basis we convert with the mean molar mass of air (28.97 g/mol) and the fuel molar mass. Representative values are about 14.7 for gasoline, 17.2 for methane, 14.5 for diesel and 34.3 for hydrogen.
The equivalence ratio phi is a dimensionless number defined as the actual fuel/air ratio divided by the stoichiometric fuel/air ratio. phi = 1 is exactly stoichiometric, phi > 1 is fuel-rich (air-deficient) and phi < 1 is lean (excess air). Spark-ignition engines are tightly controlled to phi = 1 to stay inside the three-way-catalyst window. Racing engines run rich at phi ≈ 1.1–1.2 for peak power, diesels run lean at phi ≈ 0.2–0.7, and industrial boilers run slightly lean at phi ≈ 0.85–0.9.
Excess air is calculated as (1/phi − 1) × 100 [%]. So phi = 1 gives 0% (exactly stoichiometric), phi = 0.8 gives 25% excess air, and phi = 1.25 gives −20% (i.e. air-deficient). Industrial boilers and furnaces normally operate with 10–20% excess air to guarantee complete combustion. Too much excess air carries heat away with the flue gas and lowers efficiency; too little produces unburned CO and soot. Plants typically use an O2 sensor in the flue gas to trim the air supply in real time.
Spark-ignition (gasoline) engines hold phi = 1 not for power or fuel economy but because the three-way catalyst can only oxidise CO/HC and reduce NOx simultaneously inside a very narrow window around stoichiometric (phi ≈ 0.99–1.01). The exhaust-pipe O2 (lambda) sensor reads the oxygen level and the engine ECU corrects the injector pulse width every few milliseconds, dithering phi around an average of 1. Diesels use a different aftertreatment (DPF + SCR) so they are not bound to phi = 1 and instead control power through the fuel quantity in the lean region phi < 1.
Real-World Applications
Gasoline engines (spark ignition): Hold phi = 1 strictly to keep the three-way catalyst inside its operating window. An O₂ sensor trims the mixture continuously, and the ECU widens or narrows the injector pulse by a few milliseconds to keep the average AFR at 14.7. Only during cold start is the mixture temporarily enriched (φ ≈ 1.2–1.4) to stabilise combustion until the catalyst reaches its light-off temperature, and full-throttle acceleration is sometimes allowed to dip into the power-peak region (φ ≈ 1.1) for a few seconds.
Diesel engines: Because they are compression-ignition and control power through fuel quantity (not air throttling), diesels run lean all the time at φ ≈ 0.2–0.7. The stoichiometric AFR is about 14.5, but real operation sits between A/F = 20 and 70. Lean operation produces NOx easily, so a DPF (diesel particulate filter) + urea SCR (selective catalytic reduction) combination is used. Three-way catalysts simply don't work this far on the lean side.
Industrial boilers and furnaces: Operate with 10–20% excess air (φ ≈ 0.83–0.91) to account for imperfect mixing. The flue-gas O₂ concentration is measured and the fuel/air valves are feedback-controlled to keep O₂ at 2–4%. Too much excess air dumps heat out the stack and hurts efficiency, so the O₂ sensor and O₂ trim control are the keys to fuel savings. Modern gas burners can now reach low-excess-air combustion with O₂ as low as 1%.
Hydrogen and ammonia combustion: Hydrogen (A/F ≈ 34.3) and ammonia (A/F ≈ 6.05) are being studied as decarbonised fuels. Hydrogen has a fast burning velocity and stays stable when very lean, so the mainstream strategy is to run extremely lean (φ ≈ 0.3–0.5) to suppress NOx formation. Ammonia is the opposite — slow to burn and hard to ignite — so two-stage combustion is being studied, where the burner is first stabilised slightly rich (φ ≈ 1.05) and the mixture is then diluted.
Common Misconceptions and Pitfalls
The biggest pitfall is to assume "stoichiometric AFR = peak-power AFR". In fact peak power occurs in the slightly rich region around φ ≈ 1.1–1.2, where output is a few percent higher than at stoichiometric. The reason is that adding "just a little extra" fuel eliminates the locally air-starved pockets in the combustion chamber, so the average flame temperature and burning velocity are higher. Peak fuel economy, by contrast, lies in the slightly lean region around φ ≈ 0.9. It is critical to recognise that "φ = 1 is not the optimum for power or economy — it is the optimum for emissions control".
The next pitfall is to think "more excess air = more complete combustion". Extreme air shortage certainly produces CO and soot, but too much excess air causes its own problems: (1) heat loss in the flue gas rises and thermal efficiency drops, (2) the flame temperature falls and combustion becomes unstable, increasing CO again, and (3) the surplus N₂ and O₂ react at high temperature and NOx rises sharply. The optimum is a narrow band around φ ≈ 0.85–0.95; either side, emissions get worse. The "10–20% excess air" rule of thumb is just a practical way to stay near that optimum.
Finally, do not over-simplify by assuming "once you know the fuel composition the theoretical A/F is fixed". This tool assumes an idealised fuel CxHyOz that burns completely. Real fuels are mixtures — gasoline alone is a blend of hydrocarbons from C₄ to C₁₂ whose composition shifts with season and octane grade. Add nitrogen-, sulphur- or oxygen-containing additives, E10/E85 oxygenates, or LPG (propane + butane mixtures), and the actual A/F drifts a few percent from the textbook value. The iron rule for real engines is to use this tool's calculation as the "starting point of the design" and then drive the actual value with closed-loop O₂-sensor feedback.
How to Use
Enter hydrocarbon formula by specifying carbon atoms (0-20), hydrogen atoms (0-50), and oxygen atoms (0-10) in the fuel molecule
Set equivalence ratio (φ): use 1.0 for stoichiometric combustion, <1.0 for lean mixture, >1.0 for rich mixture
Click Calculate to obtain molar O₂ requirement, stoichiometric A/F ratios (molar and mass basis), actual A/F ratio, excess air percentage, and mixture classification (stoichiometric/lean/rich)
Worked Example
For gasoline approximated as C₈H₁₈: carbon=8, hydrogen=18, oxygen=0, equivalence ratio=1.0. Combustion equation requires 12.5 mol O₂ per mol fuel. Stoichiometric A/F (molar)=59.5 mol air/mol fuel; stoichiometric A/F (mass)=15.1 kg air/kg fuel. At φ=0.95 (5% lean), actual A/F becomes 15.9 kg air/kg fuel with 5.3% excess air, producing a lean-burn condition typical of modern spark-ignition engines.
Practical Notes
Diesel (C₁₂H₂₃) requires ~14.8 kg air/kg fuel stoichiometrically; real engines operate at φ=0.85–0.95 for emission control
Natural gas (CH₄) needs 17.2 kg air/kg fuel; industrial furnaces often run φ=1.05–1.10 (fuel-rich) to prevent incomplete combustion and CO emissions
Oxygenated fuels like ethanol (C₂H₆O) reduce O₂ demand by ~7%; verify nitrogen content separately as N₂ comprises 79% of intake air but does not participate in stoichiometric balance