Air Fuel Ratio Calculator

How air-fuel ratio and lambda work

The air-fuel ratio (AFR) is the weight of air an engine takes in divided by the weight of fuel burned with it. Every fuel has one ratio at which there is exactly enough oxygen to burn all of it: the stoichiometric ratio. It is about 14.7 for gasoline, 9.0 for ethanol and 6.47 for methanol, because alcohols already carry oxygen in the molecule. Less air than that is a rich mixture, more is lean.

Lambda (λ) takes the fuel out of the picture. It is the actual AFR divided by the stoichiometric AFR of that fuel, so λ = 1 is stoichiometric whatever is in the tank, below 1 is rich and above 1 is lean. An AFR of 12.5 on gasoline is λ 0.850, meaning about 15% less air than complete combustion needs; λ 0.80 is the same strength of mixture on gasoline, E85 or methanol. Engine researchers also use the equivalence ratio φ, which is simply the inverse of lambda: above 1 is rich. As a lambda calculator and an AFR calculator in one, the tool gives all three.

Wideband oxygen sensors measure lambda, not AFR. A gauge that displays AFR multiplies that lambda by a stoichiometric ratio stored in the gauge, normally gasoline’s. On any other fuel the number on the gauge is a gasoline-scale AFR: still a correct lambda in disguise, but not the real ratio of what you burn. The Gauge reading tab converts it.

What to enter and where to find it

• AFR or lambda. A figure from the engine’s documentation or your engine builder, or a reading from a wideband sensor.
• Fuel. E10, gasoline with up to 10% ethanol, is the usual US pump fuel. For E85 or any flex blend choose the ethanol blend option and enter the ethanol content.
• Ethanol content. Fuel sold as E85 ranges from 51% to 83% ethanol with the season and the region. The calculator starts at 77%, the average a national survey of pump E85 measured outside the winter months, but a test kit or a flex-fuel sensor reading beats both that figure and the name on the pump. The e85 calculator works out the content of a mix.
• Gauge stoichiometric ratio. The ratio your gauge uses to turn lambda into AFR, normally 14.7. Some gauges let you change it; if yours is set to the fuel you burn, its reading is already the real AFR.

Air-fuel ratio and lambda formulas

Four definitions and the blend rule. None of them is empirical: the only uncertainty is in the stoichiometric ratios, which vary slightly with the exact composition of the fuel.

1. λ = AFR ÷ stoichiometric AFR of the fuel
2. AFR = λ × stoichiometric AFR of the fuel
3. φ = 1 ÷ λ
4. Real AFR = gauge reading ÷ gauge’s stoichiometric ratio × stoichiometric AFR of the fuel
5. Blend stoichiometric AFR = w × 9.0 + (1 − w) × 14.7, where w = V × 0.789 ÷ (V × 0.789 + (1 − V) × 0.74) and V is the ethanol fraction by volume

The blend rule works because the air each component needs simply adds up by weight. Ethanol content is quoted by volume, as pumps and test kits give it, so it is first converted to a weight fraction w with the densities of ethanol and gasoline. That is why E85 at 83% ethanol has a stoichiometric ratio of 9.92, and at 51% one of 11.70: two fuels sold under the same name that need noticeably different amounts of air.

Gasoline’s own figure is a round number for a fuel that is really a blend of many hydrocarbons; published values differ in the first decimal. The value used here is the one wideband gauges and engine calibration software use, so the gauge conversion matches what you see on the dash.

Typical lambda for power and for economy

For gasoline engines, engine-management references put maximum power at a slightly rich mixture, around λ 0.85 to 0.95, and the lowest fuel consumption at a slightly lean one, around λ 1.1 to 1.2. On gasoline that is about 12.5 to 14.0 and 16.2 to 17.6 AFR. Both bands are shaded on the scale under the calculator.

Engines with a three-way catalytic converter hold λ = 1 nearly all the time, because the converter can only clean up all three main pollutants in a narrow window around stoichiometric. Turbocharged and supercharged engines are commonly run richer than the maximum-power band at full boost to hold combustion and exhaust temperatures down.

These are typical figures from published references, shown for orientation. They are not targets for any particular engine: the right mixture depends on the engine, the fuel, its octane and the load, and is decided by whoever calibrates the engine.

Reading a gasoline-scale gauge on E85 or methanol

Because a wideband sensor measures lambda, a gasoline-scale reading is easy to translate: divide it by the gauge’s stoichiometric ratio to get lambda, then multiply by the stoichiometric ratio of your fuel. In the example below, a reading of 11.5 with E70 in the tank is λ 0.782, a real air-fuel ratio of 8.32.

The practical lesson is that lambda is the number to compare between fuels. A mixture that reads the same lambda is equally rich on gasoline and on E85, while the real AFRs are miles apart. That is why lambda is the usual unit whenever more than one fuel is involved, and why the table under the calculator lists the same mixture on every fuel.

Worked example

Three typical conversions, worked out with the same functions that run the calculator.

Stoichiometric ratio by fuel

The stoichiometric ratios below are by weight. Single fuels come from engine reference data; the E10 and E85 rows are computed from their ethanol content with the blend rule above, for both ends of the E85 range and for the 77% pump average. The last column is how much more fuel each needs than gasoline at the same lambda, the factor that drives injector and pump sizing for spark-ignition engines.

Diesel engines are a special case: they run lean overall at every load, with power set by the amount of fuel injected rather than by the air, so their overall AFR is usually well above stoichiometric. A same-lambda comparison with gasoline means nothing for them, which is why the table leaves that cell blank. Propane’s figure is for the pure gas; LPG sold as a propane and butane mix differs slightly. For what the fuel factor means in injector and pump size, see the fuel injector calculator and the fuel pump calculator.

Common mistakes

• Comparing AFRs across fuels. An AFR of 12.5 is λ 0.85 on gasoline but λ 1.22 on E85 at 77% ethanol, a lean mixture. Compare lambda instead.
• Forgetting what the gauge assumes. A gauge set to gasoline shows gasoline-scale numbers on every fuel. Check its stoichiometric setting before converting.
• Taking the name E85 literally. Pump E85 can be anywhere in its specified range, and its stoichiometric ratio moves from 11.70 to 9.92 with it.
• Mixing up lambda and equivalence ratio. Above one, λ means lean but φ means rich. They are inverses of each other.
• Expecting a narrowband sensor to give AFR. A conventional switching oxygen sensor only tells whether the mixture is rich or lean of stoichiometric. An AFR or lambda figure away from stoichiometric needs a wideband sensor.