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Air fuel ratio calculator

Pick a fuel and enter a lambda or an air fuel ratio. See the other one, the same lambda for every fuel, a table from lambda 0.70 to 1.20, and what a gasoline-scale gauge reading means on your fuel.

Fuel and value

Fuel

I have

Value

Enter a value above zero.

Lambda 1 is the chemically correct mixture for any fuel. Below 1 is richer, above 1 is leaner. This tool converts numbers only and does not suggest a mixture to run: that is a job for your tuner.

Lambda to AFR table

AFR on a gasoline-scale gauge

Gauge reading

AFR

The AFR number your wideband gauge shows. Enter a value above zero.

Many wideband gauges show AFR as lambda × 14.7 whatever fuel you run. If yours is set to a different fuel, divide by that fuel's stoich instead. The gauge manual tells you which scale it uses.

Lambda and AFR

The air fuel ratio (AFR) is the mass of air divided by the mass of fuel. Every fuel has a stoichiometric ratio: the AFR at which all the fuel can burn with all the oxygen. Lambda compares your AFR with that point:

λ = AFR ÷ stoichiometric AFRAFR = λ × stoichiometric AFR

Lambda 1 is stoichiometric on any fuel, below 1 is rich and above 1 is lean. Because it does not depend on the fuel, tuners work in lambda. An AFR of 12.5 means one thing on gasoline and something very different on E85, while λ 0.85 means the same mixture strength on both.

Stoichiometric ratios used

Gasoline 14.7: the conventional value. Real pump gasoline varies, and oxygenated blends are lower.
Ethanol 9.0, methanol 6.47 and propane 15.7: worked out from the combustion equation of each fuel, with oxygen at 23.14% of air by mass.
Custom: enter any stoichiometric ratio.

Ethanol blends such as E85

Ethanol blends are sold by volume, but AFR is by mass. The tool first turns the ethanol volume share into a mass share with the densities (ethanol 0.789 g/ml at 20 °C, gasoline 0.74 g/ml as an assumption you can change), then weights the two stoichiometric ratios by mass:

w = e × 0.789 ÷ (e × 0.789 + (1 − e) × 0.74)blend AFR = w × 9.0 + (1 − w) × 14.7

Worked example

E85 at a true 85% ethanol by volume: w = 0.85 × 0.789 ÷ (0.85 × 0.789 + 0.15 × 0.74) = 0.6707 ÷ 0.7817 = 0.858. Blend AFR = 0.858 × 9.0 + 0.142 × 14.7 = 9.81.

At λ 0.80 that fuel runs at 0.80 × 9.81 = 7.85 AFR. The same λ 0.80 is 11.76 on gasoline and 7.20 on pure ethanol.

Gasoline-scale gauges

Many wideband gauges display AFR as λ × 14.7 no matter which fuel is in the tank. A reading of 11.76 on such a gauge is λ 11.76 ÷ 14.7 = 0.80, which on E85 is the 7.85 AFR above. Convert the reading to lambda first, then to your fuel's AFR, or just work in lambda.

If you are switching fuels, the E85 mix calculator works out the blend, the octane mix calculator estimates mixed octane, and the fuel injector size calculator and fuel pump size calculator cover the extra fuel flow. For boosted engines, see the boost calculator.

Questions

How do I convert lambda to AFR?

Multiply lambda by the stoichiometric ratio of the fuel. On gasoline (14.7), λ 0.80 is 11.76 and λ 0.90 is 13.23. On E85 at a true 85% ethanol (9.81), λ 0.80 is 7.85.

What is the stoichiometric AFR of E85?

About 9.81 if it really holds 85% ethanol by volume, using mass weighting with ethanol at 0.789 g/ml and gasoline at 0.74 g/ml. At 70% ethanol it is about 10.63, so the real ethanol content matters.

Why do tuners use lambda instead of AFR?

Lambda is fuel independent. λ 1 is stoichiometric on gasoline, ethanol, methanol or propane alike, so one target number works when the fuel changes, while the AFR for the same mixture changes with the fuel.

My gauge reads 11.76 but I run E85. What does that mean?

If the gauge shows gasoline-scale AFR (λ × 14.7), 11.76 is λ 0.80. On E85 at 85% ethanol that is an AFR of 7.85. Check the gauge manual to confirm which scale it uses.