AFR ↔ Lambda Calculator

AFR, lambda and stoichiometric mixture

Lambda is simply the ratio of the actual air-fuel mix to the ideal (stoichiometric) one for that fuel:

λ = AFR ÷ stoichiometric AFR  ·  AFR = λ × stoichiometric AFR

Stoich AFR is 14.7 for petrol, ~9.8 for E85, 9.0 for ethanol, 6.4 for methanol and 14.5 for diesel. λ < 1 is rich (more fuel, cooler, more power up to a point); λ > 1 is lean (less fuel, more economy, but more heat under load). Because λ normalises for fuel, wideband tuners increasingly target lambda directly.

Typical lambda targets

Idle & cruise (closed loop): λ 1.00 · Lean cruise: λ 1.02–1.05 · NA wide-open throttle: λ 0.86–0.90 · Boosted WOT: λ 0.75–0.82. These are starting points — knock, EGT and the specific engine decide the final number.

AFR to lambda chart

Both directions and every fuel. Generated by running the calculator above, so a row here cannot disagree with the tool.

Lambda to AFR chart (petrol)

For petrol at 14.7:1 stoichiometric. Reading it backwards works just as well — find your AFR in the middle column to get lambda.

Stoichiometric AFR by fuel

The same lambda means the same mixture strength on every fuel — only the AFR number moves. That is the entire argument for tuning in lambda.

The same AFR is a different mixture on every fuel

This is the trap the whole page exists to prevent. An AFR of 12.5:1 on petrol is λ 0.850 — a healthy wide-open-throttle mixture. Type the same 12.5 with E85 selected and it is λ 1.28, which is dangerously lean under load. Nothing about the number changed; the fuel did.

It runs the other way too. A tuner used to seeing 12.5 at full throttle will look at an E85 map showing 8.3 and assume something is badly wrong, when 8.3 on E85 is the same λ 0.85 mixture. Lambda removes the ambiguity entirely: λ 0.85 is 15% richer than stoichiometric on every fuel there is, and it is the only number you can carry from one map to the next without recalculating anything.

If you run a flex-fuel setup where the ethanol content moves with every tank, this stops being a preference and becomes the only workable option — the stoichiometric point is moving under you, so an AFR target is a moving target and a lambda target is not.

Diesel does not play by these rules

Petrol engines throttle the air and match fuel to it, so they live in a narrow band around λ 1. A diesel does the opposite — it takes in all the air it can and meters only fuel, so it is lean essentially everywhere. Idle can sit above λ 6; full load rarely goes richer than about λ 1.2, and anything approaching λ 1 is where the smoke starts.

That is why a diesel AFR figure looks alarming to a petrol tuner. An AFR of 32:1 on diesel is λ 2.21 — completely normal at part load, not a fault. It also means AFR is close to useless as a diesel tuning target on its own: what actually constrains a diesel is exhaust gas temperature, smoke and turbo speed, with lambda as the sanity check rather than the goal.

Reading a wideband, and what a narrowband cannot tell you

Only a wideband sensor gives a number you can tune to. It reports across roughly λ 0.7 to λ 1.3 or wider, and its controller converts that into a linear analogue output — commonly 0–5 V across a stated range, which varies by controller. Always read the mapping from your controller's documentation; there is no universal voltage-to-lambda scale.

A narrowband sensor is a different instrument doing a different job. It is a switch, not a gauge: it sits near 450 mV at stoichiometric and swings hard either side, so it can tell the ECU "richer than stoich" or "leaner than stoich" and essentially nothing else. A reading of 780 mV on a narrowband means rich — and that is genuinely all it means, because the sensor's output saturates and cannot distinguish λ 0.95 from λ 0.80. Tuning wide-open throttle off a narrowband is guessing with extra steps.

FAQ