AFR Calculator - Air-Fuel Ratio, Lambda and Equivalence Ratio
Enter the mass of air and fuel, or pick a fuel type to get the stoichiometric benchmark, and this calculator instantly gives you the air-fuel ratio (AFR), lambda (the normalized mixture ratio), equivalence ratio (phi), percent excess air, and a plain-English verdict on whether the mixture is rich, stoichiometric, or lean. Switch between direct mass inputs and the fuel-preset mode to explore mixture tuning for any combustion application.
Formula
Worked example
A gasoline engine ingests 14.7 g of air for every 1.0 g of fuel. AFR = 14.7 / 1.0 = 14.7:1. The stoichiometric AFR for gasoline is 14.7, so lambda = 14.7 / 14.7 = 1.0 and phi = 1/1.0 = 1.0. Excess air = 0%. If the same engine is running rich at 13.0:1, lambda = 13.0 / 14.7 = 0.884, phi = 1.131, and excess air = -11.6%.
What is air-fuel ratio (AFR)?
The air-fuel ratio is the mass of air divided by the mass of fuel in a combustion mixture. It tells you how much air is present relative to the fuel being burned. For a gasoline engine the ideal (stoichiometric) ratio is 14.7:1, meaning 14.7 grams of air are needed to completely combust one gram of petrol without leftover oxygen or unburned fuel. Ratios below the stoichiometric value (rich mixtures) leave unburned fuel and produce carbon monoxide; ratios above it (lean mixtures) leave excess oxygen and can cause rough running or misfires in spark-ignition engines.
Lambda and equivalence ratio explained
Lambda (greek letter lambda) is the actual AFR divided by the stoichiometric AFR for the same fuel. It is a dimensionless, fuel-independent way to describe mixture strength: lambda = 1.0 is always stoichiometric, lambda below 1.0 is always rich, and lambda above 1.0 is always lean, regardless of whether you are burning gasoline, ethanol, methane, or hydrogen. The equivalence ratio (phi) is the reciprocal of lambda (phi = 1/lambda). Phi greater than 1.0 means rich, phi below 1.0 means lean. Engineers in academic combustion research often prefer phi, while automotive calibrators typically use lambda. Percent excess air equals (lambda minus 1) times 100, so lambda 1.10 corresponds to 10% excess air.
Stoichiometric AFR by fuel type
Stoichiometric AFR varies widely depending on the hydrogen-to-carbon ratio and oxygen content of the fuel. Hydrogen has the highest stoichiometric AFR (34.3:1) because it contains no carbon and burns with only oxygen. Methane (CNG) follows at 17.2:1. Gasoline sits at 14.7:1 and diesel at 14.5:1. Oxygenated fuels like ethanol (9.0:1) and methanol (6.5:1) require far less air because they already carry oxygen in their molecular structure. E85 blends fall between gasoline and pure ethanol at around 9.8:1. Understanding these differences is critical when converting an engine to an alternative fuel: a fuel system sized for gasoline will over-fuel on methanol without recalibration.
Rich vs lean and why it matters for tuning
A rich mixture (lambda below 1.0) produces more power up to a point because excess fuel prevents detonation and cools combustion chamber temperatures. Motorsport applications often target lambda 0.85 to 0.92. However, running rich increases fuel consumption, raises CO and unburned hydrocarbon (HC) emissions, and can foul spark plugs. A lean mixture (lambda above 1.0) improves fuel economy and reduces CO, but taken too far it causes misfires, rough idle, high exhaust temperatures, and elevated NOx emissions. Modern three-way catalysts work most efficiently within a tight band around lambda 1.0, which is why closed-loop fuel injection systems constantly hunt around that value using an oxygen sensor. Diesel engines run unthrottled and always lean (lambda 1.2 to 8+), controlling power via fuel quantity rather than mixture ratio.
Stoichiometric AFR by fuel type
| Fuel | Chemical Formula | Stoichiometric AFR | Typical Application |
|---|---|---|---|
| Gasoline | C8H18 | 14.70:1 | Spark-ignition car engines |
| Diesel (No. 2) | C12H23 | 14.50:1 | Compression-ignition engines |
| E85 | E85 | 9.76:1 | Flex-fuel vehicles |
| Ethanol (E100) | C2H5OH | 9.00:1 | Racing, Brazil flex market |
| Methanol | CH3OH | 6.47:1 | Drag racing, IndyCar |
| Propane (LPG) | C3H8 | 15.67:1 | Forklifts, fleet vehicles |
| Methane (CNG) | CH4 | 17.19:1 | CNG trucks, power generation |
| Hydrogen | H2 | 34.30:1 | Fuel cells, hydrogen engines |
Mass-based air-fuel ratios required for complete combustion. Higher ratios mean more air is needed per gram of fuel.
Frequently asked questions
What is a normal AFR for a gasoline engine?
The stoichiometric AFR for gasoline is 14.7:1. A healthy idle typically runs slightly rich at around 14.0 to 14.7:1. Wide-open throttle on a naturally aspirated engine is often tuned to 12.5 to 13.5:1 (rich) for maximum power. Cruise conditions may run 15:1 or leaner for economy. Anything below 11:1 or above 17:1 indicates a significant fueling problem.
Why does ethanol have such a low stoichiometric AFR?
Ethanol (C2H5OH) contains one oxygen atom per molecule, so it brings its own oxygen to the combustion reaction. This reduces the amount of air needed from outside. The stoichiometric AFR for pure ethanol is 9.0:1 versus 14.7:1 for gasoline. When switching to E85 or E100, fuel injectors must flow roughly 30-40% more volume to supply the same energy, and the engine management must be recalibrated accordingly.
What does lambda 1.0 mean and why is it important?
Lambda 1.0 means the mixture is exactly stoichiometric - neither rich nor lean. It is the point where all the fuel can theoretically combust with exactly the available oxygen. Three-way catalytic converters achieve their best efficiency (converting CO, HC, and NOx simultaneously) within about plus or minus 0.01 lambda of 1.0. That is why fuel-injected road engines use a narrowband oxygen sensor to keep the mixture cycling around this value.
What is the difference between lambda and equivalence ratio (phi)?
They are reciprocals: phi = 1/lambda. Lambda greater than 1 is lean; phi greater than 1 is rich. Both express the same information about mixture strength relative to stoichiometric. Lambda notation is standard in European automotive engineering and on wideband O2 sensor displays. Equivalence ratio (phi) is common in academic combustion literature and aerospace. Either can be used as long as you remember which direction is rich.
How is AFR measured in a running engine?
A wideband (or broadband) oxygen sensor in the exhaust measures residual oxygen content and outputs a current that an AFR gauge converts to a lambda or AFR value. Narrowband sensors only give a lean/rich signal around lambda 1.0, not an absolute ratio. For testing purposes, exhaust gas analyzers measure CO, CO2, O2, HC, and NOx concentrations, from which exact lambda can be back-calculated using the Brettschneider formula.