Air-Fuel Ratio Calculator

Introduction

This air–fuel ratio (AFR) calculator helps you quantify how much air is supplied relative to the fuel burned in a combustion process. By entering air and fuel mass, and selecting a fuel type with an associated stoichiometric AFR, the tool computes the actual AFR, the relative mixture strength (lambda, λ), and whether the mixture is rich or lean compared with ideal complete combustion.

The calculator is useful for engine tuners, combustion engineers, emissions specialists, and students who want a quick way to compare mixtures across different fuels such as gasoline, diesel, ethanol, liquefied petroleum gas (LPG), and hydrogen. All calculations are based on mass, not volume, which aligns with how combustion chemistry is typically represented and avoids confusion when comparing very light fuels like hydrogen to heavier liquid fuels.

What is Air–Fuel Ratio (AFR)?

The air–fuel ratio is the mass of air supplied to the combustion chamber divided by the mass of fuel consumed over the same interval. In engines and burners, AFR is a primary control variable because it governs flame temperature, power output, fuel economy, and exhaust emissions. A higher AFR (more air relative to fuel) is called a lean mixture, while a lower AFR (more fuel relative to air) is called a rich mixture.

In simple algebraic form, the AFR is defined as:

AFR = m_a / m_f

where:

• m_a is the mass of air (for example in kilograms).
• m_f is the mass of fuel (using the same mass units as the air).

As long as the mass units are consistent (kg, g, lb, etc.), the ratio is dimensionless. The calculator accepts masses in kilograms by default, but you may use any mass unit as long as you use the same unit for both air and fuel, because the units cancel in the division.

Key formulas used in the calculator

The following relationships are evaluated when you press the calculate button. For clarity, the core AFR equation is also shown in MathML format:

• Air–fuel ratio: AFR = m_a / m_f
• Lambda (λ), the relative air–fuel ratio: λ = AFR / AFRstoich
• Equivalence ratio (φ): φ = 1 / λ

Here, AFR_stoich is the stoichiometric air–fuel ratio for the chosen fuel. It is the theoretical ratio that supplies exactly enough oxygen for complete combustion with no leftover fuel or oxygen, assuming ideal mixing and reaction.

Lambda, equivalence ratio, and mixture richness

Because different fuels have different stoichiometric air requirements, the absolute AFR alone is not always easy to compare across fuels. For this reason, combustion engineers often use lambda (λ) or the closely related equivalence ratio (φ):

• Lambda (λ): ratio of the actual AFR to the stoichiometric AFR.
  • λ = 1 → stoichiometric mixture.
  • λ > 1 → lean mixture (excess air).
  • λ < 1 → rich mixture (excess fuel).
• Equivalence ratio (φ): reciprocal of lambda: φ = 1 / λ.
  • φ = 1 → stoichiometric mixture.
  • φ > 1 → rich mixture.
  • φ < 1 → lean mixture.

In spark-ignition engines (gasoline and similar fuels), lambda is often kept very close to 1.0 under most operating conditions so that the three-way catalytic converter can simultaneously reduce nitrogen oxides (NO_x), oxidize carbon monoxide (CO), and burn unburned hydrocarbons (HC). In contrast, diesel engines usually operate significantly lean (lambda > 1) over much of the load range because fuel is injected into already compressed hot air and there is no throttle valve controlling the airflow.

Stoichiometric AFR for common fuels

Stoichiometric air–fuel ratios depend on the chemical composition of the fuel and the assumed composition of air (commonly taken as approximately 21% O₂ and 79% N₂ by volume). Representative mass-based stoichiometric AFR values for the fuels included in the calculator are summarized below.

These values are sufficiently accurate for most educational and preliminary design calculations. For regulatory work or detailed engine calibration, consult fuel-specific standards, test data, or manufacturer documentation.

Worked example

Consider a situation where 3.5 kg of air are supplied to burn 0.2 kg of gasoline. Using the formulas above:

1. Compute the actual AFR.
   AFR = m_a / m_f = 3.5 / 0.2 = 17.5
2. Determine the stoichiometric AFR for gasoline.
   From the table, AFR_stoich for gasoline is 14.7.
3. Calculate lambda (λ).
   λ = AFR / AFR_stoich = 17.5 / 14.7 ≈ 1.19
4. Calculate the equivalence ratio (φ).
   φ = 1 / λ ≈ 1 / 1.19 ≈ 0.84

Because λ > 1 (and φ < 1), this is a moderately lean mixture: it uses more air than required for ideal complete combustion. In a gasoline engine, such a mixture tends to reduce fuel consumption but can increase combustion temperatures and NO_x emissions if sustained without mitigation.

Interpreting the calculator results

The calculator typically reports three key outputs based on your entries:

• Actual AFR: the mass ratio of air to fuel you specified.
• Lambda (λ): how your mixture compares to stoichiometric for the selected fuel.
• Mixture description: simple classification such as rich, stoichiometric, or lean based on the computed lambda.

As a rule of thumb for many fuels:

• λ between about 0.95 and 1.05 is effectively stoichiometric in practical systems.
• λ significantly greater than 1.1 indicates lean combustion.
• λ significantly less than 0.9 indicates rich combustion.

The exact acceptable range depends on the engine or burner design, the presence of aftertreatment systems, and goals such as fuel economy or emissions reduction. For example, high-performance spark-ignition engines may run rich under full load for knock suppression and component cooling, while lean-burn technologies deliberately target lambda values greater than 1.4 for efficiency gains under light load.

Comparison: rich vs stoichiometric vs lean

The table below summarizes typical qualitative differences between mixtures that are rich, near stoichiometric, or lean. These descriptions are general trends rather than strict rules and may vary by fuel and combustion system.

Assumptions and limitations

The calculations provided by this tool are based on idealized combustion theory and standard reference data. Before applying the results to real hardware or regulatory work, consider the following assumptions and limitations:

• Ideal, complete combustion: The underlying formulas assume that all fuel is fully oxidized and that combustion goes to completion with no intermediate species. Real engines and burners often have incomplete combustion zones, flame quenching near walls, and mixture stratification that deviate from this ideal.
• Standard air composition: Air is assumed to have a fixed composition close to 21% oxygen and 79% nitrogen by volume, with trace species neglected. Humidity, altitude, and recirculated exhaust gas (EGR) are not modeled, although they can affect effective AFR and combustion behavior.
• Representative fuel properties: The stoichiometric AFR values used are typical reference numbers for common fuel formulations. Real fuels vary by supplier, region, and season (for example, winter and summer gasoline blends), so actual stoichiometric AFR can differ slightly from the values used here.
• Mass-based ratios only: All calculations are on a mass basis. For gases, it is common to discuss volume-based mixtures as well (for example, hydrogen by volume). This tool does not convert between mass-based and volume-based AFRs, and it does not account for gas compressibility or non-ideal behavior.
• No transient or dynamic effects: The tool represents steady-state conditions using average air and fuel flow. Transient phenomena in engines, such as tip-in enrichment or turbocharger lag, are outside the scope of this calculator.
• Educational and preliminary use: Results are intended for education, conceptual design, and quick estimation. They should not be used on their own to set regulatory compliance strategies, certify engines, or finalize calibration maps without detailed testing or simulation.

For more rigorous work, refer to combustion textbooks, engine manufacturer documentation, or standards from bodies such as SAE International and ISO that define measurement methods and reference fuel properties. The stoichiometric AFR values and explanations in this calculator are periodically reviewed against such sources, but they are not a substitute for official specifications.

Practical usage tips

To make the most of the calculator, keep these points in mind:

• Use consistent mass units for both air and fuel. If you enter air in kilograms and fuel in grams, the computed AFR will be incorrect.
• When comparing different fuels, use lambda or equivalence ratio instead of raw AFR, as the stoichiometric values vary significantly.
• For systems with oxygen sensors or wideband lambda sensors, you can compare the measured lambda to the calculator’s predictions to reason about expected versus actual mixture strength.
• If you are tuning an engine, always consider manufacturer guidance and safety margins; operating too lean or too rich can damage components even if the theoretical AFR appears acceptable.