Excess Air Ratio: Formula, O2 Lookup Table and Target Values

Suppose a boiler manual from a Japanese supplier gives the combustion setting as "空気比 1.2," an air ratio (kuki-hi) of 1.2. Your team talks about excess air in percent, and your flue gas analyzer reads oxygen in percent. The first two are the same quantity in different forms, and O₂ can be used to estimate them, but mixing the three up leads to wrong tuning decisions.

Air ratio (symbol m) is the supplied combustion air divided by the theoretical air needed for complete combustion. Excess air is the same quantity expressed as a percentage above 100%, so an air ratio of 1.2 equals 20% excess air. On a dry basis, you can estimate it from flue gas oxygen with m ≈ 21 / (21 − O₂).

This guide covers the conversion, an O₂ lookup table, a worked calculation from fuel and air flow, and the reference values in Japan's energy conservation guideline. It ends with a checklist and questions for the Japanese supplier.

Contents

1. Air Ratio vs. Excess Air: Two Ways to Say the Same Thing
2. How to Calculate Air Ratio from O2
3. Calculating Air Ratio from Fuel and Air Flow
4. Why Too Much or Too Little Air Costs You
5. What Air Ratio Is Right? Target Values
6. Controlling Air Ratio: Dampers, Fan Speed, and O2 Trim
7. Checklist: Before You Act on an O2 or Air Ratio Number
8. Questions to Ask the Japanese Supplier
9. Limits of This Guide
10. FAQ
11. Sources

Air Ratio vs. Excess Air: Two Ways to Say the Same Thing

Japanese documents, including the government guideline covered below, express combustion air as a ratio. US sources such as Department of Energy tip sheets use excess air in percent. Both rest on the same definition.

Figure 1: Air Ratio 1.4 = Theoretical Air + 40%

Breakdown of the supplied air for a fixed amount of fuel, with theoretical air set to 1.

This is a ratio of air supplied. It does not mean the flue gas contains 40% oxygen.

The air ratio has no unit. Its denominator depends on the amount and composition of the fuel, so if the fuel rate changes while the fan delivers the same airflow, the air ratio changes too.

In theory, an air ratio of 1.0 supplies exactly the oxygen needed for complete combustion. Real burners cannot mix fuel and air perfectly, so operators supply more air than the theoretical amount to avoid unburned fuel, and the unused oxygen ends up in the flue gas.

An air ratio of 1.0 is therefore a theoretical minimum, not a recommended setting. Burners need a margin within the manufacturer's operating range to burn stably.

Use this quick conversion when a Japanese document and your own procedure use different terms:

Air ratio (m)	1.05	1.10	1.20	1.30	1.40
Excess air	5%	10%	20%	30%	40%

Excess Air Is Not Flue Gas Oxygen

The "extra 40%" at an air ratio of 1.4 is measured against theoretical air. It does not mean 40% of the total supplied air is left over, and it does not mean the flue gas contains 40% oxygen.

If theoretical air is 100, supplied air is 140, and the difference of 40 is the excess air. To see how the ratio moves, separate two cases: adding air without adding fuel, and increasing fuel and air in the same proportion.

Flue gas oxygen, by contrast, is the share of leftover oxygen in the total flue gas after combustion. Carbon dioxide and water vapor from the fuel also count in that denominator, so you cannot read the air ratio directly as an oxygen concentration.

How to Calculate Air Ratio from O₂

When combustion is close to complete, you can estimate the air ratio from the oxygen content of the dry flue gas. Enter O₂ as a percentage: for 4% O₂, enter 4, not 0.04.

Figure 2: Air Ratio and Excess Air from Dry Flue Gas O₂

O₂ is in percent by volume, dry basis. Air ratio is rounded to two decimals and excess air to the nearest percent.

Estimate from residual oxygen in dry flue gas

m ≈ 2121 − O₂    Excess air (%) ≈ O₂21 − O₂ × 100

m ≈ 2121 − 4 = 2117 ≈ 1.24 (about 24% excess air)

m: air ratio (dimensionless)   O₂: oxygen in dry flue gas (vol%). The example assumes 4%.

O2 (dry)	1%	2%	3%	4%	5%	6%	7%	8%
Air ratio m	1.05	1.11	1.17	1.24	1.31	1.40	1.50	1.62
Excess air	5%	11%	17%	24%	31%	40%	50%	62%

These are conversions, not recommended settings. Do not enter wet-basis readings, and check for air in-leakage before using a value.

Japanese sources, including the government guideline discussed below, use 21 for the oxygen content of air. Many US sources use 20.9. In the 1–8% O₂ range, the difference changes excess air by less than 1 percentage point.

The formula rests on three assumptions:

• Combustion is complete.
• The fuel contains no oxygen or nitrogen of its own.
• Nitrogen makes up about 79% of the dry flue gas, the same share as in air.

Because real fuels deviate from these assumptions, the O₂-based value will not exactly match an air ratio calculated from measured flows. Do not use it to evaluate incomplete combustion.

Dry vs. Wet O₂: Check Your Analyzer First

Dry gas is flue gas with the water vapor removed. Wet gas includes the water vapor, so the same flue gas gives a lower O₂ reading on a wet basis because the denominator is larger.

In-situ zirconia analyzers inserted directly into the flue measure on a wet basis, while extractive analyzers that cool the sample and remove condensate measure on a dry basis. Some zirconia models can also calculate and output a dry-basis value, so check the actual output setting rather than assuming from the sensor type.

If you feed a wet reading into the dry-basis formula, you will read a different air ratio for the same combustion condition. Check the measurement basis and sampling point before you use the table.

Oxygen in the Flue Gas Does Not Prove Complete Combustion

The air ratio shows the overall air balance for the whole unit. It does not guarantee that oxygen reaches every part of the flame, and in poorly mixed zones some fuel can stay unburned while the flue gas still contains oxygen.

If O₂ is in the normal range but CO rises or smoke appears, check combustion first. Before adding air just to bring the numbers back in line, inspect the burner and fuel supply following the manufacturer's inspection procedure.

Calculating Air Ratio from Fuel and Air Flow

If you know the fuel and air quantities, you can calculate theoretical air from the combustion reaction and compare it with the actual supply. The example below uses 1 mol of methane, with every volume expressed at the same reference conditions.

Figure 3: From 1 mol of Methane to an Air Ratio of 1.4

Find the oxygen needed from the reaction, divide by the oxygen fraction of air, then compare with the supplied air.

Oxygen required → theoretical air → air ratio

V_O2 = n_O2 × V_m = 2 × 22.4 = 44.8 NL

A₀ = V_O2x_O2 = 44.80.21 ≈ 213 NL

m = AA₀ ≈ 300213 ≈ 1.4

V_O2: oxygen required (NL)   n_O2: oxygen required (mol)   V_m: molar volume (NL/mol)   A₀: theoretical air (NL)   A: supplied air (NL)   x_O2: volume fraction of oxygen in air (dimensionless)   m: air ratio (dimensionless). A is assumed to be 300 NL.

Volumes are dry at 0°C (32°F) and 101.325 kPa (14.696 psia), gases are treated as ideal, and air is taken as 21% oxygen. Water produced is shown in mol.

Step 1: Oxygen Required from the Combustion Equation

Methane (CH₄, molecular weight about 16) burns completely to carbon dioxide and water. The reaction coefficients show that 1 mol of methane uses 2 mol of oxygen, which is about 44.8 NL.

NL here means liters at 0°C and 101.325 kPa, dry, the "normal" conditions used in Japanese documents (Nm³ for cubic meters). US documents often use standard cubic feet at a different reference temperature, so convert both flows to the same basis before you compare them.

The same applies when you compare with actual volumes in hot ducts or piping.

Step 2: Theoretical Air from the Oxygen Content of Air

Dry air is roughly 78% nitrogen, 21% oxygen, and about 0.93% argon, so supplying air takes a larger volume than supplying pure oxygen. Dividing the oxygen required by the oxygen fraction (0.21) gives about 213 NL of theoretical air for this amount of fuel.

For a fuel with several components, calculate the oxygen required for each one and add them up by composition. Whether you include water vapor also changes the flue gas volume, so keep the flue gas calculation separate from the theoretical air calculation.

Step 3: Divide Supplied Air by Theoretical Air

If the supplied air is 300 NL, the air ratio is about 1.4, meaning about 40% more air than theoretical. The 213 NL figure is rounded, but the unrounded value also gives about 1.4.

This example assumes pure methane. Do not reuse it for the actual composition of city gas (piped gas) or LPG; calculate the oxygen required from the fuel supplier's composition data instead.

Worked Example with Continuous Flow Rates

For continuous operation, express fuel and air as flow rates over the same time unit and follow the same steps. Assume, for illustration, pure methane at 10 Nm³/h and dry air at 120 Nm³/h, both corrected to 0°C and 101.325 kPa.

The result, about 1.26, is the supply ratio at these flows. It is calculated differently from the O₂-based value in Figure 2, so if the two disagree, do not assume a fault right away; check the fuel composition, the flow correction settings, and the flue gas measurement basis in turn.

Watch for one common mismatch: an air flowmeter that reads actual volume in the duct while only the fuel flowmeter is corrected to standard conditions. Check the units, the temperature and pressure compensation settings, and whether pressure is absolute or gauge in the instrument specifications.

Also confirm that fuel and air use the same time unit (per hour vs. per minute) before you divide.

Why Too Much or Too Little Air Costs You

Too much air heats air that does nothing for combustion and sends it up the stack, so more heat leaves with the flue gas. Too little air produces carbon monoxide (CO) and soot, which is why cutting air alone cannot deliver both efficiency and stable combustion.

Other factors to weigh:

• Fan load (forced draft fan power).
• Low-temperature (acid dew point) corrosion with sulfur-bearing fuels.
• Effects on NOx, depending on combustion conditions.
• Furnace pressure, which also depends on the exhaust side; a high air ratio and positive furnace pressure are separate issues.

Fuel type is one factor, but it alone does not set the right value.

What Air Ratio Is Right? Target Values

There is no single correct number. The right range depends on the fuel and steam output, and also on the combustion method, the load, and the specific model, so the operating setting must come from the manufacturer's conditions and the observed combustion.

Example from Japan: Reference and Target Air Ratios

Japan's Energy Conservation Act (shoene-ho) is backed by a government guideline for factories, often called the handan kijun ("judgment criteria"). It sets two different values for boilers and industrial furnaces: a reference air ratio (kijun kuki-hi) to be met and a stricter target air ratio (mokuhyo kuki-hi) to work toward.

The table below shows the boiler values for liquid and gaseous fuels as reproduced by the Energy Conservation Center, Japan (ECCJ). It is shown here so you can recognize these numbers in Japanese documents, not as a setting to copy.

Figure 4: Boiler Air Ratios in Japan's Energy Conservation Guideline (Example)

Liquid and gaseous fuels only. Approximate dry O₂ is calculated with 21 / (21 − O₂).

Boiler category	Load factor	Reference: liquid	Reference: gas	Target: liquid	Target: gas	Reference gas as dry O2
General boiler, 30 t/h or more	50–100%	1.1–1.25	1.1–1.2	1.05–1.15	1.05–1.15	about 1.9–3.5%
General boiler, 10 to under 30 t/h	50–100%	1.15–1.3	1.15–1.3	1.15–1.25	1.15–1.25	about 2.7–4.8%
General boiler, 5 to under 10 t/h	50–100%	1.2–1.3	1.2–1.3	1.15–1.3	1.15–1.25	about 3.5–4.8%
General boiler, under 5 t/h	50–100%	1.2–1.3	1.2–1.3	1.15–1.3	1.15–1.25	about 3.5–4.8%
Small once-through boiler	100%	1.3–1.45	1.25–1.4	1.25–1.4	1.2–1.35	about 4.2–6.0%

t/h = steam output. Values apply at the boiler outlet, after periodic inspection, under stable combustion at constant load. The table also covers utility boilers, solid fuels, and by-product gases, and it lists many exclusions (for example, waste-heat boilers and units converted to a different fuel). The edition of the reproduced table is not stated; check the current official text before citing it.

Read the categories carefully. A "general boiler" (ippan-yo boiler) and a "small once-through boiler" (kogata kanryu boiler) are defined by Japanese safety and air pollution regulations, not by appearance or size alone, so match the table's notes against the equipment specification before picking a row.

The same guideline has a separate table for industrial furnaces. For example, it lists 1.20 for gas-fired continuous steel reheating furnaces and 1.25 for gas-fired batch heat treatment furnaces.

US Reference Points

US Department of Energy (DOE) tip sheets give comparable rules of thumb. A steam tip sheet states that about 10% excess air is attainable on well-designed natural gas-fired systems, and a process heating tip sheet says most furnaces and boilers run at about 10–20% excess air at high fire.

The same process heating tip sheet describes 2–3% O₂ with only 10–50 ppm of combustibles as ideal for most systems. Like the Japanese table, these are general guides, not settings for a specific burner.

What to Cross-Check Before Using a Number

Before turning any published value into an operating setting, compare these three sources:

Figure 5: Cross-Checks Before a Published Value Becomes a Setpoint

An example of how to read guideline tables. It does not define current requirements or settings.

Source	Conditions to check	Common misreading
Energy conservation guideline table	Fuel, steam output, scope, notes	Reference and target air ratios are different values
Manufacturer's specifications	Model, combustion method, allowable load range	Values from another model do not carry over
Operating records	Load, O2, CO, flue gas temperature, smoke	Also check whether combustion was stable

A Japanese Ministry of the Environment case report lists 1.2–1.3 as the reference value for city gas boilers with 5 to under 10 t/h of steam output. That was a value for that case, not a recommended value for all boilers.

Keep Reference Values and Your Own Setpoints Separate

Even the guideline's reference table attaches conditions such as load factor and combustion method, not just fuel type. Use it as a benchmark, and set your control values from each model's adjustment range rather than treating the table as a burner procedure.

If you refer to the guideline in practice, check the applicable conditions in the latest official text. Record the date you checked and the document you used in the plant's operating standards.

A setting that is stable near rated load may not suit low load, so check it separately. Start with the load bands where the unit runs longest, and evaluate startup and load-change values apart from steady-state records.

When you assess an improvement, compare air ratio, CO and other combustion indicators, and flue gas temperature under the same conditions. A lower O₂ reading alone does not tell you how much efficiency improved or how emissions changed.

Controlling Air Ratio: Dampers, Fan Speed, and O₂ Trim

Combustion air is adjusted either by changing the damper opening or by changing the fan speed with a variable frequency drive (VFD). Both act on the air supply, matching airflow to the fuel rate and load.

Figure 6: Where Air Is Adjusted and Where Flue Gas Is Measured

The fan and damper sit upstream of the burner. The O₂ analyzer reads the flue gas after combustion.

Schematic of a typical layout. Even with O₂ trim, do not judge combustion safety from the analyzer reading alone.

In O₂ trim control, the airflow is first set by the fuel rate or load, and the analyzer reading then corrects it. Check CO, smoke, and flame condition according to the manufacturer's procedures, and confirm that combustion stays stable when the load changes.

If O₂ suddenly rises at the same load, look beyond increased airflow: the fuel flow may have dropped, or the analyzer may have drifted. As Figure 6 shows, air leaking in upstream of the measuring point raises the O₂ reading even when the burner is not getting more air.

For fan speed control, weigh the equipment cost and power savings along with the required pressure and the range of airflow variation. Record air ratio and flue gas temperature under the same load conditions to compare before and after adjustment.

Choosing Between Damper and Fan Speed Control

A damper works by changing flow resistance, so percent opening does not equal percent airflow. Linkage misalignment and sticking also affect results, so check the commanded position and the actual movement separately.

Fan speed control runs the fan to match the required airflow and can also cut power use on units with varying load. Minimum speed and required fan pressure differ by model, however, so speed alone does not decide whether a retrofit is feasible.

To compare the options, look at the annual load profile and fan power, and include maintenance cost as well as installation cost. Avoid rules like "small units always use dampers, large units always use VFDs," and confirm compatibility with the existing burner with the manufacturer.

Rule Out Measurement Errors Before Adjusting

When you compare a fixed analyzer with a portable one, first match the sampling point, the load, and the dry or wet basis. Sample line leaks and analyzer response time also affect the result, so do not judge calibration from a momentary reading taken before the display settles.

High O₂ together with rising CO points to poor mixing or uneven combustion rather than just an overall air shortage. If the fuel flow is steady but O₂ differs by sampling location, investigate air in-leakage in the flue or uneven concentration across the duct.

In zirconia analyzers, combustibles such as CO and hydrogen can burn inside the heated sensor and consume oxygen, making the reading lower than actual. If the O₂ and CO trends do not make sense together, add the manufacturer's measuring principle and application limits to your checks.

Compare Results at the Same Load

For the baseline record before adjustment, note the date and time, the fuel, a load indicator such as steam output, fuel flow, and flue gas temperature. Also record the O₂ and CO measuring points and their dry or wet basis, so the comparison still works after staff or instruments change.

Comparing high-load winter data with low-load summer data would count unrelated differences as savings. Collect records from the same load band, and check feedwater and ambient conditions as you read the change in fuel use.

Actual setting changes should be made by personnel qualified to judge combustion, following the manufacturer's adjustment procedure and the plant's operating rules. If CO rises, the flame goes out, or another abnormality appears, stop chasing efficiency and follow the unit's abnormal-condition procedure.

Checklist: Before You Act on an O₂ or Air Ratio Number

Run through these points before you compare values or change a setting:

• Is the value an air ratio (m), excess air (%), or flue gas O₂ (%)? Convert to one form first.
• Is the O₂ reading dry or wet basis? Check the analyzer's output setting, not just the sensor type.
• Where is the sampling point, and could air leak in upstream of it?
• Was 21 or 20.9 used for the oxygen content of air?
• Is CO low and stable at the same time? O₂ alone does not confirm complete combustion.
• For flow-based ratios: are fuel and air on the same reference conditions and the same time unit? Absolute or gauge pressure?
• Is the fuel composition current (city gas, LPG, fuel oil), or is the calculation based on an assumed fuel?
• Is any target value a reference or a target air ratio, and for which boiler category and load range?
• Were the before and after records taken at the same load band?
• Who is authorized to change burner settings, and which manufacturer procedure applies?

Questions to Ask the Japanese Supplier

When a Japanese boiler or burner document gives an air ratio, these questions help you turn it into something your team can use:

• Is the stated air ratio (kuki-hi) measured at the boiler outlet, and on a dry or wet O₂ basis?
• What O₂ and CO ranges correspond to that air ratio at low, medium, and high fire?
• Which fuel composition was the setting based on? Does it apply to our local gas or oil?
• Is the value a design point, a guaranteed value, or a reference from Japan's energy conservation guideline?
• Does the burner control use O₂ trim? If so, what are the trim limits and the analyzer type?
• What is the minimum fan speed or damper position, and what procedure do you require for re-tuning?

A short inquiry you can adapt:

"Your commissioning report lists an air ratio (kuki-hi) of 1.2 at 100% load. Please confirm whether this is based on dry or wet flue gas O₂ at the boiler outlet, and provide the corresponding O₂ and CO values at 25%, 50%, and 100% load for our fuel composition (attached)."

Limits of This Guide

• The O₂ formula is an approximation for complete combustion on a dry basis. It is not valid for incomplete combustion or for wet-basis readings.
• The methane examples assume a pure fuel and ideal gases. Real fuels need their own composition data.
• The Japanese guideline table is shown as an example of how Japanese documents state air ratios. It is not a statement of current legal requirements, and its edition must be confirmed against the official text.
• Settings for a specific boiler, furnace, or burner depend on the model, load, and combustion method. The manufacturer and qualified plant staff decide them.
• Emission limits for CO, NOx, and other pollutants depend on local regulations and permits, which this guide does not cover.

FAQ

How Do I Calculate Excess Air from O₂?

On a dry basis, excess air (%) ≈ O₂ / (21 − O₂) × 100, with O₂ entered as a percentage. For example, 4% O₂ gives about 24% excess air, or an air ratio of about 1.24. Many US sources use 20.9 instead of 21, which changes the result only slightly.

Is Air Ratio the Same as Air-Fuel Ratio?

No. The air-fuel ratio is air divided by fuel, while the air ratio is supplied air divided by theoretical air. When you read an air-fuel ratio, also check whether it is by mass or by volume, and do not compare the number directly with an air ratio.

Can I Use a Wet-Basis O₂ Reading in the Lookup Table?

No. The table is for dry flue gas, so wet readings that include water vapor cannot be entered directly. Check the analyzer's dry/wet setting, and if you only have wet values, confirm the correct conversion method, including moisture content, with the manufacturer.

If O₂ Is High, Should I Reduce the Air?

Not before you confirm that the burner is actually getting too much air. Rule out a wet-basis reading, air in-leakage, and analyzer problems first. Adjust only within the manufacturer's range and the plant's operating procedures, and do not treat a lower O₂ reading as a goal in itself.

Does Lowering the Air Ratio Cut Fuel Use by the Same Percentage?

No. The percentage drop in air ratio and the percentage drop in fuel are different numbers. The change in heat loss depends on flue gas temperature and combustion conditions, so evaluate savings from fuel use at the same steam load or from a heat balance.

Sources

• Air ratio approximation and its assumptions: SME Support, Japan (J-Net21), air ratio approximation (Japanese)
• Reference vs. target air ratios: SME Support, Japan (J-Net21), air ratio reference and target values, October 23, 2019 (Japanese)
• Boiler and furnace air ratio tables: Energy Conservation Center, Japan (ECCJ), tables from the energy conservation judgment criteria (Japanese)
• Case value for city gas boilers: Ministry of the Environment, Japan, emission reduction in business activities (Japanese)
• Measurement notes for boiler flue gas: Ministry of the Environment, Japan, feedwater preheating with boiler flue gas (Japanese)
• O₂ measurement and air control in boilers: Yokogawa Electric, boiler flue gas O₂ measurement (Japanese)
• Dry vs. wet O₂: Yokogawa Electric, difference between dry and wet gas oxygen concentration (Japanese)
• Effect of combustibles on zirconia analyzers: Yokogawa Electric, zirconia oxygen analyzer precautions (Japanese)
• Excess air ranges and O₂ guidance: US DOE, Process Heating Tip Sheet #2, "Check Burner Air to Fuel Ratios"
• Excess air on natural gas boilers: US DOE, Steam Tip Sheet #4, "Improve Your Boiler's Combustion Efficiency"
• Methane properties: NIST Chemistry WebBook, methane
• Gas constant for ideal gas volumes: NIST, teqp constants
• Composition of dry air: NOAA JetStream, the atmosphere