NOx O2 Correction Formula and Japan’s Reference O2 Levels

A boiler test report from Japan lists "NOx 60 ppm (O₂ 5% kansan)." Your air permit sets a limit in ppmvd at 3% O₂, or in mg/Nm³ at 6% O₂. You cannot compare the two numbers until they share the same oxygen reference, moisture basis, and units.

O₂ kansan (O2換算) means "O₂ correction." It is the calculation that restates a measured NOx or dust (particulate) concentration as if the flue gas contained a fixed reference amount of oxygen. Japan uses the formula C = C_s × (21 − O_n) / (21 − O_s), and the reference level O_n is set by law for each type of facility.

This guide explains what the formula does and why it uses 21, then walks through a dilution example. It lists Japan's reference O₂ levels, compares them with US, EU, and Indian practice where we could verify it, and shows how to restate a Japanese supplier's figure on your own basis. It ends with a checklist, questions for the supplier, and an email template.

Contents

1. What O2 Correction Means on a Japanese Spec Sheet
2. Why Emissions Are Corrected to a Reference O2
3. Worked Example: Dilution Does Not Change the Corrected Value
4. Japan's Reference O2 Levels by Facility Type
5. How Japan's Reference O2 Compares with the US, EU, and India
6. Dry Basis, ppm, and mg/Nm3: What Else Must Match
7. Restating a Japanese Supplier's NOx Figure on Your Basis
8. Checklist and Questions for the Japanese Supplier
9. Limits of This Guide
10. FAQ
11. Sources

What O2 Correction Means on a Japanese Spec Sheet

Japanese specifications and test reports write the oxygen basis next to the value, for example "NOx 150 ppm (O₂ 4%換算)" or "O₂ 12%換算値." Read this as "corrected to 4% O₂" or "at 12% O₂." The legal reference level is called hyojun sanso nodo (標準酸素濃度), or standard oxygen concentration.

The formula comes from the Enforcement Regulations of Japan's Air Pollution Control Act (Taiki Osen Boshi Ho, 大気汚染防止法), in the notes to its emission-standard tables for dust and nitrogen oxides:

Japanese law states NOx as cm³ per m³ of flue gas, converted to 0°C and 1 atm. One cm³ in one m³ is 1 ppm by volume, so you can enter ppm directly. Dust uses the same formula, with the unit g per m³ of flue gas at 0°C and 1 atm.

The "21" is the oxygen content of air. Dry air is about 20.95% oxygen by volume, and Japan rounds this to 21. As shown later, US EPA rules use 20.9 instead.

Each of the four values in the formula has a different source:

Figure 1: The Four Values in the O₂ Correction Formula

Two values are measured, one is set by law, and one is the result.

C_s MeasuredNOx or dust concentration from the analyzer

O_s Measured O₂Oxygen in the same gas. Values above 20% are entered as 20%

O_n Reference O₂Set by law for each facility type and pollutant

C CorrectedThe value compared with the emission standard

The 20% cap on O_s comes from the notes to Appended Tables 2 and 3-2 of the Enforcement Regulations (dust and NOx).

You do not choose O_n. It depends on the facility type and on the pollutant (NOx or dust). A boiler that burns only gas, for example, uses 5%; the main values are in the table later in this article.

Why Emissions Are Corrected to a Reference O2

The correction gives every facility the same yardstick. A boiler or incinerator burns fuel with oxygen from the air, and the oxygen that is not used leaves the stack with the flue gas. As a result, air is 21% oxygen, but flue gas contains less.

The figure below shows where the oxygen goes:

Figure 2: How Combustion Lowers the Oxygen Level

Combustion uses up oxygen from the air. Only what is left over reaches the flue gas.

The O₂ level in the flue gas depends on how much excess air is supplied relative to the fuel (the air ratio).

The flue gas O₂ level depends heavily on the air ratio the unit runs at. A higher air ratio means more oxygen in the flue gas, and a lower one means less.

The air ratio (kuki-hi, 空気比; also called excess air ratio or lambda) is the actual air supplied divided by the air needed for complete combustion.

Because the O₂ level changes with operation, raw concentrations from two units cannot be compared on the same scale. Correcting every result to one fixed O₂ level solves this.

A Numerical Example of Dilution

Take a flue gas flow of 100 Nm³/min at 3% O₂. Nm³ (normal cubic meter) is a volume converted to 0°C and 1 atm.

If the gas contains 200 ppm NOx, the NOx flow is 100 × 200 × 10⁻⁶ = 0.02 Nm³/min. The oxygen flow is 3 Nm³/min.

A ppm value is only a concentration, so mixing in outside air can push it as low as you like. Add 100 Nm³/min of fresh air, and the total becomes 200 Nm³/min. That air carries 21 Nm³/min of oxygen, so total oxygen rises to 24 Nm³/min, or 12%.

The figure below shows the mass balance:

Figure 3: Diluting Flue Gas with Air

The amount of NOx stays the same. Only the concentration drops.

Flue gas100 Nm³/min, 3% O₂
O₂: 3 Nm³/min
NOx: 0.02 Nm³/min (200 ppm)

+ Fresh air100 Nm³/min, 21% O₂
O₂: 21 Nm³/min
NOx: 0 Nm³/min

= Diluted flue gas200 Nm³/min, 12% O₂
O₂: 24 Nm³/min
NOx: 0.02 Nm³/min (100 ppm)

The NOx flow is still 0.02 Nm³/min, so the concentration falls to 0.02 ÷ 200 = 100 ppm. The same amount of NOx leaves the stack, but the number is cut in half.

A concentration limit would mean little if dilution could meet it. O₂ correction closes this gap by asking what the concentration would be at a fixed O₂ level, such as 6%. Japan's Ministry of the Environment states that the standard-oxygen correction was adopted to prevent operators from meeting emission standards by diluting the flue gas with air.

Worked Example: Dilution Does Not Change the Corrected Value

Now correct both states from the previous section to 6% O₂. The first is the basic calculation; the second confirms what happens after dilution.

Before Dilution

For flue gas at 3% O₂ with 200 ppm NOx, enter O_s = 3 and O_n = 6. The corrected value is about 167 ppm:

The measured O₂ (3%) is below the reference (6%), so the corrected value is lower than the measured 200 ppm.

After Diluting with Excess Air

After adding 100 Nm³/min of fresh air, the gas is at 12% O₂ with 100 ppm NOx. Corrected to 6% O₂, the result is again about 167 ppm:

Because of this, adding air to increase the total gas volume no longer helps a facility slip under a concentration limit. The comparison below puts both states side by side:

Figure 4: Dilution Halves the Raw Value, Not the Corrected One

The measured concentration drops by half, but both cases come to 167 ppm at 6% O₂.

Before dilution

After adding 100 Nm³/min of air

Flue gas flow

Before: 100 Nm³/min

After: 200 Nm³/min

O₂ level O_s

Before: 3% (3 Nm³/min)

After: 12% (24 Nm³/min)

NOx flow

Before: 0.02 Nm³/min

After: 0.02 Nm³/min (unchanged)

Measured NOx C_s

Before: 200 ppm

After: 100 ppm

NOx at 6% O₂ (C)

Before: about 167 ppm

After: about 167 ppm

The corrected values match because all of the added oxygen came from the dilution air.

The ratio (21 − O_s)/21 explains why. It is the share of the flue gas that is combustion gas, not dilution air. At 3% O₂ that share is 18/21; at 12% it is 9/21.

Dividing a measured value by this share takes it back to the undiluted concentration, the "0% O₂" equivalent. Both 200 ÷ (18/21) and 100 ÷ (9/21) come to about 233 ppm. O₂ correction then multiplies by the reference share, 15/21 when O_n = 6: 233 × 15/21 ≈ 167 ppm.

To remember which goes where: the reference (O_n) is on top, and the measured value (O_s) is on the bottom. The further the measured O₂ is above the reference (the more diluted the gas), the more the corrected value rises above the measured one.

Japan's Reference O2 Levels by Facility Type

Japan sets O_n for each facility type in the Enforcement Regulations of the Air Pollution Control Act. NOx values are in the notes to Appended Table 3-2, and dust values are in the notes to Appended Table 2. Boilers split three ways by fuel: 5% for gas, 4% for liquid fuel, and 6% for solid fuel.

The table below lists the main facility types, checked against the regulation text on e-Gov, Japan's official law database:

Figure 5: Japan's Reference O₂ (O_n) for Main Facility Types

Boilers split three ways by fuel. Diesel engines and gas turbines use high values, while gas and gasoline engines use 0%.

Facility

NOx (Appended Table 3-2)

Dust (Appended Table 2)

Boiler, gas only

NOx: 5%

Dust: 5%

Boiler, liquid fuel (heavy oil, etc.)

NOx: 4%

Dust: 4% (including liquid fuel co-fired with gas)

Boiler, solid fuel (coal, etc.)

NOx: 6%

Dust: 6%

Metal heating furnace

NOx: 11%

Dust: 11%

Cement kiln

NOx: 10%

Dust: 10%

Waste incinerator

NOx: 12%

Dust: 12%

Diesel engine

NOx: 13%

Dust: 13%

Gas turbine

NOx: 16%

Dust: 16%

Gas engine, gasoline engine

NOx: 0%

Dust: 0%

Taken from the notes to Appended Tables 2 and 3-2 of the Enforcement Regulations (e-Gov text as consulted in October 2026; check the version currently in force). For NOx, small boilers with a heat transfer area under 10 m² form separate categories (solid fuel 6%, liquid fuel 4%). For dust, some facilities, such as boilers burning black liquor and facilities that use electricity as the heat source, use C = C_s with no correction.

For many of the main facility types, NOx and dust share the same O_n. The two tables group facilities differently, though, so check which entry your facility falls under for each pollutant.

A few special cases also apply to NOx. Some lead-oxide furnaces use C = C_s with no correction, and glass melting furnaces that burn with pure oxygen multiply the corrected value by an extra factor of 1/4. If equipment falls into one of these groups, ask the supplier which formula they applied.

Example: Checking a Gas-Fired Boiler

Suppose a gas-only boiler (O_n = 5) measures 8% O₂ and 80 ppm NOx. The corrected value is about 98 ppm:

This 98 ppm is compared with the emission standard in Appended Table 3-2. For a gas-only boiler with a flue gas volume of 40,000 to under 500,000 m³N/h, the national standard is 100 cm³/m³ (100 ppm). The flue gas volume here is the maximum hourly volume converted to 0°C and 1 atm.

You can also work backward from the limit to find the raw reading that corresponds to it. Rearranging the formula gives C_s = C × (21 − O_s) / (21 − O_n):

This back-calculation is a guide for reading the analyzer during operation. Compliance is decided against the standard and conditions that actually apply to the facility, which can include transitional rules based on installation date and stricter prefectural limits.

If analyzer readings go into a report, the analyzer must also be properly calibrated.

Corrected values also help when operating conditions change. Preheating combustion air with an air preheater saves energy, for example, but you need to check that it does not raise the NOx concentration, and corrected values make the before-and-after comparison easier.

How Japan's Reference O2 Compares with the US, EU, and India

Other jurisdictions use the same idea, but often with different reference levels. The table below covers only the values we could confirm in the regulation text or a reliable secondary source. Your own permit or consent conditions take precedence over any general rule.

Equipment	Japan (On)	US (examples)	EU (Industrial Emissions Directive)	India (example)
Gas-fired boiler	5%	3% O2, dry, in many state and local boiler rules (e.g., South Coast AQMD Rule 1146 series)	3% (liquid and gaseous fuels)	Not confirmed
Oil-fired boiler	4%	Check your permit	3%	Not confirmed
Coal / solid-fuel boiler	6%	Check your permit	6%	6%, dry (thermal power plants)
Gas turbine	16%	15% (40 CFR 60 Subpart KKKK)	15%	Not confirmed
Diesel engine	13%	Check your permit	Not confirmed	Not confirmed
Gas engine	0%	15% for spark-ignition engines when limits are in ppmvd (40 CFR 60 Subpart JJJJ)	15%	Not confirmed
Waste incinerator	12%	7% (e.g., 40 CFR 60 Subpart Eb, Subpart EEEE)	11% (3% for waste oil)	Not confirmed

Three differences stand out:

• Engines. Japan corrects gas and gasoline engines to 0% O₂, while US SI-engine rules and the EU use 15%. The same engine therefore shows a figure about 3.5 times higher on the Japanese basis (21/6 = 3.5).
• Gas turbines. Japan uses 16% and the US and EU use 15%. The same gas reads 20% higher at 15% O₂ than at 16% (6/5 = 1.2).
• The constant. Japan and the EU write the formula with 21. US EPA rules use 20.9, for example C_adj = C_meas × (20.9 − 7)/(20.9 − %O₂) for 7% O₂. The effect is small: correcting 200 ppm from 3% to 6% O₂ gives 166.7 ppm with 21 and 166.5 ppm with 20.9.

Some limits are not concentrations at all. Subpart KKKK, for instance, also allows output-based limits in lb/MWh, which cannot be compared with a Japanese ppm figure through O₂ correction alone.

Dry Basis, ppm, and mg/Nm3: What Else Must Match

The O₂ reference is only one of four bases that must line up. The other three are moisture, unit, and reference temperature.

Dry vs. Wet Basis

US rules state ppmvd, "parts per million by volume, dry," and EPA defines both C_meas and %O₂ on a dry basis. EU limits are stated after correction for water vapor. Japanese compliance results are commonly reported on a dry gas basis (kawaki gasu, 乾きガス); one municipal incinerator report, for example, gives its values "on a dry gas basis, corrected to 12% O₂."

Flue gas from natural gas firing contains a lot of water vapor, so a wet-basis value reads noticeably lower than a dry one. If a Japanese data sheet does not say "dry," ask. Do not apply the O₂ formula to a wet NOx value and a dry O₂ value at the same time.

ppm vs. mg/Nm3

Japan states NOx limits in volume (cm³/m³, or ppm). The EU and India state them in mass per volume (mg/Nm³), and EU limits express NOx as NO₂. To convert ppm to mg/m³, multiply by the molar mass and divide by the molar volume at the reference temperature:

• At 0°C and 101.3 kPa (EU and Japanese "N" conditions): 1 ppm NO₂ = 46.01 ÷ 22.41 ≈ 2.05 mg/Nm³
• At 20°C (68°F) and 101.3 kPa (US EPA standard conditions under 40 CFR 60.2): 1 ppm NO₂ ≈ 1.91 mg/m³

Correct for O₂ first or last; the order does not matter, as long as both values are on the same dry basis. What does matter is using the right reference temperature. A "Nm³" from Japan or the EU is at 0°C, while "standard" in US rules means 20°C.

Restating a Japanese Supplier's NOx Figure on Your Basis

If you have the raw readings (measured NOx C_s and measured O₂ O_s, both dry), apply your own formula and reference level directly. That is the cleanest method. If you only have a corrected figure, you can move it from one reference to another, because the measured O₂ cancels out:

Follow these steps:

1. Read the Japanese basis. Find the O₂ reference (the "○% kansan" note), dry or wet, and the unit (ppm, or mg/m³N at 0°C).
2. Find your basis. Take the reference O₂, moisture basis, unit, reference temperature, and averaging time from your permit or consent, not from a general rule.
3. Re-correct the O₂ reference with the formula above, or recalculate from the raw readings.
4. Convert units if your limit is in mg/Nm³ or mg/m³, using the reference temperature your rule specifies.
5. Compare like with like. Check that the load condition, fuel, and averaging period of the Japanese test match what your limit covers.

Here are three fictional examples, worked with the constant 21:

• Gas-fired boiler. The supplier guarantees 60 ppm at 5% O₂. At 3% O₂: 60 × (21 − 3)/(21 − 5) = 60 × 18/16 = 67.5 ppm. In EU-style units (0°C, as NO₂), that is about 67.5 × 2.05 ≈ 138 mg/Nm³ at 3% O₂.
• Gas turbine. The test report shows 15 ppm at 16% O₂. At 15% O₂: 15 × (21 − 15)/(21 − 16) = 15 × 6/5 = 18 ppm.
• Gas engine. The data sheet shows 200 ppm at 0% O₂. At 15% O₂: 200 × (21 − 15)/21 ≈ 57 ppm.

The gas engine example shows why the basis matters. A Japanese figure that looks far above a 15% O₂ limit may be well within it once restated, and a gas turbine figure that looks compliant may not be. Treat these results as screening only, and confirm the final comparison with your permit, the permitting authority, or the supplier.

Checklist and Questions for the Japanese Supplier

Use this checklist before you compare a Japanese emission figure with your limit:

• O₂ reference of the Japanese figure (e.g., "O₂ 4% kansan") and of your limit
• Dry or wet basis for both the pollutant and the O₂ reading
• Unit: ppm (cm³/m³N), mg/Nm³, or a mass-rate or output-based unit
• Reference temperature and pressure (0°C, 20°C, or 25°C; 101.3 kPa)
• NOx expressed as NO₂ or as NO, if the limit is in mass units
• Formula constant: 21 or 20.9
• Load, fuel, and operating mode during the test
• Averaging time (instantaneous, 1-hour, daily) and measurement method (JIS K 0104 in Japan)
• Whether the figure is a guarantee, a design value, or a measured result
• Any special formula (no correction, or the 1/4 factor for oxy-fuel furnaces)

Questions to send to the Japanese side:

1. What O₂ reference is the NOx (or dust) value corrected to, and is it the Japanese standard O₂ for this equipment type?
2. Are both the NOx and O₂ values on a dry basis?
3. Can you provide the raw measured NOx and O₂ values from the test, before correction?
4. At what load, fuel, and ambient conditions was the test run, and over what averaging time?
5. Can you restate the guarantee at our reference conditions (O₂ %, dry basis, unit, reference temperature)?

You can adapt this email template for the request:

Limits of This Guide

• The Japanese values are national standards from the Enforcement Regulations of the Air Pollution Control Act. Prefectures can set stricter limits, and older facilities may fall under transitional rules.
• Reference O₂ levels outside Japan vary by rule, state, equipment size, and permit. The comparison table gives examples, not your applicable limit.
• Re-correcting a corrected figure assumes both are on the same dry basis and that the original correction used the standard formula. Working from the raw readings avoids that assumption.
• This article covers NOx and dust concentrations. Japan regulates sulfur oxides (SOx) differently (see the FAQ), and some limits are mass-rate or output-based.
• Compliance decisions belong to the facility's environmental team and the permitting authority. Use this guide to ask the right questions, not as a compliance determination.

FAQ

What if the measured O2 is above 20%?

Enter 20%. Under Japan's rules for dust and NOx, an O_s above 20% is treated as 20%, so a reading of 20.5% goes into the formula as 20. As O_s approaches 21%, the denominator 21 − O_s approaches zero and the corrected value becomes extremely large.

Facilities whose O_n is defined as equal to O_s, or that use C = C_s, are not corrected at all.

What does "corrected to 0% O2" mean?

It is the concentration before any dilution by air. With O_n = 0, the formula becomes C = C_s × 21/(21 − O_s). Japan uses 0% for gas engines and gasoline engines.

For example, a gas engine at 10% O_s with 300 ppm NOx gives 300 × 21/11 ≈ 573 ppm, and that is the value compared with the standard. For the same gas, a 0% figure is always larger than a 6% figure, so match the O₂ basis before comparing reports.

Does Japan apply O2 correction to SOx?

No. Japan regulates sulfur oxides with the "K-value" method, which sets an allowable hourly emission rate from the effective stack height and a regional constant K. The formula is q = K × 10⁻³ × He², where He is the corrected stack height.

Designated areas also have total-emission controls and fuel-use standards. Sulfur in the fuel can also cause low-temperature corrosion in boilers.

How is O2 correction related to the air ratio?

The air ratio m can be estimated from flue gas oxygen as m ≈ 21/(21 − O₂). On that basis, the factor (21 − O_n)/(21 − O_s) reads as "air ratio at measurement ÷ reference air ratio."

The air ratio formula is an approximation, however, so the two do not match exactly. O₂ correction is a regulatory calculation, while the air ratio is an operating value for combustion control.

Running at a lower air ratio, without going too low, reduces the heat carried away by the flue gas.

How do I convert ppm at 15% O2 to ppm at 3% O2?

Multiply by (21 − 3)/(21 − 15) = 3, or by (20.9 − 3)/(20.9 − 15) ≈ 3.03 if your rule uses 20.9. A value of 9 ppm at 15% O₂ is about 27 ppm at 3% O₂. Both values must be on a dry basis.

Sources

• Correction formula, standard O₂ levels, 20% cap, and NOx emission standards: e-Gov, Enforcement Regulations of the Air Pollution Control Act (Japanese) (Articles 3–5, Appended Tables 2 and 3-2)
• Prefectural limits stricter than national standards: e-Gov, Air Pollution Control Act (Japanese) (Article 4)
• Purpose of the correction (preventing dilution with air): Ministry of the Environment, Japan, "Dust Regulations" (Japanese)
• NOx concentration and total-emission controls: Ministry of the Environment, Japan, "Hazardous Substance Regulations" (Japanese)
• SOx K-value regulation: Ministry of the Environment, Japan, "Sulfur Oxide (SOx) Regulations" (Japanese)
• Japanese results reported on a dry gas basis (example): Sano City, incinerator emission measurement results (Japanese)
• Air preheating and checking NOx: Ministry of the Environment, Japan, SHIFT program, measure 121222 "Preheating Combustion Air with Boiler Flue Gas" (Japanese)
• Oxygen content of dry air (20.95%): NASA, "Earth Fact Sheet"
• US 7% O₂ correction with the 20.9 constant (dry basis): 40 CFR 60.2975; 40 CFR 60.58b (Subpart Eb)
• US gas turbine limits in ppm at 15% O₂ or lb/MWh: 40 CFR 60 Subpart KKKK, Table 1
• US spark-ignition engine limits in ppmvd at 15% O₂: 40 CFR 60 Subpart JJJJ, Table 1
• US standard conditions (20°C, 101.3 kPa): 40 CFR 60.2
• Boiler limits at 3% O₂, dry (state/local example): South Coast AQMD, Rules 1146/1146.1 working group presentation
• EU reference O₂ for combustion plants (6%, 3%, 15%) and reference conditions: Directive 2010/75/EU, Annex V, Part 1 (legislation.gov.uk copy)
• EU waste incineration at 11% O₂ (3% for waste oil), NOx as NO₂: Directive 2010/75/EU, Annex VI (legislation.gov.uk copy)
• India thermal power plants corrected to 6% O₂, dry basis (Gazette amendment as reproduced in a tribunal filing): National Green Tribunal, affidavit in OA 203 of 2022