Fractional effective concentration

Fractional effective concentration (FEC) is the ratio between the concentration of a fire product at a given moment and the concentration that is expected to make escape significantly less efficient. The concept comes from the toxicity chapter of the Handbook of Fire Protection Engineering of the Society of Fire Protection Engineers (SFPE). There, the smoke concentration is expressed as a fraction of the concentration considered to affect escape efficiency significantly. When the fraction reaches 1, the effect is predicted to occur. The same method applied to irritant gases is called the fractional irritant concentration (FIC).

Both fractions are tools for checking tenability criteria, the limits used to judge whether conditions in a building still allow people to escape. They differ from the fractional effective dose (FED), which adds up an inhaled dose over time. A concentration fraction looks only at the conditions of the moment. The pain caused by irritant smoke and the loss of sight in dense smoke depend on how strong the exposure is, not on how long it has lasted. In a worked example in the handbook, smoke obscuration and irritancy were the first hazards to reach their limits, while collapse from asphyxiant gases was predicted only during the fifth minute.

Concentration and dose

Toxicologists describe the effect of an inhaled substance with two basic quantities: its concentration in the air and the duration of the exposure. For many substances the effect depends on the dose, which is roughly the product of concentration and time. The FED method uses this idea. The dose received in each short period of the fire is divided by the dose that causes the effect, and these fractions are added until they reach 1. The approach works well for carbon monoxide: monkeys exposed to concentrations between 1000 and 8000 parts per million (ppm) became unconscious after inhaling about the same dose of roughly 27,000 ppm·min.

Other effects do not build up in this way. Irritant smoke products cause pain in the eyes and upper airways as soon as the exposure starts, and the severity depends on the concentration. As the exposure continues, the effects usually become weaker rather than stronger, because the person adapts to the painful stimulus although the dose keeps rising. Low oxygen and high carbon dioxide behave in a similar way once the lungs and blood have adjusted, which usually takes a few minutes. After that, their effect depends on the concentration and hardly changes with time. For this reason, sensory irritation is assessed with a fraction of the current concentration rather than with a dose.

The toxicity chapter of the SFPE Handbook distinguishes three main toxic effects in fires. Irritant gases can impair escape or incapacitate people through their concentration. Asphyxiant gases cause confusion and loss of consciousness through the dose inhaled. Lung irritants can also cause death after the fire through inflammation of the lungs, once a sufficient dose has been inhaled. Time to impaired escape, incapacitation and death is estimated by combining FIC and FED calculations for smoke, irritants and asphyxiant gases with curves of concentration against time. The chapter describes this combination as a physiological model for predicting the time to incapacitation of occupants in full-scale fires, and it is central to its treatment of fire toxicity.

The motivation is practical. Surveys in the United Kingdom showed that about half of the people killed in dwelling fires were recorded as overcome by smoke and toxic gases rather than by heat and burns. The same applied to about a third of those injured. Statistics of this kind were a major reason for developing methods to assess the hazards of smoke inhalation.

Smoke obscuration

Dense smoke affects the choice of exit, the decision to escape, the ability to find the way and the walking speed of occupants. The density of smoke is usually expressed as an optical density, the weakening of light per metre of path, with the unit m⁻¹. In practice this quantity is used more than any other to judge whether people can still find their way in smoke.

Experiments by Jin in Japan, in which people walked along a smoke-filled corridor, showed how strongly smoke slows movement. In non-irritant smoke, the walking speed fell from about 1.2 m/s without smoke to 0.3 m/s at an optical density of 0.5 per metre. Under these conditions people felt their way along the walls as if they were in darkness. In irritant smoke, made by heating wood chippings, the speed dropped to the same value at an optical density of only 0.2 per metre, and the experience was more distressing. Studies of fires in buildings found that about 30 per cent of people turned back rather than pass through smoke, on average at a visibility of about 3 m.

To turn these findings into a single design check, the handbook divides the optical density of the smoke by a limiting value. The limit is 0.2 per metre for small enclosures with short travel distances, which corresponds to a visibility of about 5 m. For large enclosures with long travel distances it is 0.08 per metre, which corresponds to about 10 m. The fraction for visual obscuration is then:

$${\mathrm{F}\mathrm{E}\mathrm{C}}_{\mathrm{s}\mathrm{m}\mathrm{o}\mathrm{k}\mathrm{e}}=\frac{OD}{0.2}\text{(small enclosures)},{\mathrm{F}\mathrm{E}\mathrm{C}}_{\mathrm{s}\mathrm{m}\mathrm{o}\mathrm{k}\mathrm{e}}=\frac{OD}{0.08}\text{(large enclosures)}$$

Symbol	Description	Unit
${\mathrm{F}\mathrm{E}\mathrm{C}}_{\mathrm{s}\mathrm{m}\mathrm{o}\mathrm{k}\mathrm{e}}$	fractional effective concentration for visual obscuration	dimensionless
$OD$	optical density of the smoke per metre of path	m−1

When the fraction reaches 1, the obscuration is predicted to be severe enough to affect escape attempts seriously. The two limits reflect the size of the space. In large spaces, occupants who do not know the building need to see much further to orient themselves and find an exit.

A simple rule of thumb links optical density to visibility. For objects that reflect light, the visibility in metres is about 1 divided by the optical density, and for objects that emit light, such as illuminated exit signs, about 2.5 divided by it. With this rule, the small-enclosure limit of 0.2 per metre gives a visibility of 5 m for a reflecting sign and 12.5 m for an illuminated one.

Some sources state smoke density as an extinction coefficient instead. In the pairs of values given in the handbook, the extinction coefficient is about 2.3 to 2.5 times the optical density per metre. An example is 1.15 m⁻¹ against 0.5 per metre. A limit quoted on one scale is therefore not directly comparable with a limit quoted on the other.

Irritant gases

Smoke irritants consist of inorganic acid gases, such as hydrogen chloride, and organic compounds, mainly small aldehydes such as formaldehyde and acrolein. More than twenty irritants have been found in smoke. The yield of acid gases depends mainly on the chemical elements in the burning material, while the yield of organic irritants depends mainly on the burning conditions. Smouldering fires and flaming fires with too little air tend to produce irritant smoke, while efficient, well-ventilated flaming fires tend to produce non-irritant smoke.

Sensory irritation is a painful stimulation of the eyes, nose, throat and lungs. It ranges from mild eye irritation to severe pain in the eyes and airways, with tears, involuntary closing of the eyes, coughing and difficulty in breathing. Irritant gases are often acid gases, in particular compounds of the halogens chlorine, fluorine and bromine, and they hamper both sight and breathing during escape.

For hydrogen chloride, concentrations of roughly 100 to 500 ppm are considered painfully irritant and may slow escape without preventing it. At about 1000 ppm and above, the effects may be so severe that escape becomes impossible. People differ widely in their response. Most are expected to be affected at about 200 ppm, some already at about 100 ppm, while others tolerate more than 500 ppm without serious effects on escape.

Because all these irritants can damage lung tissue, their effects are assumed to add up. The fractional irritant concentration therefore divides the concentration of each irritant at a given moment by the concentration that impairs escape, and adds the fractions of all irritants present. With the limiting concentrations of the handbook, the sum reads: $$\mathrm{F}\mathrm{I}\mathrm{C}=\sum _i\frac{C_i}{C_{i,\mathrm{l}\mathrm{i}\mathrm{m}}}=\frac{C_{\mathrm{H}\mathrm{C}\mathrm{l}}}{200}+\frac{C_{\mathrm{H}\mathrm{B}\mathrm{r}}}{200}+\frac{C_{\mathrm{H}\mathrm{F}}}{200}+\frac{C_{\mathrm{S}{\mathrm{O}}_{\mathrm{2}}}}{24}+\frac{C_{\mathrm{N}{\mathrm{O}}_{\mathrm{2}}}}{70}+\frac{C_{\mathrm{a}\mathrm{c}\mathrm{r}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{i}\mathrm{n}}}{4}+\frac{C_{\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{d}\mathrm{e}\mathrm{h}\mathrm{y}\mathrm{d}\mathrm{e}}}{6}+\dots$$

Symbol	Description	Unit
$\mathrm{F}\mathrm{I}\mathrm{C}$	total fractional irritant concentration	dimensionless
$C_i$	concentration of irritant $i$ in the breathing zone at the moment considered	ppm
$C_{i,\mathrm{l}\mathrm{i}\mathrm{m}}$	concentration of irritant $i$ predicted to impair escape in half the population	ppm

Gas	Impairs escape in half the population (ppm)	Incapacitates half the population (ppm)
Hydrogen chloride (HCl)	200	900
Hydrogen bromide (HBr)	200	900
Hydrogen fluoride (HF)	200	900
Sulphur dioxide (SO2)	24	120
Nitrogen dioxide (NO2)	70	350
Acrolein	4	20
Formaldehyde	6	30

The table lists the limiting concentrations together with the concentrations expected to incapacitate half of the exposed population. A total FIC of 1 is the tenability limit at which escape is expected to be impaired. A total of 0.3 is suggested to allow nearly all exposed people to escape safely, including vulnerable individuals.

For incapacitation the chapter gives several values: about 3 to 5 in one passage, a factor of about four or more in another, and about 5 to 10 in the worked example. In the table above, the incapacitating concentration of each gas is 4.5 to 5 times the concentration that impairs escape. Where acrolein and formaldehyde have not been measured, a term based on a smoke density of 0.5 per metre may be used as an indication of irritancy. In small-scale tests, the RD₅₀ of a material's smoke, the concentration that halves the breathing rate of mice, is taken as a total FIC of about 0.5 for humans.

Worked example

The handbook illustrates the method with the first six minutes of a fire in an armchair of polystyrene with polyurethane cushions and covers. The chair stood in a room of 39 m³ with an open doorway, and smoke and the main gases were measured in the doorway at a height of 2.1 m. The concentrations of hydrogen chloride, acrolein and formaldehyde were estimates, added to illustrate the calculation. In the third minute, the smoke had an optical density of 0.5 per metre, with 150 ppm hydrogen chloride, 2.0 ppm acrolein and 3.0 ppm formaldehyde. For a small enclosure, the smoke fraction follows from the limit of 0.2 per metre, and the irritant fraction from the limiting concentrations of the three gases: $$\begin{array}{rl}{\mathrm{F}\mathrm{E}\mathrm{C}}_{\mathrm{s}\mathrm{m}\mathrm{o}\mathrm{k}\mathrm{e}}& =\frac{0.5}{0.2}=2.5\\ \mathrm{F}\mathrm{I}\mathrm{C}& =\frac{150}{200}+\frac{2.0}{4}+\frac{3.0}{6}=0.75+0.50+0.50=1.75\end{array}$$

Both values are above 1, so in this minute the smoke would be expected to impair and possibly prevent escape. The handbook's table gives a total FIC of 1.83 for the same minute, because its hydrogen chloride term is 0.83 instead of 0.75. The conclusion is the same.

One minute earlier, the smoke had 0.2 per metre with 50 ppm hydrogen chloride, 0.8 ppm acrolein and 1.2 ppm formaldehyde. The same method then gives an FEC for smoke of exactly 1 and a total FIC of 0.65. The limit of 0.3 for vulnerable people had therefore already been passed in the second minute, as the handbook also concludes. According to the rule of thumb for visibility, 0.2 per metre corresponds to about 5 m for a reflecting sign.

Smoke fraction (FEC) and total irritant fraction (FIC) during the first four minutes of an armchair fire, compared with the limits of 0.3 and 1. Based on Purser (2002), pp. 2-132–2-133.

Use in hazard analysis and design

In a hazard analysis, the FEC for smoke, the FIC for irritants and the FED for asphyxiant gases and heat are each plotted against time. A limit is reached when a line crosses 1. In a full-scale test with an armchair fire in the lounge of a house, the ionisation smoke detector responded after 0.5 minutes and the optical detector after 1.5 minutes. The line for irritant smoke crossed its limit at about 1.5 minutes. From then on, eye pain, smoke and breathing difficulties would hamper, but probably not prevent, an occupant from leaving the room. The line for obscuration alone, treating the smoke as non-irritant, reached its limit of 2 m visibility one minute later.

In the worked example, the curves rise very steeply once they pass 1. As a result, even if the true incapacitating concentrations were higher than the chosen limits, the predicted time of incapacitation would change only a little. The limits apply in the breathing zone of an occupant, so some time passes between ignition and the moment they are reached. In the worked example, the head of the occupant was assumed to be in the smoke at all times. A more refined analysis can allow for a lower position in the room when the height of the smoke layer is known.

The time at which the first tenability criterion is exceeded defines the available safe egress time in the Australian and New Zealand verification methods. Their criteria use other quantities than concentration fractions. In New Zealand, C/VM2 (second edition, 2025) measures tenability at 2.0 m above the floor with the FED for carbon monoxide, the FED for thermal effects and visibility. In Australia, the Fire Safety Verification Method Standard (2022) uses a thermal FED of 0.3 and a visibility of 10 m. The visibility limit drops to 5 m in rooms smaller than 100 m² or where the exit is no more than 5 m away. Both documents note that visibility is usually the first criterion to be exceeded.

Irritant smoke enters these methods in other ways. The Australian data sheets (2020) handle it through the walking speed of occupants, which is multiplied by a factor of 0.3 at a visibility of 10 m with illuminated signs. The tenability limit itself is not changed. In the Netherlands, no limits are formally laid down. For escape through mixed smoke in non-enclosed spaces, the explanatory notes to the Dutch Building Decree (Bbl) use a visibility of at least 30 m for illuminated objects. In corridors, a visibility of only 5 m is often accepted.

Limits and uncertainty

The limits behind the FEC and FIC cannot be verified directly, because the human experiments needed to do so cannot be performed. They rest on a small number of human exposures at low concentrations, on accidents, on animal tests and on the judgement of physiologists. The proposed values are very similar to those of an expert panel of toxicologists in an international standards committee. Some critics consider them too low for practical design, while other expert groups have proposed similar or even lower limits. For hydrogen chloride, the Emergency Response Planning Guideline level 2 (ERPG-2) of the American Industrial Hygiene Association is 20 ppm. This level is meant to protect the ability to take protective action during an exposure of up to one hour, and it is an order of magnitude below the design limit of the handbook.

Sensitivity varies between people. About 15 per cent of children and 5 per cent of adults have asthma, and people with asthma can react with a severe narrowing of the airways to brief exposures at very low irritant concentrations. A limit that affects half of the population is therefore not a safe value for everyone, which is why the lower total of 0.3 is suggested. The assumption that all irritants add up is a simplification, made because data on the effects of irritant mixtures are lacking.

The smoke limits also involve judgement. Jin suggested an extinction coefficient of 0.15 m⁻¹ for occupants who know the escape route and 0.5 m⁻¹ for those who do not. Rasbash proposed a visibility limit of 10 m. Babrauskas suggested an extinction coefficient of 1.2 m⁻¹ for fires in dwellings. Large spaces, unfamiliar occupants and highly irritant smoke call for stricter limits, and the complexity of the space, the lighting and the visibility of signs also play a part. The rule of thumb that converts optical density into a visibility distance is itself only approximate.

Common misconceptions

An FEC or FIC of 1 does not mean collapse or death. It marks the point at which escape becomes impaired, while incapacitation by irritants is expected only at several times this value. A second misconception is that the fraction behaves like a dose. The FED can only grow during an exposure, but a concentration fraction describes the conditions of the moment and falls again when the concentration drops. In the worked example, the hydrogen chloride term fell from 1.39 to 1.11 between the fifth and sixth minutes as its concentration decreased.

The amount of visible smoke is also a poor guide to irritancy. Some fires produce large amounts of sooty smoke that blocks the view but hardly irritates. In other cases a highly irritant atmosphere has been reported with little or no visible smoke. Finally, the fractions for smoke, irritants, asphyxiants and heat are not added into one number. Each hazard has its own line, and a tenability limit is reached when any of these lines crosses 1.

See also

• Visibility in smoke
• Optical density
• Haber's rule
• Oxygen depletion
• Carbon dioxide

References

• Australian Building Codes Board. (2020a). Data sheets: Fire Safety Verification Method (Handbook annex, Print version 1.1).
• Australian Building Codes Board. (2022). Fire Safety Verification Method Standard 2022.
• Ministry of Business, Innovation and Employment. (2025b). Verification Method C/VM2: Framework for fire safety design (2nd ed.).
• Purser, D. A. (2002). Toxicity assessment of combustion products. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 2-83–2-171). National Fire Protection Association; Society of Fire Protection Engineers.
• Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.