Seeing and using exit signs

Information given to occupants must be perceived, paid attention to and comprehended before they act on it (Kuligowski and Kinateder 2026, Ch. 65, p. 2113); our reading: this applies to exit signs. Visibility through smoke gives Jin’s law V = C/K for the distance at which a sign is barely seen. Below are the steps between seeing a sign and acting on it, the waypoint method that applies Jin’s law along a line of sight to a sign, and the studies that measured how often occupants detect and follow signs.

Terms

The sources use the same words for different thresholds. This page uses:

• Seen. The sign is barely visible: Jin’s obscuration threshold (Seeing a sign versus reading it). Börger et al. (2024, Table 2, p. 9) call a sign that passes their test “visible”. Models › Wayfinding calls it legible.
• Detected. The occupant noticed the sign during a trial, as judged from questionnaires and video (Xie et al. 2012, p. 371) or from eye fixations (Zhu et al. 2021, p. 4).
• Read or identified. The occupant can make out the content of the sign: its letters, symbol or arrow. Jin (1978, Fig. 7, p. 143) and Xie et al. (2007) call this legible. Models › Wayfinding uses “read” and “reading distance” for the seeing test instead.
• Followed. The occupant took the direction the sign gives. The sources also say complied or accepted.

From seeing a sign to using it

The decision model in SFPE Ch. 65 puts perception, attention and comprehension before any protective action (Kuligowski and Kinateder 2026, p. 2110). Xie et al. (2012, p. 368) split sign use into visibility, detection (‘see the sign and correctly interpret the information’) and acceptance (following it).

Our reading: no study measures all of these steps for one sign in smoke. Each measures one or two of them:

• Seen: the smoke density at which a sign of known location vanishes. Jin 1970–1972 (see Visibility).
• Detected: the share of people who noticed the sign. Xie et al. 2012; Galea et al. 2014; Zhu et al. 2021.
• Read: the sign size, distance or smoke density at which the content is made out. Wong and Lo 2007; Xie et al. 2007; Cheung et al. 2026 (thresholds); Fujii et al. 2014 via SFPE Ch. 68.
• Understood and followed: the share of those who detected the sign and took its direction. Xie et al. 2012; Galea et al. 2014; Zhu et al. 2021.

Our reading: Xie et al. (2012) report interpretation and following together (“correctly interpret and follow”, p. 375); Galea et al. (2014) report only that those who saw the sign “chose to go left following the direction indicated by the sign” (p. 1135). Neither separates understanding from following.

The waypoint method

Börger, Belt and Arnold (2024) apply Jin’s law along the line of sight from each grid cell of a floor plan to each exit sign, instead of at the cell alone. They state that visibility “is not considered to be a local quantity” (p. 3). The equations below are in their notation; σ̄ is a mean extinction coefficient, written \(\bar K\) in the notation table.

The map. A cell i, j is marked 1 for the sign at waypoint \(W_k\) at time t when the available visibility reaches the distance to the sign (Eq. 2, p. 3):

$$ M^t_{i,j,k} = \begin{cases} 1, & V^t_{i,j,k} \ge L_{i,j,k},\\ 0, & \text{otherwise,} \end{cases} $$

with \(L_{i,j,k}\) the horizontal distance between cell and sign; the vertical height difference is ignored (Eq. 3, pp. 3–4). A cell is passable at time t if at least one sign is visible from it (Eq. 4, p. 4).

The view angle. Signs are treated as Lambertian radiators, “although this assumption is highly simplified depending on the sign’s light source and surface” (p. 4). The visual distance falls with cos θ, citing DIN ISO 3864-1, and a sign cannot be seen at θ ≥ 90° (Eq. 7, p. 4). They motivate the factor by the smaller projected area of the sign at an angle, and hold it valid in smoke because Beer–Lambert attenuation is linear in intensity (p. 4):

$$ A_{i,j,k} = \max\!\left(0,\ \frac{\sin\alpha_k\,(X_i - X_k) + \cos\alpha_k\,(Y_j - Y_k)}{L_{i,j,k}}\right) $$

with \(\alpha_k\) the rotation angle of the sign’s observation normal. Only the horizontal angle is taken into account. Signs above doors sit above the evaluation level, which the authors call “a particular though minor degree of uncertainty” (p. 5).

The one regression of visibility on the angle in smoke that we found is reported second-hand in the SFPE Handbook (Yamada and Akizuki 2026, Ch. 68, Eq. 68.2, p. 2205), from Fujii et al. (2014, in Japanese; not read):

$$ V = -0.59 + \frac{3.68}{C_s} + 137.19\,S\cos\theta $$

with V the visible distance [m], \(C_s\) the extinction coefficient [1/m] (Ch. 68: “optical smoke density”), S the sign area [m²] and θ the yaw angle [degree]; adjusted \(R^2\) = 0.734. Twenty young volunteers with visual acuity above 1.0 viewed a sign of 251 cd/m² in white smoke at 114 lx, at yaw angles of 0–80° (Fig. 68.9, p. 2205). They had to “recognize the pictogram” (p. 2204), so this is a reading threshold, like Xie et al. (2007), not a law for seeing a sign. The angle enters through the sign-area term, added to the smoke term. Our arithmetic, assuming S ≈ 0.026 m²: in light smoke (\(C_s\) ≈ 1 1/m) the angle reduces V much less than cos θ; near \(C_s\) = 5 1/m the two are close.

The obstruction. \(U_{i,j,k}\) is 1 if the cell is not hidden from the sign by a wall, 0 otherwise. It comes from a ray cast from the sign and rasterised on the grid; anti-aliased lines keep the collision detection reliable where obstruction cells do not form a closed barrier (p. 5).

The mean extinction. Along the line of sight (Eq. 8, p. 5):

$$ \bar\sigma^t_{i,j,k} = \frac{K_m(\lambda)\int_0^{L_{i,j,k}} \rho^t_{s,k}(l)\,dl}{L_{i,j,k}} $$

with \(\rho_s\) the smoke density and \(K_m\) the mass-specific extinction coefficient; they note that 8700 m²/kg for red light at 633 nm is “widely adopted” as the default of many fire models (p. 5). Assuming the same path length in every traversed cell turns the integral into the arithmetic mean over the cells \(P_\text{cells}\) (Eq. 9, p. 5):

$$ \bar\sigma^t_{i,j,k} = \frac{K_m(\lambda)}{|P_\text{cells}|}\sum_{p\in P_\text{cells}} \rho^t_{s,k,p} $$

They describe the loss of accuracy as “tolerable, given a sufficiently fine discretisation of the floor” (p. 5).

The visibility. Eq. 10 (p. 5), as printed:

$$ V^t_{i,j,k} = \min\!\left(U_{i,j,k}\cdot A_{i,j,k}\cdot\frac{C_k}{\bar\sigma^t_{i,j,k}},\ V_{\max}\right) $$

\(C_k\) is Jin’s constant for the sign, “usually C = 3 for reflecting signs and C = 8 for light emitting signs” (Table 1, p. 5).

The cap. \(V_{\max}\) is “usually 30 m” (p. 4). The authors write that “in performance based design, visibility is often limited to an arbitrary upper boundary value” of 30 m, “since Jin’s relation is purely empirical and would imply an infinite visibility in the absence of smoke”, and add that “the exit signs have a maximum visual distance even in a smoke-free environment” (p. 5). They give no sign size, luminance or measurement for that distance. In their comparison, the FDS visibility slice “was calculated with C = 3 and truncated at a maximum boundary of 30 m” (Fig. 6 caption, p. 7). The paper names no FDS parameter and does not say whether FDS or the post-processing applied this truncation.

The plane. The eye is assumed at the height of the signs, and the extinction is read from one horizontal slice “at a height of 2 m above the floor level” (p. 4). The authors call this and the 2D approach “technical limitations” for future work (p. 4).

The authors also write that Jin’s model “needs to be fundamentally revised”: it does not account for the different absorption and scattering of flaming and smouldering smoke, and gives limited scope for ambient light (p. 9).

Detection and reading studies

Our reading: none of these studies used real fire smoke with occupants under threat.

Study	Setting	People	Smoke
Xie et al. 2007	39 m corridor, signs turned to 0–80°	48	none
Wong and Lo 2007	18 m corridor, normal and emergency light	30	none
Xie et al. 2012	university building, instructed trials	68	none
Galea et al. 2014	same building, dynamic sign	53	none
Zhu et al. 2021	T-junction drills, eye tracking	23–33 per drill	none
Kobes et al. 2010	hotel, unannounced night drills	83	visible smoke in two scenarios
Cheung et al. 2026 (thresholds)	smoke chamber, three sign types	5	white smoke

Reading distance and the observation angle (Xie et al. 2007)

Building regulations implicitly treat the region from which a sign can be read, the visibility catchment area (VCA), as a semicircle centred on the sign, independent of the observation angle (pp. 48 and 62). Xie et al. assume instead that the eye resolves a fixed minimum angle; the VCA is then a circle approximately tangent to the sign (Eq. 4, p. 47; p. 48), with a diameter about equal to the radius of the regulatory semicircle (p. 48).

Forty-eight volunteers, 29 men and 19 women, walked towards a sign in a 39 m corridor under strong artificial light until they could resolve half the letters. The sign was turned to 0°, 30°, 60°, 70° and 80° (pp. 49–51). For the three signs, the mean distance fell from 19.8–33.1 m at 0° to 4.6–6.3 m at 80° (Table 2, p. 52). The data form “a slightly flattened circle” (p. 53). The luminance of the signs was not considered (p. 49).

Our arithmetic: for Sign 1, cos 60° × 23.38 m = 11.7 m, while 14.82 m was measured (Table 2), so at large angles the data lie above a pure cos θ law. The authors find the data close to their theoretical circle (p. 53), which is itself a cos θ law (our reading of Eq. 4). This is a reading threshold in clear air; it does not test the cos θ factor of the waypoint method, which applies to seeing in smoke. Eq. 68.2 under The view angle is also a reading threshold, measured in smoke.

Detected, identified, identified with confidence (Wong and Lo 2007)

Thirty volunteers aged 18–55 looked at signs at the end of an 18 m corridor, in clear air (p. 1837). For each sign they reported whether the content was detected, identified or identified with confidence; the measured quantity is the height of the sign content needed for each (p. 1838). Under normal lighting, 115 lx on the floor, identification needed 30–40 mm; under emergency lighting, 5 lx, it needed 53–60 mm (p. 1840; lighting levels in the note to Table 3, p. 1839). Under emergency lighting, detection needed 31–37 mm (p. 1840), so the gap between seeing and reading the content was measured directly. Their ‘detected’ is a threshold for a sign at a known location, closer to seen above than to detected in the field studies.

Detection and following in a building (Xie et al. 2012)

Sixty-eight people, 41 unfamiliar and 27 familiar with the building, were told to leave a university building as quickly as possible, one at a time, without running, by any route they chose (p. 370). The signs were reflective, 0.1 × 0.3 m, in well-lit areas above 100 lx (p. 369). Whether a person detected a sign was judged mainly from a questionnaire, checked against video (p. 371).

Pooled over two decision points, so that each person counts twice:

• 38 % (31/82) of the unfamiliar and 30 % (16/54) of the familiar encounters detected the sign;
• of those who detected it, 97 % (30/31) and 94 % (15/16) “correctly interpret and follow the information conveyed by the sign” (p. 375).

At the sign approached head-on, unfamiliar people who detected it decided in 2.6 s on average, those who did not in 5.6 s (Table I, p. 372). The authors note that the earlier buildingEXODUS model assumed that agents inside the VCA see the sign and then comprehend and follow it, “ideal assumptions and not based on real-world data” (p. 376).

A dynamic sign (Galea et al. 2014)

The same set-up, with a sign that added lit, flashing elements, was run with 53 people unfamiliar with the building (pp. 1130 and 1138). At the first decision point, 41 (77 %) said they saw the sign, and all of them followed it, against 38 % detection for the static sign (p. 1135).

Detection by eye tracking, and following other people (Zhu et al. 2021)

Participants wore eye-tracking glasses, and a sign counted as detected when the gaze stayed on it longer than 0.1 s (p. 4). Ten drills of 23–33 participants each met a T-junction with the sign at the bottom or the top, and 0, 1 or 3 “disturbers”, strangers or acquaintances (Table 1, p. 3). For the top sign, detection was below 20 % with no disturbers, 41 % with one and 33 % with three (p. 4). Among those who detected the sign, about 20 % followed the disturbers instead (22 %, p. 6; “around 20 %”, p. 7). The authors state that the probabilities hold only for the crowds and environment tested (p. 16).

The SFPE Handbook describes a related experiment by Zhu et al., from a room into a corridor, in which participants complied with the sign more often when alone or with three actors than with one actor (Kuligowski and Kinateder 2026, Ch. 65, p. 2123).

Exit choice with smoke and low signs (Kobes et al. 2010)

Eighty-three volunteers staying overnight in the hotel (p. 540) were woken at night by a phone call and told to leave. The scenarios were: no smoke with ceiling-level signs (20 people), smoke poured into the corridor from a room with ceiling-level signs (39), and smoke with signs at floor level (24) (pp. 539–540, Table 1). The nearest fire exit was used by 45 %, 64.1 % and 75.0 % (p. 546). Of the people who said they had used the exit signs, 22.2 % in the first and 33.3 % in the second scenario did not leave by the nearest fire exit, against 6.7 % with floor-level signs (p. 547). The authors find self-assessments and interviews after an evacuation “a disputable method” and real-time observation more reliable (abstract, p. 537).

Sign types in smoke (Cheung et al. 2026, thresholds)

Cheung et al. (2026, Visibility performance thresholds of exit signs) tested an internally illuminated, a photoluminescent and a reflective exit sign in a smoke chamber. Five men aged 25–39, with visual acuity 0.8 to above 1.2, adjusted the light until they could identify the running-man symbol or read 28 mm text (§2.2–2.3, pp. 3–4). Our reading: this is a reading threshold; the authors compare their values with Jin’s obscuration threshold. They report σV = 3–7 for the lit sign and 0.5–2 for the photoluminescent and reflective signs (abstract, p. 1). The observers knew where the sign was (§2.4, p. 4). Smaller details, such as 16 mm text or arrows, “were often unrecognizable in dense smoke or at longer distances”, so a sign “may be detected as glowing objects” while its information is not conveyed (§4.1, p. 9).

Signs among other lights

A field survey in an underground shopping mall found exit signs “often masked by other background light noises” (Yamada and Akizuki 2026, Ch. 68, p. 2216).

Known limits

• Laboratory and drill conditions. The detection studies used clear air; Kobes et al. used smoke poured into a corridor during an unannounced drill. Our reading: no study above measured detection or following in real fire smoke.
• Known sign locations. Jin’s observers and those of Cheung et al. (thresholds, §2.4, p. 4) knew where the sign was; for Jin’s data, see Visibility › Known limits. Cheung et al. (thresholds) write that this may overestimate visibility (§4.1, p. 9).
• No threat of fire. Xie et al. (2012, p. 370) state that their method examines sign use “in ideal conditions”, without fire effluent or interaction with other occupants. Our reading: instructed trials and drills carry no real threat of fire, like the stated-choice studies on Exit choice › Known limits.
• Binary and graded outcomes. Jin’s threshold and the waypoint map are yes or no. Wong and Lo grade the response in three steps, and the field studies report probabilities of detecting and following.
• Self-report. Detection in Xie et al. (2012) and Galea et al. (2014) is mainly what participants said afterwards; Kobes et al. question that method, and Zhu et al. measure gaze instead.
• Small samples. Cheung et al. (thresholds) had five observers; Zhu et al. state that their values hold only for the people and setting tested.

How pyFDS-Evac uses this: a sign-legibility test, a variant of Börger et al.’s method, decides which neighbouring nodes an agent learns; the coded form and where it departs from the paper are on Models › Wayfinding.

How it is verified: Familiarity.

Sources

• Börger, K., Belt, A., & Arnold, L. (2024). A waypoint based approach to visibility in performance based fire safety design. Fire Safety Journal, 150, 104269. Eqs. 2–4 and 7–10, pp. 3–5; Table 1, p. 5; Fig. 6, p. 7; Table 2 and conclusions, p. 9. doi:10.1016/j.firesaf.2024.104269
• Cheung, W. K., Bielawski, J., Arnold, L., Huang, X., & Węgrzyński, W. (2026). Visibility performance thresholds of exit signs in smoky indoor environments. Fire Safety Journal, 163, 104779. doi:10.1016/j.firesaf.2026.104779
• Galea, E. R., Xie, H., & Lawrence, P. J. (2014). Experimental and survey studies on the effectiveness of dynamic signage systems. Fire Safety Science, 11, 1129–1143. doi:10.3801/IAFSS.FSS.11-1129
• Kobes, M., Helsloot, I., de Vries, B., Post, J. G., Oberijé, N., & Groenewegen, K. (2010). Way finding during fire evacuation; an analysis of unannounced fire drills in a hotel at night. Building and Environment, 45, 537–548. doi:10.1016/j.buildenv.2009.07.004
• Kuligowski, E. D., & Kinateder, M. (2026). Human behavior in fire in the built environment. SFPE Handbook of Fire Protection Engineering, 6th ed., Ch. 65. pp. 2110, 2113 and 2123. doi:10.1007/978-3-031-59212-6_65
• Wong, L. T., & Lo, K. C. (2007). Experimental study on visibility of exit signs in buildings. Building and Environment, 42, 1836–1842. doi:10.1016/j.buildenv.2006.02.011
• Xie, H., Filippidis, L., Gwynne, S., Galea, E. R., Blackshields, D., & Lawrence, P. J. (2007). Signage legibility distances as a function of observation angle. Journal of Fire Protection Engineering, 17, 41–64. doi:10.1177/1042391507064025
• Xie, H., Filippidis, L., Galea, E. R., Blackshields, D., & Lawrence, P. J. (2012). Experimental analysis of the effectiveness of emergency signage and its implementation in evacuation simulation. Fire and Materials, 36, 367–382. doi:10.1002/fam.1095
• Yamada, T., & Akizuki, Y. (2026). Visibility and human behavior in fire smoke. SFPE Handbook of Fire Protection Engineering, 6th ed., Ch. 68, Eq. 68.2 and Fig. 68.9, p. 2205; p. 2216. doi:10.1007/978-3-031-59212-6_68
• Zhu, Y., Chen, T., Ding, N., Chraibi, M., & Fan, W.-C. (2021). Follow people or signs? A novel way-finding method based on experiments and simulation. Physica A, 573, 125926. doi:10.1016/j.physa.2021.125926

Cited through Ch. 68, not read: Fujii, Sano and Ohmiya (2014), Journal of Environmental Engineering (AIJ), 79(702), 639–648, in Japanese.

Jin (1970, 1972, 1978) and Cheung et al. (2026, Reappraisal of Jin’s visibility through fire smoke experiment) are listed on Visibility through smoke.