# What is the minimum angle off horizontal before a line visually appears inclined at first glance?

Here is a straight line, which visually looks like a straight line:

At first look (lets say minimum 2–3 sec.) the line below looks straight, but after some time you can see that it is actually an inclined line. You need some time (more then 5–8 sec.) to classify that line as a inclined line.

Here is an inclined line, which looks like an inclined line at first look:

Question: Is there any study that determines the minimum angle at which a line should be inclined to be visually classified at first look as an inclined line?

Citing Muller et al’s, (1955) work on electronic displays, Eastman Kodak’s (1983) Ergonomics Design for People at Work states that people can discriminate 24 different absolute angles of inclination under optimum viewing conditions. This implies that an angle of 360/24 = 15 degrees can be readily classified as inclined rather than flat.

However, I’d say 15 degrees is probably overly conservative. It applies to discriminating one arbitrary angle of inclination from another when each is shown in isolation. Discriminating flat (0 degrees) from inclined is apparently a special case that is easier to do, as indicated by the study cited by Josh where people quickly detected inclinations as small as 0.5 degrees.

Assuming you’re talking about imagery you create in the built environment (e.g., for an information display), there are often vertical and horizontal references to compare the line to (e.g., the edges of a page, the bezel of a monitor, the doorway to a room). In fact, the presence of such references probably defines what “flat” means (e.g., people will still call your first line above “flat” even if they cock their head a bit to look, or even if their respective tablets/laptops are in their laps and not completely level). So, in a built environment (and outside a field-dependence laboratory), detecting an inclined line often has a degree of relative discrimination that I expect helps a lot. As for detecting inclinations in the natural world, well, there’s a reason carpenters use levels.

If you’re building an information display (e.g., a graph), you can go to smaller angles by adding reference marks, as shown below.

This changes the viewers’ task from recognizing an inclination to recognizing vertical gap size. People can spot a gap as small as few arc-minutes of visual angle.

References:

Muller PF Jr, Sidorsky RC, Slivinski AJ, Alluisi EA, & Fitts PM (1955). The symbolic coding of information on cathode ray tubes and similar displays Technical Report 55-375. Wright Air Development Center, Wright-Patterson AFB, October.

Eastman Kodak Company (1983). Ergonomic design for people at work. New York: Van Norstrand.(link)

• Wait, what? 15 degrees sounds like a lot. Am I missing something here? Are we talking the kind of degrees where 360 degrees equals a whole circle? Commented Jul 21, 2014 at 14:42
• Yeah, this doesn't fit with other research that has looked at this kind of perceptual judgment.
– Josh
Commented Jul 21, 2014 at 14:42
• In the study referenced in my answer below, exposure time was 600ms.
– Josh
Commented Jul 21, 2014 at 19:30
• I believe the OP was concerned with detecting an inclined line in isolation, not detecting a change to an inclined line. I've edited my answer to clarify the application. Commented Jul 21, 2014 at 21:01
• The judgments in the study below were also in isolation. Stimuli were presented 5s apart and participants were comparing to their 'memory' of a horizontal line, not to another visually presented line.
– Josh
Commented Jul 21, 2014 at 21:14

Vogels and Orban (1985) asked subjects to complete several thousand angle judgments at near-principal angles (horizontal or vertical). They found that the just-noticeable difference (JND), the threshold at which people could reliably detect deviation from a horizontal line, was 0.5 degrees after a 600ms exposure to the stimulus.

The real purpose of their study was to compare learning effects for judgments of deviations from principal orientations with judgments of deviations from oblique (diagonal) angles. They found that while people could double their sensitivity over extensive training to small changes in oblique angles, the principal angles showed no such learning effects, as you can see in this graph:

Additionally, the threshold for detection of changes from principal angles was about twice as good as the oblique angles, even after 5000 trials of practice discriminating oblique angles.

Reference

Vogels, R., & Orban, G. A. (1985). The effect of practice on the oblique effect in line orientation judgments. Vision research, 25(11), 1679-1687.

• So I think you are saying that the principal angle detection showed no improvement with practice, and the other angles started off twice as bad but improved to be as good as the principal angles? Seems like a tautology to me: we are better at some things than others, have inherent limitations, and can become good at most things we are bad at. Is there more to it?
– user9634
Commented Oct 5, 2016 at 12:07