# How long does it take to read a sentence with X number of characters?

How does the time needed to read a sentence scale with the number of characters? Or does this time scaling depend on something more than just character count?

For example, let $X$ be the number of characters and $F(X)$ the seconds to read an entire sentence of $X$ characters long. There are 3 options:

1. Linear $F(X) \in \Theta(X)$: Is the relationship linear? That is, if it takes 0.5 seconds to read "hello", it would take 1.0 second to read "hello world": $F(X) = 0.1 X$

2. Sublinear $F(X) \in o(X)$: Or does it decay? That is, as people read a long sentence, their reading speed increases (crazy example $F(X) = 1 / X$)

3. Super-linear $F(X) \in \omega(X)$: Or is it like quadratic? That is, each additional character ads more time than the previous word? (example: $F(X) = X ^ 2$)

Which of the above 3 options best describes reading speed based on length of text? Is the specific functional form of this relationship known?

### Motivation

I am creating an iPhone app where I need to show transient confirmation messages. For example, when a user submits a comment, I pop up a message saying "thanks for submitting your comment". Shortly after, the message will fade away. There exist many such transient messages all over my iPhone app.

What I would like to do is to calculate the optimal time to show each message based off of the number of characters in that message. I want users to have enough time to comfortably read the message, but not so long that the message annoys them. The purely UX version of this question is here:

How long does it take to read X number of characters?

• I wrote an android app that takes a note entered by the user and displays it later as a Toast. You are limited to LENGTH.LONG (~3 seconds) and LENGTH.SHORT (~2 seconds). If the note entered exceeds 50 characters, the Toast is of LENGTH.LONG.
Jun 15, 2012 at 23:07
• I reposted my comment on ux.stackexchange.com before some mod migrated my question to cogsci.
– JoJo
Jun 16, 2012 at 0:35
• Honestly this is fine on either site, and will probably get different answers on both; more focused on academic research here, with probably a more practical and simple (possibly less precise but more actionable) on UX. I'm fine with it being on both if Cog Sci welcomes it Jun 16, 2012 at 0:42
• I made a significant edit to the question to make it focus on the scientific aspect of the question. Please edit the UX version to focus on the UX-part and not be a copy-and-paste of the original Q. If you think I changed the spirit too much, feel free to roll-back my edits, but keep in mind we are not UX and prefer scientific questions. Jun 16, 2012 at 1:05
• @J.R. I think your answer is fine, you state the important features (that words matter more than characters) and that is is weird to expect sub-linear. However, if you feel inclined to expand your answer with more background on the psychology of reading, then that would be super! Jun 16, 2012 at 1:22

I've studied this a little bit within the context of timing responses to personality test items. General models of reading speed look at both the time to read the words as well as to comprehend. From memory, eye tracking studies have shown how the eyes will often back track to confusing parts of a sentence (apologies for lack of reference).

Some general findings that I've found in my own data on time to answer personality test items of different lengths:

• Expect an initiation period. I.e., the time between displaying a message and the commencement of reading. In mathematical terms, this will translate to a non-zero constant in your model of reading time as a function of properties of the text.
• The more familiar the content and the words are to the reader, the quicker they will be. This translates both in absolute terms that simple words are quicker to read, and also to interactions between individuals and the content.
• In general, character count, word count, and syllable count tend to be highly correlated in normal prose. From my own data, these indices tend to have a relatively linear effect on reading speed.
• More complex sentences (e.g., ones with negation, multiple clauses, etc.) take longer to read. For example, I found that sentences with "not" took systematically longer to process.
• Individuals differ substantially in reading speed. Expect to see a distribution of individual differences that is a little bit positive skewed from normal. Thus, if you are designing a system where you determine the length of time text is displayed, you may need to pitch the speed of your system to capture a certain percentage of that distribution (e.g., 95, 99% etc.). Various factors explain variation in reading speed including whether English is a second language and education.
• There are also outliers. People get distracted. Thus, there is reading time when people are focussed and there is reading times that incorporate distraction and other processes.

More generally, if you have the resources, you can do some pilot testing on a sample of individuals where you time how long people take to read the text, ideally within the context of the application. This could allow you to develop a domain specific model of reading speed.

Although a little tangential, some articles that discuss speed of item responding in a personality testing context include Casey and Tyron (2001) and Wagner-Menghim (2002).

### References

• Casey, M.M. & Tryon, W.W. (2001). Validating a double-press method for computer administration of personality inventory items.. Psychological assessment, 13, 521.
• Wagner-Menghin, M. (2002). Towards the identification of non-scalable personality questionnaire respondents: Taking response time into account. Psychologische Beiträge, 44(1), 62-77.
• Your fifth point (that people read at different speeds) might prompt the system designers to have a setup option whereby individual users can tailor how long they would prefer the messages to appear.
– user851
Jun 16, 2012 at 9:31

If you really wanted to know you could use models of reading behaviour - e.g. EZ-Reader or Swift. The Rayner reviews are the classic go-to to outlne this kind of thing:

Rayner, K. (2009). Eye movements and attention in reading, scene perception, and visual search. The Quarterly Journal of Experimental Psychology (2006) (Vol. 62, pp. 1457-506).

It will depend on: - Size of text - Language - Word frequency - Word length - Predictability - and a whole host of other factors.

Of all the words put together, plus any occasions where regressions to previous words are made because the observer has failed to understand the text.

In practice, it's probably not worth worrying about to this level of complexity so just beta test it with some people and make sure they don't complain that they don't get enough time to read the messages.

A few thoughts spring to mind:

1. Part of the answer might depend on the maximum value of X (if all the messages are relatively short, that's a key piece of information).

2. It doesn't decay, I don't think. The more information presented to the user, the more it all has to put into context with each other. But I don't think it's quadratic, either; that seems too steep.

3. If X is the number of characters, and W is the number of words, the time might be more dependent on W than X.

Do you remmeber tihs erxesice? It's fnuny how wlel you can raed wrods as lnog as the fisrt and lsat ltteers saty cnonstat. Wehn redanig, our birans seem iclinned to prcoses by the wrod, mroe tahn by the ltteer.

EDIT: Those were my initial thoughts, when this question was first posed on English Language & Usage. I won't pretend I'm an expert (I'm not), but there does seem to be quite a bit of research that would support my third hypothesis – that readers often parse by word, more so than by letter, so the number of words in a text string might be more significant than the number of letters. I'll cite one paper I managed to track down and peruse:

Inhoff, Albrecht Werner, Integrating information across eye fixations in reading: The role of letter and word units. Acta Psychologica (73:3), April 1990, Pp. 281–297

• Why did this get downvoted so quickly? LOL.
– Jasper Loy
Jun 15, 2012 at 22:59
• @JasperLoy: Evidently, someone didn't like my answer. It's not the first time that happened, and it probably won't be the last. C'est la vie. :^) P.S. Maybe it's all the typos in my quote. Someone from PETSC? (People for the Ethical Treatment of Spell Checkers).
– J.R.
Jun 15, 2012 at 23:03
• I am not sure if the downvotes came before or after the migration to CogSci... but as it stands now, your answer lacks sufficient scientific evidence to stand as a good answer on this site. Most good answers here need to cite reference papers or studies.
– Josh
Jun 16, 2012 at 13:06
• @Josh: The first downvote came before the migrate. (EL&U had been going through a lot of unusual downvoting that day, hence the ensuing conversation above). Also, after this question got migrated, I wondered aloud if my answer would be too unscientific for this site, explaining that I had answered from an English perspective. One user indicated that, despite it's lightweight nature, my answer might be okay, although it wouldn't hurt to back it up with a bit more research.
– user851
Jun 16, 2012 at 18:17
• Let's give you a reference then! Your "typo" text is actually called "transposed text": see [ White, S. J., Johnson, R. L., Liversedge, S. P., & Rayner, K. (2008). Eye movements when reading transposed text: the importance of word-beginning letters. Journal of Experimental Psychology: Human Perception and Performance, 34(5), 1261-1276. ] Jun 16, 2012 at 18:36

I just had a project where I had to figure this out. I found that a good rule of thumb was the following:

$$timeToRead = 1300 + (chars * 65);$$

So that's an initial time of 1300ms to adjust to what you need to be reading and about 65ms per character including spaces.

• thanks for your answer travis. did you test other models as well, or did you assume a linear relationship? also, do you know the $r^2$ from your dataset?
– Jeff
Dec 8, 2012 at 20:56
• This is based purely on a completely unscientific approach of tweaking the numbers and having a script rotate through several different paragraphs of differing lengths. I read each one slowly enough to completely comprehend what i was reading and if it rotated through too fast, then i increased the timing, too slow, i decreased it until i found the sweet spot. But it would seem that the reading speed for me, at least, is not entirely linear as some paragraphs seemed far faster to read than others of similar lengths. Dec 9, 2012 at 0:25