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

Question

I am creating an iPhone app where I need to show transient confirmation messages (called a toast in Android). 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. I realize that Android and two preset times - "short" and "long", but I'm recreating it on iPhone where I have total control.

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 impedes their usage of the app.

X = number of characters.
F(X) = seconds to read entire sentence given X

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Is it 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

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Does it decay? That is, as people read a long sentence, their reading speed increases?

F(X) = 1 / X

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Or is it quadratic? That is, each additional character ads more time than the previous word?

F(X) = X ^ 2

Answer 1

According to wikipedia's speed reading entry it's 200 wpm

I really don't think the science is the main issue with this solution. You need to test and evaluate real use.

Answer 2

Adult literate people don't read by the character. They do that only for foreign languages in the first stages of learning that language, and even that mostly for languages using a script very different from the languages they do know (as an English speaker would for Arabic, but not for German). Otherwise the word registers in the brain as a whole, pretty much immediately. Perhaps for the word "encyclopedia" it would take longer than for the word "ant", but the difference is a matter of milliseconds at best, and probably not even that. Also, it's both extremely subjective (based on how frequently that person uses that word) and extremely difficult to measure.

In short, just do some user testing. Get a few people, show them a few messages with different fadeout times, and see what feels the most comfortable. Or play around with some apps already doing it (preferably by a developer who has probably researched this - e.g. Apple), and try to reverse engineer their solution.