Skip to main content
Search IntMath

Readability calculations

By Murray Bourne, 12 Jan 2009

There is math behind readability. I'm talking about readability in books and magazines, as well as readability on the Web.

Ever wondered why legal documents are so hard to follow and why it’s such a chore to churn through certain books?

Writers would like to know if their words will be understood by the intended audience. There are several different readability tests that authors can use to get a handle on the readability of their work.

One of the best known tests is the Flesch Kincaid Readability Test which was developed by Rudolph Flesch. Flesch was a mid-20th century expert in readability who wrote Why Johnny Can't Read. This book criticized the "reading by sight" method, and advocated a return to learning to read using phonics.

How do you determine readability in a reliable way? Readability depends in part on word familiarity and length, and also sentence construction and length. It's not possible to quantify everything that is involved in readability (for example, long words are not necessarily difficult to understand and not all short ones are easy to understand). So some compromises are inevitable.

Flesch Reading Ease Score

The Flesch Reading Ease Score is calculated as follows:

206.835 − 1.015 × (average words per sentence) − 84.6 × (average syllables per word)

A score of 100 means it is very easy to read, and 0 means it is almost impossible. In general, the score indicates:

90 to 100: Easily understood by an average 11 year old student
60 to 70: Easily understood by an average 13 to 15 year old student (Readers Digest level)
0 to 30: College graduate level

A related score is the Flesch Kincaid Grade Level which gives an approximate grade level for a passage. Its formula is:

0.39 × (average words per sentence) + 11.8 × (average syllables per word) − 15.59

Some Thoughts

As students read fewer books, and tend to scan for information on computer screens, I suspect the definition of "average 11-year old" will need to be changed.

Also, college graduates do not read as much as their pre-Internet seniors did, and this will affect these calculations.

Of course, a mathematical analysis of a piece of writing will not tell you if the words make sense or it is an interesting story. However, an understanding of these tests will help you to improve your writing.

Tools for Readability

Microsoft Word has an in-built tool which calculates the Flesch Reading Ease and Grade. It is normally turned off by default. Check your Word help menu for advice on how to turn it on for your version.

You can also check readability using this online tool. Apart from the Flesch score, it also lists the Coleman Liau index, ARI (Automated Readability Index) and SMOG.

Readability on the Web

As more teaching and learning is being carried out online, it is important for educators to know how to make Web pages as reading-friendly as possible. There’s a lot of advice on this topic on the Web. Jakob Nielsen has done extensive eye tracking research and has several articles on Web readability.

Should Math Students - and Teachers - Care?

You bet. To be employable in the 21st century, you’ll certainly need to know how to write well.

See the 5 Comments below.

5 Comments on “Readability calculations”

  1. John says:

    I imagine the Flesch Reading Ease Score is a good first approximation, but I wonder where it breaks down. For example, I expect it would be easier to read common multi-syllable words than obscure one-syllable words.

    I ran my blog through a program that reported that the blog is written on a high school reading level. I do try to write short sentences and cut out unnecessary words, but I often write about math and statistics, sometimes at a fairly advanced level. I suppose the writing style can be at one educational level while the content is at another level.

  2. Murray says:

    Yes, you are quite right, John. Even though the size of the words used and the number of words per sentence can be suggest basic readability, the concepts might be through the roof for most readers.

    in fact, I am becoming more convinced that this is the problem at school level - we assume the students can read and follow, but it is like a foreign language.

  3. David Simpson says:

    Nice to see a blog post about Flesch Kincaid. I've just launched an online readability test [no longer available] so that I can check my blog posts for Flesch Kincaid and the various other grade level readability indicators.

    It works by referer much in the same way as the "Valid XHTML" & "Valid CSS" links at the bottom of this page.

  4. Murray says:

    It's a great tool, David. Thanks for letting us know.

    Here's an issue, though... If I have already published my post and then find its readability is awful, I need to make updates. This is not good in the sense that the post has already been pinged around the cyber-ether.

    Any plans for a WordPress plugin that calls your readability checker before the publish step?

  5. David Simpson says:

    Good point about pinging. I'm thinking of writing a Firefox extension to check webpages that my site can't access e.g. Secured intranets. Maybe it could target textareas too!

    I've got a JSON web service in the pipeline too, so that could be used with WordPress as and when time permits.

Leave a comment

Comment Preview

HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

  1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
    `a^2 = sqrt(b^2 + c^2)`
    (See more on ASCIIMath syntax); or
  2. Use simple LaTeX in the following format. Surround your math with \( and \).
    \( \int g dx = \sqrt{\frac{a}{b}} \)
    (This is standard simple LaTeX.)

NOTE: You can mix both types of math entry in your comment.


Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.