Examples of Mathematical Algorithms that can be used to measure the readability of books or web pages. To obtain a PowerPoint format download of this presentation, go to the following page: http://passyworldofmathematics.com/pwerpoints/

2. C ALCULATING R EADABILITY
Mathematical Formulas / Algorithms
examine how long sentences are, and
how many syllables are in the words
on a page. These values are then
“number crunched” together to
Produce results such as:
Gunning Fog Index as well as
Flesch Reading Ease and
Flesch-Kincaid Grade Level values.

3. G UNNING -F OG I NDEX
GFI = (Average_Words_Sentence + Difficult_Words ) * 0.4
To determine the Gunning-Fog index:
Calculate the average number of words per sentence.
Calculate the percentage of “Difficult Words” in the
sample (“Difficult Words” have three or more syllables).
Add the totals together, and multiply the sum by 0.4

4. G UNNING -F OG I NDEX
The Gunning-Fog index value, is a measure of how
many years of schooling it would take someone to
understand the content.
Eg. If the G-F value is “10” for a given book, or web
page, then a 15 year old should be able to read and
understand it.
Results over seventeen are reported as seventeen,
where seventeen is considered to be post-graduate
University level.

5. G UNNING -F OG I NDEX
Gunning-Fog Index Typical Sources
6 TV guides, The Bible, Mark Twain
8 Reader's Digest
8 - 10 Most popular novels
10 Time, Newsweek
11 Wall Street Journal, Fin Review
14 The Times, The Guardian, The Age
15 – 20 Technical and Academic papers
Source: Phillip Chalmers from http://www.benefit-from-it.com/

6. F LESCH R EADING E ASE
FRE = 206.835 - (1.015 * average_words_sentence) - (84.6 * average_syllables_word)
To determine the Flesch Reading Ease:
• Calculate the average number of words per sentence.
• Calculate the average number of syllables per word.
• Multiply the average number of
syllables per word multiplied by
84.6 and subtract it from the
average number of words multiplied
by 1.015
• Subtract the result from 206.835 Image Source: http://cache1.asset-cache.net

7. F LESCH R EADING E ASE
The result of the Flesch calculation is an index
number that rates the text on a 100-point scale.
The higher the score, the easier
it is to understand the document.
Authors should aim to produce
a Flesch Reading score of
approximately 60 to 70.
Image Source: http://www.tailored.com.au

8. F LESCH -K INCAID GRADE LEVEL
FK = (0.39 * average_words_sentence) + (11.8 * average_syllables_word) - 15.90
To determine the Flesch-Kincaid grade level:
Calculate the average number of words per sentence.
Calculate the average number of syllables per word.
Multiply the average number of words by 0.39
and add it to the average number
of syllables per word multiplied
by 11.8
Subtract 15.90 from the result.
Image Source: http://brandmelive.com

9. F LESCH -K INCAID GRADE LEVEL
The result of the Flesch-Kincaid algorithm is a grade level.
Like the Gunning-Fog index, it is a rough
measure of how many years of schooling
it would take someone to understand
the content.
Negative results are reported as zero,
and numbers over twelve are reported as twelve.
Image Source: http://wwwdelivery.superstock.com

10. C ONCLUSIONS
For a document to be easily understood, the writing style should
be clear and simple. This involves a writing style that is direct, and
familiar to the intended reader. The structure of the document
should be logical, unambiguous, and avoid redundant words.
Being mathematically based, readability tests are unable to
determine whether a document is comprehensible, interesting,
or enjoyable. It's possible to obtain sensational readability
scores with any text that contains short sentences made up of
monosyllabic words.
Nonetheless, Readability Tests are extremely useful for checking the
age level content of Books, as well as Web Pages on the Internet.

11. F URTHER READING
There is an Online Calculator for readability at this great website:
http://juicystudio.com/services/readability.php
In fact this website is where I found out about all of the Readability
Algorithms in this Powerpoint. Go there to read more 
The Online Calculator allows you to type in
the Web Address of a Page, and then click
to get a full Readability Analysis.
We tried this out our own ICT website:
http://passyworldofict.blogspot.com/
and the results are shown on the next slide.
Image Source: http://wwwdelivery.superstock.com

12. PASSY ’ S W ORLD OF ICT
R EADABILITY
Summary Value
Total sentences 978
Total words 2744
Average words per Sentence 2.81
Words with 1 Syllable 1254
Words with 2 Syllables 452
Words with 3 Syllables 300
Words with 4 or more Syllables 738 (Very High)
Percentage of word with three or
37.83% (High – should be < 20%)
more syllables
Average Syllables per Word 2.19
Gunning Fog Index 16.25 (Technical & Academic)
Flesch Reading Ease 18.69 (Not very easy to read)
Flesch-Kincaid Grade 11.35 (11 years of schooling)

13. R EFERENCES
All technical information was obtained from :
http://juicystudio.com/services/readability.php
It has a very complete discussion about Readability Tests.
Images were obtained
from Google Images.
Further cool mathematics
items are available at
the Passy’s World of
Mathematics website.
(See next slide for link)

14. http://passyworldofmathematics.com/