WRT333

Readability Indices

Syllabus | Table of Pages

Robert Gunning's "Fog Index"

Readability formulas are mathematical techniques used to determine how difficult it is for someone to read and understand a piece of writing. More than 100 different readability formulas exist, and many are being used by government agencies and businesses in an attempt to improve writing. For this reason, you should become familiar with how they work.

Most readability formulas are based on an idea that short words and sentences are easier to understand than long words or sentences. For example, Robert Gunning's "Fog Index" works like this:

  1. Find the average number of words per sentence (L), using a 100+ word passage. Count all of the words (W) and all of the independent clauses (C) and divide (W÷C). Dates count as a single word.
  2. Find the number of difficult words (D), defined as those with three or more syllables. Gunning regarded proper names (Kennedy), combinations of simple words (manpower) and three-syllable verbs ending in -es or -ed as exceptions.
  3. Add the average sentence length to the number of difficult words and multiply by 0.4. This will give you an estimate of the average grade level that a reader should have obtained to understand the writing. That is, Gunnings Fog Index = 0.4 * (L + D).

Example of Use of the Gunning "Fog Index."

In describing the humpback whale song, we will adhere to the following designations. The shortest sound that is continuous to our ears when heard in "real time" will be called a "unit." (Some units when listened to at slower speeds, or analyzed by machine, turn out to be a series of pulses or rapidly sequenced, discrete tones. In such cases, we will call each discrete pulse or tone a "subunit.") A series of units is called a "phrase." An unbroken sequence of similar phrases is a "theme," and several distinct themes combine to form a "song."

{From "Songs of Humpback Whales." 1971. Payne, R. S. & S. McVay. Science 173: 585-597.}

This passage has seven sentences (5 plus 2 independent clauses (underlined)) and 96 words: The average sentence length is 13.7. There are nine difficult words (boldface). Gunning's Fox index = 0.4 * (13.7 + 9) = 9.08.

Conclusion: The passage can be well understood by the average highschool freshman

Other Readability Formulas:

Flesch-Kincaid Grade Level = 0.39*(avg. words / sent.)+11.8*(avg. syls./ word)-15.59

Flesch Reading Ease Score =206.835-1.015*(avg. wrds./sent.)+.846*(syls./100words), where [90-100 = Very easy (4th grade); 80-90 = Easy (5th); 70-80 = Fairly Easy (6th); 60-70 = Standard (7-8th grade); 50-60 = Fairly Difficult (Some H.S.); 30-50 = Difficult (H.S.-College); 0-30 = Very Difficult (College and more).]