A Simplified Flesch Reading Ease Formula

Davis Foulger
Florida Technological University (now the University of Central Florida)
Modified by author in 2003

As originally submitted to Journalism Quarterly as Research in Brief.

(more papers by Davis Foulger)

Readability formulas have appeared and disappeared regularly for about forty-five years now.(1) Of these formulas, three, all developed in the late 1940's and early 1950's, stand out. The first, the Cloze procedure,(2) isn't really a formula at all. It is a behavioral research method which requires time for survey and analysis. The second, the Dale-Chall formula,(3) is the result of the collaboration of two researchers who had been working on the problem of readability for several years prior to their successful joint venture. Although their formula is the best of the many formulas for estimating the readability of a document, it is complicated, requiring consultation of lists of commonly used words.(4) Neither the Dale-Chall formula nor the Cloze procedure are practical for the editor who wants to compare his newspaper to others, the reporter who wants to make his articles more readable, or the students who is learning what makes good journalism.

A more practical formula is the Reading Ease formula,(5) the best of several such formulas developed by Rudolph Flesch.(6) Although very nearly as accurate a measure as the Dale-Chall formula, the reading ease formula is considerably easier to use, requiring no comparisons with word lists. The computations involve only the counting of words, syllables,and sentences. From these counts sentence length and word length are combined to compute the actual scale score. This score can range from zero, for extremely difficult reading, to one hundred, for very easy reading.

Although the Flesch reading ease formula is probably the best combination of simplicity and meaningfulness yet built, many researchers have not considered the scale simple enough. As a result, several scales requiring less counting have been developed.(7) The work reduction has, however, been invariably accompanied by a change in the equation and a decline in the accuracy of the measurement. Perhaps the most complete counting reduction was that accomplished by Irving Fang.(8). His formula collapsed the elements of the Flesch scale into a single measure of the excess syllables in each sentence. The logic of the scale is that readability declines as word length and/or sentence length increases. By counting the excess syllables (the number of syllables in a word minus one) short sentences with overlong words and overlong sentences are both detected. The beauty of the scale is that it only requires one count of a manuscript. The scale accomplishes this, however, at some expense to accuracy. Measurement of the role of sentence length is minimized in the formula.

The original Flesch reading ease procedure: Words: 1 2   3 4 5 6 7 8    
Syllables 1 2 3 4 5 6 7 8 9 10 11
Sentences                     1
Sample Sentence: The meth- od saves two counts of the man- u- script.
The simplified Flesch reading ease procedure: Excess Syllables     1             2 3
Words: 1 2   3 4 5 6 7 8    
Figure 1: The original and Revised reading ease procedure. The Flesch procedure entails three counts of the manuscript. The simplified procedure entails only two.
The irony of this work, which undoubtedly consumed --many hours research, is that the reading ease formula and procedures can be simplified to the point where calculation of the Flesch formula requires very little greater effort than would be required to compute the Fang formula. This can be accomplished, moreover, with no loss in accuracy. The key to this simplification is the Fang procedure. Instead of counting words, syllables, and sentences in three separate counts, as required by the Flesch formula, one need only count the words and excess syllables in each sentence. A list of words and excess syllables, by sentence, will yield the number of sentences without additional reference to the document. In Figure 1, the counts required by the original Flesch procedure are shown above the sentence. Those required by the revised procedure are shown below. It should be apparent that the revised procedure results in a considerable savings in counting time, as the overall count will go no higher than it would, in the original procedure, for the syllable count alone. The results can then be summed and inserted into the revised Flesch reading ease formula:
Figure 2: Formula for a simplified Flesch Reading Ease procedure

where R.E. is the reading ease score, X is the excess syllables in each sentence, Y is the number of sentences, and Z is the number of words in each sentence. Although the equation may appear more complicated than the original, it is actually much more flexible and simple to compute. The use of a hand calculator makes the job even simpler, easy enough, in fact, for almost anyone to compute rather quickly. The revised formula was derived from the original Flesch reading ease formula as follows:

  1. (The original Flesch Reading Ease Formula, where R.E. is reading ease, wl is the number of syllables in a 100 word sample, and sl is the average length of the sentences in that 100 word sample:
  2. If we decompose wl into its constituents (e.g. the number of words (100) and the number of additional syllables(X)), where X = wl - 100, we can derive a series of changes to the reading ease formula. 100 is the defined length, in words, of a sample in the Flesch Reading Ease procedure. The results of inserting X into the Flesch Reading Ease formula are as follows:

    Note in particular the final reduction of the constant to 122.235 as we derive X (additional syllables) from wl. This change may be the most important one we will make to the formula here, insofar as it instantly clarifies the meaing of the formula. To acheive a fourth grade reading level in text (Flesch's benchmark for a score of 100 points on a text sample), the average sentence length and the number of additional syllables can equal 22. In other words, reading ease is maximized with you use short sentences and minimize use of long words.
  3. It is possible to dispose of sample size as a limitation in computing the Flesch Reading ease formula. To enable this we will define a variable Z as number of words, noting again that in the original Flesch Reading Ease formula Z is assumed to equal 100. Note that this assumption caused some problems for Flesch in computing the Reading Ease formula, and the procedure documented for computing R.E. includes a work around for solving the problem. Here we willl solve the problem directly by modifying the formula to allow samples of any length.
  4. The average length of a sentence is defined by Flesch as the number of words in a sample divided by the number of sentences in that sample. If we define Y to be the number of sentences, we can decompose sl as follows: Y = sl * Z. The results of inserting Y into the Flesch Reading Ease formula are as follows:

    Note in particular that the derived equation only assumes raw values (e.g. the number of sentences, the number of words, and the number of additional syllables associated with those words). This simplies computation a little by allowing Reading Ease to be computed in one computation. More importantly, however, it allows us to treat sentences as the fundamental unit of computation for Flesch Reading Ease. We aren't quite there yet, but this move will allow us to estimate the Flesch Reading Ease of individual sentences.
  5. At this point we have removed most of the assumptions that force a Flesch Reading Ease procedure sample to be 100 words. The remaining assumption involves the of excess syllables (X) and its ratio to the number of words (presumed to be 100). We can resolve this problem by multiplying X by the ratio of the number of words in the actual sample to the number of words in Flesch's assumed sample size (e.g. the ration of Z to 100). This multiplication is neutral to the original Flesch formula, as Z is forced to 100 and the result is multiplication of X by 1. The results of inserting this multiplication into the formula are as follows:

    This change substantially increases the range of applications in which the Flesch Reading Ease formula can be used reliably. Documents or document components of any size can be assessed for their readability, right down to a single sentence. Hence the sentence "This is a short sentence" would have a readability score of 100, corresponding to a fourth grade reading level. It is up the reader to decide if this is useful in normal practice (e.g. flagging particularly difficult sentences in a word processor). It does, however, set up the modified Flesch Reading Ease Procedure which is the core of this papers early argument.
  6. A document is, at one level, a collection of sentences. It is convenient, in the current procedure, to view Flesch Reading Ease as being the result of the sum of the readability of all of the individual sentences in the document, where each sentence (Z=1) has some number of words (Y) and additional syllables (X). If we view the Reading Ease formula in this way, the last derived equation above can be usefully restated as follows:

    Note that this formula is identical to that presented in Figure 2.


  1. For a detailed history and description of readability formulas, see: George R. Klare, The Measurement of Readability (Ames, Iowa: Iowa State University Press, 1963
  2. Wilson L. Taylor, "Cloze Procedure: A New Tool for
    -Measuring Readability." Journalism Quarterly, 30: 415-433 (1953). "Recent Developments in the Use of the Cloze Procedure." Journalism Quarterly, 33: 42-48 (1953).
  3. Edgar Dale and Jeanne S. Chall, "A Formula for Predicting Readability." Educational Research Bulletin, 27: 11-20 (21 January 1948).
  4. Edgar Dale and Jeanne S. Chall, A Formula for Predicting Readability: Instructions." Educational Research Bulletin, 27: 37-54 (18 February 1948).
  5. Rudolph F. Flesch, "A New Readability Yardstick." Journal of Applied Psychology, 32: 221-233 (1948).
  6. Rudolph F. -Flesch, "Estimating the Comprehension Difficulty of Magazine Articles." Journal of General Psychology, 28: 63-80 (1943). "Measuring the Level of Abstraction." Journal of Applied Psychology, 34: 384-390 (1950).
  7. James N. Farr, James J. Jenkins, and Donald G. Patterson, "Simplification of the Flesch Reading Ease Formula." Journal of Aoplied Psychology, 35: 333-337 (1951). R. Gunning, The Technique of Clear Writing (New York: McGraw-Hill, -1952).
  8. lrving E. Fang, "The 'Easy Listening Formula.'" Journal of Broadcasting, 11: 63-68 (Winter 1966-67).

Notes on the 2003 Modifications to this Paper

An edited version of this paper appeared as "Research in Brief" in Journalism Quarterly in 1978. A number of important elements of that paper, including detail of the measurement prodedures and detail of the derivation of the formula, were edited out of the published version. It is hoped that republication of the complete paper will have value to someone.

In republishing this paper on the web, some alterations have been made to the text. Those alterations have are indicated by the use of italics. The reader will quickly observe that most of the paper remains unaltered (although even the unaltered sections deserve some additional comment). The primary alterations are at the end of the paper. In scanning this paper in for republication on the web, an error was discovered in the logic of the equation and its derivation. While the error is a small one, it does result in an overestimation of readability for small sample sizes and and underestimation of readability for large samples. For what its worth, if anyone ever noticed the problem, no one has ever commented on it that I am aware of. In any case, here is the original equation as published in Journalism Quarterly:

Anyone with a spreadsheet can quickly model the errors that are made in this formula. They can also just as easily model the newly derived formula and see its consistency with the original Flesch formula.

The primary modifications to the paper, then, are the insertion of a somewhat different formula (note that most of the essentials remain unchanged) and an elaborated explanation of the derivation of the formula from the original Flesch Reading Ease Formula. The derivation follows the same logic as the original derivation, but corrects for an error in the computation of the effects of sentence length that resulted from an oversimplification of sentence length computation. I have added some additional discussion and explanation to the derivation in the interests of:

The only other change to the manuscript is at the end of the discussion of Fang's procedure and formula. Dr. Fang wrote to me about this article about a year after its appearance in JQ complaining that I had used "strong words" in describing his procedure as accomplishing its goals "at the expense of accuracy". That description is unduly harsh. In accomplishing most of the work of Flesch's formula with a single count of excess syllables, Fang highlights the dominant importance of word complexity to readability and provides a tool that accomplishes most of the work of the Flesch Reading Ease Formula with minimal measurement effort. While it remains that, in discounting the importance of sentence length, that Fang's formulation does sacrifice accuracy in favor of rapid measurement (one can be sure that Flesch had the option of not measuring sentence length and chose to include sl in the R.E. equation). it doesn't give up much compared with Flesch's formulation, and easy measurement mattered at the time of his article. While, minimizing measurement effort is probably less important now, it remains that Fang's article was the "shoulders" (to paraphrase Issac Newton) that this article stands on. Hence I have modified my strong language to read :at some expense to accuracy" and have added the clarifying sentence: "Measurement of the role of sentence length is minimized in the formula."