## Corollaries To Flesch-Kincaid Index

By Nirmaldasan

The Flesch-Kincaid Index (FKI) = 0.39AWS + 11.8ASW – 15.59. Based on the average number of words per sentence (AWS) and the average number of syllables per word (ASW), this formula is a simplification of the Flesch Reading Ease (FRE) and predicts grade levels of 1 to 17+.

Two corollaries to the FKI are what I would like to call the X Corollary and the P Corollary.

X Corollary (XC): Excess syllables (X) are the number of syllables more than one per word in a passage. Davis Foulger simplified the FRE by incorporating the idea of the excess syllables in it. The FKI may be similarly simplified.

Let W and S be the number of words and syllables in a passage respectively. S = W + X.  Now, 11.8ASW – 15.59 = 11.8 (S/W) – 15.59 =   11.8{(W + X) / W} – 15.59. On simplification, FKI (XC) = 0.39AWS + 11.8AXW – 3.79; AXW is the number of excess syllables per word. The advantage of this simplification is that it suffices to count only the excess syllables. The FKI (XC) yields the same answers as the FKI.

P Corollary (PC): Harry McLaughlin, creator of SMOG Grading, discovered ‘a law relating the number of syllables in a passage to the percentage of polysyllabic words, defined as words of three or more syllables’. He writes: “For practical purposes, the total number of syllables per 100 words may be calculated by this rule of thumb: multiply the number of polysyllabic [P] words by 3 and add 112.” (SMOG Grading — A New Readability Formula, Journal Of Reading, May 1969)

If we take a sample of 100 words, then FKI = 0.39AWS + 0.118S – 15.59. Applying McLaughlin’s rule of thumb, 0.118S – 15.59 = 0.118 (3P + 112) – 15.59. On simplification, FKI (PC) = 0.39AWS + 0.354P – 2.374. Since the McLaughlin law is not an exact equation but an approximation, the FKI (PC) may not yield the same answers as the FKI.

Application: Let us take a sample of 100 words from the Ruskin Bond Omnibus. In the introduction, Ruskin Bond writes: “I grew up on a heady mixture of crime, mystery and detective fiction, but their influence was purely of a literary nature; I have yet to commit a major crime, just as the majority of readers are innocent of murder and mayhem. I cannot honestly say that I have never had the urge to commit one. The wish to put someone unpleasant out of the way (permanently) is strong in most of us; but commonsense and civilized norms prevail over our baser instincts, and we step back from committing that most terrible and unnatural of crimes — the murder of a …”

Number of sentences = 3

Number of syllables (S) = 150

Number of excess syllables (X) = 50

Number of polysyllabic words (P) = 13

Average number of words per sentence (AWS) = 100/3 = 33.33…

FKI = 0.39AWS + 0.118S – 15.59 = 0.39 (33.33) + 0.118 (150) – 15.59 = 13 + 17.7 – 15.59 = 15.11

FKI (XC) = 0.39AWS + 0.118X – 3.79 = 13 + 0.118 (50) – 3.79 = 9.21 + 5.9 = 15.11

FKI (PC) = 0.39AWS + 0.354P – 2.374 = 13 + 0.354 (13) – 2.374 = 10.626 + 4.602 = 15.228.

Digression: I was tempted to test the Ruskin Bond passage with the Strain Index (S3/10; S3 is the number of syllables in 3 sentences). 150/10 = 15.