SMOG

A readability index developed by G. Harry McLaughlin and published in his 1969 Journal of Reading paper SMOG Grading: A New Readability Formula. SMOG is an acronym for Simple Measure of Gobbledygook. McLaughlin built it as a faster, more accurate replacement for the Gunning Fog Index: same predictors, cleaner mathematics, less hand-counting.

The formula

The full McLaughlin formula:

$\text{SMOG} = 1.0430 \sqrt{ \text{polysyllables} \times \frac{30}{\text{sentences}} } + 3.1291$

The simplified bedside version, which McLaughlin promoted for hand-calculation:

$\text{SMOG grade} \approx 3 + \sqrt{\text{polysyllable count}}$

A polysyllable is a word of three or more syllables. The formula assumes a 30-sentence sample drawn as 10 consecutive sentences from the start, middle, and end of the text.

Why the square root

McLaughlin's main mathematical move was the square root. Fog uses a linear percentage of complex words; SMOG uses the square root of the raw count over a fixed-length sample. The square root encodes a psycholinguistic intuition: as a text grows denser in polysyllables, each additional polysyllable adds less difficulty than the previous one. Fog's linear scaling overshoots on technical text; SMOG's nonlinearity tracks reader self-report more accurately.

McLaughlin claimed in the original 1969 paper that SMOG predicts the grade at which 100% comprehension is required, while Fog and FKGL predict the grade at which roughly 50–75% comprehension is achieved. This is one reason SMOG scores read 1–2 grades higher than Fog or FKGL on the same text. SMOG aiming at full comprehension means a higher grade level for the same difficulty.

Methodology: sampling and counting

The original procedure is sample-based and explicit:

1. Count out 10 consecutive sentences near the beginning, 10 near the middle, and 10 near the end. Total: 30 sentences.
2. Count every word of three or more syllables in those 30 sentences. Each occurrence counts separately, even if the same word repeats.
3. Apply the formula.

For texts shorter than 30 sentences McLaughlin gives a scaling correction. The sampling discipline is part of why SMOG was popular in the pre-software era: three 10-sentence samples are tractable by hand in a way that whole-text counting is not.

Modern software implementations usually skip the 30-sentence sampling and apply the formula to the whole text at once. This produces slightly different scores, and is an inter-tool variance source catalogued in Text Metric Implementation Variance.

Where SMOG is the right choice

SMOG is the readability formula of record in healthcare communication. The U.S. National Institutes of Health, the CDC, and most patient-information style guides require SMOG grades for patient-facing materials, on the grounds that SMOG's full-comprehension orientation matches the consequence model — a patient who only 70% understands dosing instructions is at risk in a way that a magazine reader who 70% understands an essay is not.

For ELT use SMOG is most valuable at the very-difficult end of the scale, where Fog and FKGL compress and SMOG continues to discriminate. Academic source texts at the C1–C2 boundary often score SMOG 14–17, where Fog plateaus at 15.

Why SMOG and Fog disagree

Both indices use 3+-syllable words and sentence length. Their disagreements come from three places:

• Scaling: SMOG's square root vs Fog's linear percentage.
• Comprehension target: SMOG predicts full comprehension; Fog predicts approximate comprehension.
• Complex-word exclusions: Fog's original spec excludes proper nouns, compounds, and -ed/-es/-ing inflections; SMOG counts every 3+-syllable token without exclusion.

On natural prose SMOG scores typically run 1–3 grade levels above Fog. The relationship is stable enough that converters exist, but treating them as interchangeable is a mistake.

Key References

• McLaughlin, G. H. (1969). SMOG grading: A new readability formula. Journal of Reading, 12(8), 639–646.
• DuBay, W. H. (2004). The Principles of Readability. Impact Information.
• Wang, L. W. et al. (2013). Assessing readability formula differences with written health information materials: Application, results, and recommendations. Research in Social and Administrative Pharmacy, 9(5), 503–516.

See Also

• Gunning Fog Index: the predecessor SMOG was designed to replace
• Readability: the umbrella construct
• Flesch-Kincaid Grade Level / Flesch Reading Ease: the formula family SMOG sits alongside in default tool reporting
• Text Metric Implementation Variance: why whole-text SMOG and 30-sentence-sample SMOG produce different scores