Smog Index Calculator
Calculate the SMOG readability index based on polysyllabic word count. Determine the education level needed to understand your text.
Smog Index Calculator
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Formula: SMOG Grade = 3 + sqrt(Polysyllabic Words x (30 / Total Sentences))
Worked example — SMOG Grade: 7.5 | Middle School level | Appropriate for general public
Formula
SMOG Grade = 3 + sqrt(Polysyllabic Words x (30 / Total Sentences))
The SMOG formula counts words with 3+ syllables (polysyllabic words) and normalizes to a 30-sentence sample. The square root transformation and addition of 3 converts the count into an estimated US grade level required for 100% comprehension.
Worked Examples
Example 1: Health Brochure Assessment
Problem:A health brochure has 30 sentences with 20 polysyllabic words across 450 total words. What is the SMOG grade level?
Solution:SMOG Index = 3 + sqrt(polysyllabic words x (30 / sentences)) SMOG = 3 + sqrt(20 x (30 / 30)) SMOG = 3 + sqrt(20) SMOG = 3 + 4.47 SMOG = 7.47 Polysyllable density: 20/450 = 4.4% Reading level: approximately 7th-8th grade
Result:SMOG Grade: 7.5 | Middle School level | Appropriate for general public
Example 2: Academic Paper Analysis
Problem:A research paper excerpt has 25 sentences with 60 polysyllabic words across 500 total words.
Solution:SMOG = 3 + sqrt(60 x (30 / 25)) SMOG = 3 + sqrt(60 x 1.2) SMOG = 3 + sqrt(72) SMOG = 3 + 8.49 SMOG = 11.49 Polysyllable density: 60/500 = 12% Reading level: approximately college level
Result:SMOG Grade: 11.5 | College level | Requires educated adult readership
Frequently Asked Questions
What is the SMOG Index and how is it calculated?
The SMOG (Simple Measure of Gobbledygook) Index is a readability formula developed by G. Harry McLaughlin in 1969. It estimates the years of education a person needs to understand a piece of writing. The formula counts polysyllabic words (words with three or more syllables) in a sample of 30 sentences, then applies the calculation: SMOG grade = 3 + square root of the polysyllabic word count. For samples that are not exactly 30 sentences, a conversion factor adjusts the count by multiplying the polysyllabic words by 30 divided by the number of sentences. The SMOG Index is considered one of the most accurate readability formulas, particularly for healthcare materials, because it correlates strongly with reader comprehension at 100 percent understanding.
How does SMOG differ from other readability formulas?
The SMOG Index differs from other readability formulas in several important ways. While the Flesch-Kincaid Grade Level uses both sentence length and syllable count per word, SMOG focuses exclusively on polysyllabic words, which research shows are the strongest predictor of text difficulty. The Gunning Fog Index is similar to SMOG but uses a different mathematical approach and tends to produce slightly lower grade level estimates. The Flesch Reading Ease Score produces a 0 to 100 scale rather than a grade level. SMOG is unique in that it predicts 100 percent comprehension rather than the 50 to 75 percent threshold other formulas target. This makes SMOG especially valuable for critical documents like medical consent forms and safety instructions.
What is a polysyllabic word and how do I count them?
A polysyllabic word is any word containing three or more syllables. To count syllables, count the vowel sounds in the word, not necessarily the vowel letters. For example, 'beautiful' has three syllables (beau-ti-ful), 'understanding' has four syllables (un-der-stand-ing), and 'communication' has five syllables (com-mu-ni-ca-tion). Proper nouns, compound words, and hyphenated words are counted as single words. Common polysyllabic words that increase text difficulty include words like 'approximately,' 'nevertheless,' 'particularly,' and 'administration.' When counting for SMOG, include every polysyllabic word even if it repeats. The higher the proportion of polysyllabic words, the more difficult the text is to read.
What SMOG score should I aim for in my writing?
The target SMOG score depends entirely on your audience. For general public communications, aim for a SMOG score between 6 and 8, which corresponds to a 6th to 8th grade reading level. This is important because the average American adult reads at roughly an 8th grade level. For healthcare materials, the American Medical Association recommends writing at or below a 6th grade level (SMOG score of 6 or less), as patients under stress have reduced comprehension. Government plain language guidelines suggest targeting 6th to 8th grade levels. For business communications and marketing copy, a SMOG score of 8 to 10 is generally appropriate. Academic and professional writing typically falls between 12 and 18.
How can I lower my SMOG score to improve readability?
Reducing your SMOG score primarily means reducing polysyllabic words. Replace long words with shorter synonyms: use 'help' instead of 'facilitate,' 'end' instead of 'terminate,' 'use' instead of 'utilize,' and 'start' instead of 'commence.' Break complex sentences into shorter ones, which does not directly affect SMOG but improves overall comprehension. Avoid jargon and technical terms when simpler alternatives exist. Use active voice rather than passive voice, as passive constructions often require additional polysyllabic words. Define technical terms when they must be used. Consider using bulleted lists to break up dense paragraphs. Read your text aloud to identify unnecessarily complex phrasing, and test revised versions to track your improvement.
Why does the SMOG formula call for a 30-sentence sample?
McLaughlin derived and validated the formula on samples of exactly 30 sentences, conventionally taken as ten consecutive sentences from the beginning, ten from the middle and ten from the end of a document. The constant 3 and the square-root transformation are fitted to a polysyllable count drawn from that fixed sample size. Sampling from three places also guards against an introduction or a summary that is unrepresentative of the body of the text.
How does the conversion factor adjust a text that is not 30 sentences long?
When the text has a different number of sentences, the polysyllable count is scaled to a 30-sentence equivalent by multiplying it by 30 divided by the actual sentence count. A 60-sentence passage has its polysyllable tally halved, a 15-sentence passage has it doubled. The scaling keeps grades comparable across documents of different lengths, but it also amplifies sampling noise on very short texts, so treat results from fewer than ten sentences as indicative only.
What SMOG grade does a text with 36 polysyllabic words in 30 sentences produce?
Apply the formula directly: the conversion factor is 30 divided by 30, which is 1, so the adjusted polysyllable count stays at 36. The square root of 36 is 6, and adding the constant 3 gives a SMOG grade of 9. Note how flat the curve is because of the square root: to fall from grade 9 to grade 8 the polysyllable count must drop from 36 to 25, a reduction of about 30 percent.
What counts as a sentence when preparing a SMOG sample?
Because the conversion factor divides by the sentence count, sentence boundaries have to be settled before any polysyllable tallying begins. A sentence is a word string closed by a full stop, question mark or exclamation mark, and McLaughlin treated independent clauses joined by a semicolon or colon as separate sentences, since each carries its own load. Headings, captions and bullet fragments lacking terminal punctuation are normally excluded, otherwise they distort the polysyllables-per-sentence ratio the grade rests on.
When should I use SMOG rather than the Gunning Fog Index?
Both formulas key on long words, but Fog blends the percentage of complex words with average sentence length and is calibrated to the level at which a reader grasps most of a text. SMOG ignores sentence length entirely and is calibrated to full comprehension. Choose SMOG for material where a misunderstanding has consequences, such as consent forms, dosing instructions or safety notices. Choose Fog when sentence structure also concerns you and you want one blended difficulty signal.
References
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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