SMOG Index: the 30-sentence readability formula

SMOG stands for “Simple Measure of Gobbledygook.” G. Harry McLaughlin published it in 1969, and the name tells you his attitude toward bloated prose. The formula is unusual in two ways. It ignores sentence length as a separate measure, and it was built for a fixed sample of 30 sentences.

The formula

SMOG grade = 1.0430 × √(polysyllables × 30 ÷ sentences) + 3.1291

A polysyllable here is any word of three or more syllables. Repeats count each time: if “medication” appears four times, that is four polysyllables.

McLaughlin also gave a shortcut for counting by hand. Take 10 sentences from the start of a text, 10 from the middle, and 10 from the end. Count the polysyllables in those 30 sentences. Find the nearest perfect square, take its square root, and add 3. If you count 25 polysyllables, the square root is 5, and the grade is about 8.

The fuller formula above gives nearly the same answer. With 25 polysyllables in 30 sentences:

• 25 × 30 ÷ 30 = 25
• √25 = 5
• 1.0430 × 5 + 3.1291 = 8.34

Why 30 sentences

The 30-sentence sample is the design, not a detail. The formula counts polysyllables per 30 sentences. Because the count is per sentence rather than per word, long sentences push the score up indirectly: more words per sentence means more chances for a long word. That is how SMOG captures sentence length without measuring it.

Thirty sentences also gives the count room to settle. One polysyllable more or less hardly matters. Going from 25 to 26 moves the grade by only about 0.1.

What happens with short text

Most people don’t paste 30 sentences. When a text is shorter, the formula scales up whatever it finds, as if the text went on at the same rate for 30 sentences. That multiplies any quirk in a small sample.

Take a 5-sentence paragraph:

• 3 polysyllables: 3 × 30 ÷ 5 = 18, √18 ≈ 4.24, grade ≈ 7.6
• 4 polysyllables: 4 × 30 ÷ 5 = 24, √24 ≈ 4.90, grade ≈ 8.2

A single extra long word moved the grade by about 0.7. In a 30-sentence sample, the same word would move it by 0.1. In a two-sentence text, one word can swing it by a grade or more.

So Op-Ed Insight’s readability checker still shows a SMOG grade for short text, but warns you when the sample has fewer than 30 sentences. Read the number as a rough hint until you have a full sample.

Watch out: SMOG can’t go below about 3.1. A text with no polysyllables at all scores 3.1291, the formula’s floor. That is fine for a children’s book but tells you little about adult writing.

Why health writers often use SMOG

SMOG is commonly recommended for patient leaflets, consent forms, and other health information. A few features explain why.

It aims at full understanding. McLaughlin’s yardstick was complete comprehension: the grade at which readers could answer all the test questions on a passage. Many other formulas were fitted to a looser standard. As a result, SMOG tends to give a higher grade than Flesch–Kincaid for the same text. When the cost of a misunderstanding is a wrong dose, a cautious estimate makes sense.

It is quick by hand. Counting long words in 30 sentences and taking a square root takes a few minutes with a pencil. That mattered when clinics and health departments checked materials without software.

It targets the right problem. Health writing gets hard mostly through long words: “hypertension,” “contraindicated,” “gastrointestinal.” SMOG’s single count goes straight at them.

Still, SMOG measures only one thing. A leaflet can score well and confuse readers if its steps are out of order, its headings are vague, or its key instruction sits in the last paragraph. Testing with a few real readers catches what the count can’t.

Before: If you experience persistent nausea or abdominal discomfort, discontinue the medication and contact your healthcare provider immediately.

17 words · 1 sentence · grade 20.9

After: If you feel sick to your stomach and it does not go away, stop taking the pills. Call your doctor or nurse right away.

24 words · 2 sentences · grade 3.3

The Before packs eight polysyllables into one sentence: “experience,” “persistent,” “abdominal,” “discomfort,” “discontinue,” “medication,” “provider,” and “immediately.” The After has none.

SMOG compared with other formulas

SMOG and the Gunning Fog Index both count words of three or more syllables. Fog adds average sentence length on top and has extra exceptions for proper nouns and familiar compounds. SMOG has no exceptions: every word of three or more syllables counts, which makes it simpler to apply consistently.

Since both depend on syllable counts, both inherit the same counting problems. Is “every” two syllables or three? Is “fire” one or two? A different answer can tip a word over the three-syllable line. See counting syllables.

For what grade to aim at, see what readability score to aim for.