Flesch-Kincaid vs SMOG vs ARI: One Passage, Three Grades

Flesch-Kincaid Grade Level, the SMOG index and the Automated Readability Index (ARI) all report a US school grade. They count different things, so the same passage can get three different grades. This article scores one short passage with all three, shows the arithmetic, and explains where the gaps come from.

Every score below comes from this site's readability checker. Paste the sample passage into it and you will get the same numbers.

The three formulas

Flesch-Kincaid Grade Level uses average sentence length and average syllables per word:

0.39 × (words ÷ sentences) + 11.8 × (syllables ÷ words) − 15.59

J. Peter Kincaid and colleagues published it in 1975 for the US Navy, calibrated on Navy training-manual passages. Microsoft Word reports it, which is why many writers meet it first.

SMOG counts only polysyllables, words of three or more syllables. G. Harry McLaughlin published it in 1969. His method takes ten sentences from the start, middle and end of a text, 30 in all. This calculator uses the short form from his paper:

3 + √(polysyllables × 30 ÷ sentences)

The "× 30 ÷ sentences" part converts the count to a rate per 30 sentences, so you can score a text of any length. The paper also gives a regression version, 1.0430 × √(polysyllables × 30 ÷ sentences) + 3.1291, which lands a few tenths higher.

The Automated Readability Index uses characters instead of syllables:

4.71 × (characters ÷ words) + 0.5 × (words ÷ sentences) − 21.43

E. A. Smith and R. J. Senter published it in 1967. It was built to be computed by machine, without a syllable count. This calculator rounds the result up to a whole grade.

All three use sentence length. They differ in how they measure word difficulty. Flesch-Kincaid averages syllables over every word. SMOG counts only the long words. ARI uses spelling length.

The sample passage

Take one tablet by mouth every morning. Do not take it with antacids. Call your doctor if you feel dizzy or notice swelling in your legs. Keep this medicine away from children.

This is an invented example of patient instructions, written for this article. The calculator counts:

"Every" counts as two syllables here, the way it is usually spoken ("ev-ry"). If you count it as three, it becomes a polysyllable and SMOG rises.

The results

Flesch-Kincaid: 0.39 × 8.0 = 3.12. Then 11.8 × 1.41 = 16.59. Add them and subtract 15.59: 4.1.

ARI: 4.71 × 4.41 = 20.75. Sentence length adds 0.5 × 8.0 = 4.0. Subtract 21.43 and you get 3.3, which the calculator rounds up to 4.

SMOG: 2 × 30 ÷ 4 = 15. The square root of 15 is 3.87. Add 3: 6.9. The regression version gives 7.2.

The calculator's other three formulas put the same passage at 5.7 (Gunning Fog), 6.4 (Coleman-Liau) and 79.7 on Flesch Reading Ease. The consensus grade is 5.7.

All three formulas agree the passage is easy. They disagree by about three grades on how easy. If your target is "grade 6 or below", Flesch-Kincaid and ARI say yes and SMOG says no.

Why SMOG reads higher

SMOG's gap is not an error. McLaughlin set SMOG to the grade at which a reader would fully understand the text. Flesch-Kincaid was calibrated to a lower comprehension standard. So on the same plain text, SMOG usually gives a higher grade. The short form also never goes below 3, because the square root starts at zero and 3 is added.

SMOG also counts only long words. A leaflet with simple sentences and a few medical terms can score low on Flesch-Kincaid and higher on SMOG. Flesch-Kincaid averages those terms in with the short words around them.

A 2013 review by Wang and colleagues found SMOG best suited for health care applications. For more on the formula, see SMOG Index Explained.

Why short samples are shaky

McLaughlin asked for 30 sentences. The 30-sentence scaling does not push scores up on its own: it turns the count into a rate. The problem with short text is that each long word carries a lot of weight.

On the sample, one more polysyllable would take SMOG from 6.9 to 7.7. That is the difference between counting "every" as two syllables or three. On a 30-sentence sample, one extra word moves SMOG much less.

So treat a SMOG score from a few sentences as rough. Score the whole document if you can, or check a short piece with Flesch-Kincaid as well.

Why ARI ignores syllables

ARI counts letters, so it sees "children" (8 letters, 2 syllables) and "antacids" (8 letters, 3 syllables) as equally long. Flesch-Kincaid and SMOG tell them apart.

Counting characters needs no syllable rules, so it behaves the same on product names and unusual words. The cost is words whose spelling and sound differ. "Queue" has 5 letters and 1 syllable. "Idea" has 4 letters and 3 syllables.

To see ARI's inputs for your own text, use the ARI calculator. Coleman-Liau is another formula that counts letters instead of syllables.

Which formula to use

No formula is right for every text. Ask which one's blind spots matter least for yours.

1. Short text, under about 30 sentences: lead with Flesch-Kincaid or ARI. Treat SMOG as rough.
2. Long medical or technical documents: SMOG picks up dense long words. Report Flesch-Kincaid next to it.
3. Brand names or unusual spelling: use ARI as a cross-check and read the flagged words yourself.
4. Early readers, or where decoding matters: don't rely on any of the three alone. Review word by word.
5. Comparing drafts: use one formula throughout. Switching formulas makes the comparison meaningless.

For how other formulas fit different kinds of content, see Which Readability Formula to Use for Which Context. For what two popular writing tools report, see Grammarly vs ProWritingAid.

Common mistakes

• Treating one number as the grade. On the sample, the three formulas spread over about three grades. Name the formula when you report a grade.
• Reading a short-text SMOG score as precise. One word can move it by most of a grade.
• Chasing the score instead of the reader. Shorter sentences and shorter words lower every formula without always making text clearer. When it matters, as with consent forms and medication instructions, test with real readers.

Readability formulas are screening tools. They tell you where to look, not whether a text works.

Bottom line

Flesch-Kincaid averages syllables, SMOG counts long words against a 30-sentence rate, and ARI counts letters. On one short patient-instruction passage they gave 4.1, 4 and 6.9. SMOG reads higher mainly because it was set to full comprehension. Choose the formula that fits your text, say which one you used, and check the flagged words by hand.