Readability formulas explained

A guide to the six readability formulas this site scores — Flesch Reading Ease, Flesch-Kincaid Grade Level, Gunning Fog, SMOG, Coleman-Liau, and the Automated Readability Index. Where each one came from, what it measures, when to trust it, and how to use them together.

Last updated 8 October 2026

What readability formulas actually do

A readability formula is a mathematical estimate of reading difficulty. It takes countable text features — sentence length, word length, syllable count, share of complex words — and combines them into a single number, usually a US school grade.

None of the formulas reads or understands text. None of them measures clarity, accuracy, persuasiveness or quality.

The idea behind every formula is the same: longer sentences and longer words tend to make text harder to read. Each formula's authors fitted those counts to passages whose difficulty had been measured with readers.

A brief history

The first attempts to quantify reading difficulty came out of education research in the 1920s. Two well-known formulas followed in 1948: Edgar Dale and Jeanne Chall's word-list-based formula, and Rudolf Flesch's Reading Ease score. Flesch's score became widely used. He consulted for the Associated Press, and Microsoft Word reports the score today.

1952: Robert Gunning, a writing consultant, publishes the Fog Index in The Technique of Clear Writing.

1967: E. A. Smith and R. J. Senter develop the Automated Readability Index for the US Air Force. It uses only character, word and sentence counts.

1969: G. Harry McLaughlin publishes SMOG (usually expanded as "Simple Measure of Gobbledygook") in the Journal of Reading. SMOG is set to complete comprehension.

1975: Two publications. J. Peter Kincaid, Robert Fishburne, Richard Rogers and Brad Chissom publish Flesch-Kincaid Grade Level for the US Navy — a recalibration of the 1948 Reading Ease formula onto a US grade-level scale. Meri Coleman and T. L. Liau publish the Coleman-Liau Index, a character-based formula designed for machine scoring.

These formulas have changed little since they were published. They are rough estimates with known limits.

The two families

The six formulas split into two families based on what they count for word complexity:

Syllable-based

• Flesch Reading Ease — total syllables per word
• Flesch-Kincaid Grade Level — total syllables per word
• Gunning Fog Index — percentage of complex (3+ syllable) words
• SMOG Index — count of complex (3+ syllable) words

Character-based

• Coleman-Liau Index — characters per word
• Automated Readability Index — characters per word

The practical difference: syllable counts are estimates, and they can be wrong for unusual spellings, technical terms and names. Letter counts are exact. The two families can still differ by several grades on the same text.

Side-by-side comparison

Which formula for which use case

If you're writing for a general audience

Start with Flesch-Kincaid. It is widely used, and Microsoft Word reports it. Pair it with Flesch Reading Ease if your team prefers a 0–100 score.

If you're writing for healthcare or patient information

Use SMOG. A 2013 review of readability formulas found it best suited to health care, and it is set to complete comprehension. The most widely cited target for patient-facing content is a 6th-grade level, attributed to the American Medical Association.

If you're writing for business or policy

Try Gunning Fog. It counts the share of words with three or more syllables, so writing full of long words scores higher.

If you're writing technical documentation

Try Coleman-Liau or ARI. They count letters, which is exact. Syllable counts are estimates that can be wrong for technical terms and names.

If you don't know your audience yet

Score against all six and look at the consensus grade. Use the calculator to see all six side by side.

How to use multiple formulas together

Formulas often disagree. A 2013 review found that they varied by up to five grade levels on the same text. Looking at several guards against leaning on one.

The differences can hint at where to look. Treat these as rough clues, not rules:

• SMOG usually runs above Flesch-Kincaid on this calculator, even on plain text. It is set to complete comprehension and its lowest possible score is 3.
• Gunning Fog and SMOG react to words of three or more syllables. If they are high, look at long words.
• Coleman-Liau and ARI measure word length in letters. Flesch-Kincaid and Flesch Reading Ease count syllables.
• All six respond to sentence length. If every score is high, look for long sentences first.

This is what the calculator on the home page does: it computes all six as you type and shows them side by side.

What readability formulas don't measure

Readability formulas count word and sentence length. They do not measure:

• Whether the writing is good. A paragraph of word salad with short sentences and small words scores as easy.
• Whether the writing is true. Misinformation is just as readable as accurate information.
• Whether the writing serves its audience. A sixth-grade reading level isn't right for a journal of theoretical physics.
• Whether the structure makes sense. A document can score perfectly while being incoherent at the paragraph or section level.
• Whether the audience knows the vocabulary. A passage full of medical terms may score as very difficult but be perfectly readable to nurses.
• The reader's prior knowledge. Familiarity with a subject lowers effective reading difficulty in ways no formula can capture.

The formulas are useful because they are reproducible. They mislead when treated as a measure of quality. The right mental model: readability is a constraint to satisfy, not an objective to maximise. Once your text is comfortably readable for your audience, every other quality dimension matters more.

Frequently asked questions