Readability formula and readability index: Flesch, Flesch–Kincaid, Fog, SMOG, Coleman–Liau, ARI

A readability formula turns sentence length and word length into a number, the readability index. The best known, Flesch Reading Ease, is 206.835 − 1.015 × (words per sentence) − 84.6 × (syllables per word); the higher the result, the easier the text. Grade-level formulas such as Flesch–Kincaid express the same inputs as a US school grade. Readability is not a direct ranking factor, but it shows where a page is overloaded and readers may give up. You can calculate it with our readability checker, which returns several indices at once.

What the Indices Mean

Classic readability formulas are based on simple features: the average number of words per sentence and the average number of syllables per word. The result is usually related to the level of education required for easy understanding of the text. The formulas were developed for English, so for Russian and other languages, their values are interpreted as guidelines rather than verdicts.

Readability formulas: the six classic indices

Every classic readability formula is built from three or four countable features: ASL, the average number of words per sentence; ASW, the average number of syllables per word; the share of "complex" words (three syllables or more); or the number of letters. The authors fitted their coefficients on English texts and tested them on readers. Below are the formulas as the original sources and standard references give them.

Flesch Reading Ease (Rudolf Flesch, 1948)

FRE = 206.835 − 1.015 × (words / sentences) − 84.6 × (syllables / words)

The scale runs roughly from 0 to 100; higher means easier. Unusual texts can push it outside that range, below zero included. That is a property of a linear formula, not a calculation error.

Flesch–Kincaid Grade Level (Kincaid et al., 1975)

FKGL = 0.39 × (words / sentences) + 11.8 × (syllables / words) − 15.59

Same inputs, but the output is a US school grade. It was developed for US Navy technical manuals.

Gunning Fog (Robert Gunning, 1952)

Fog = 0.4 × [(words / sentences) + 100 × (complex words / words)]

Complex words have three or more syllables. The manual method excludes proper nouns, familiar compounds and words that reach three syllables only through suffixes such as -es or -ed; automated calculators, ours included, usually count every three-syllable word, so their Fog tends to run higher.

SMOG (G. Harry McLaughlin, 1969)

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

Uses only words of three or more syllables. The method assumes a 30-sentence sample, so on short passages it jumps around.

Coleman–Liau Index (1975)

CLI = 0.0588 × L − 0.296 × S − 15.8
L = letters per 100 words, S = sentences per 100 words

Counts letters instead of syllables, because it was designed for machine scoring.

ARI — Automated Readability Index (1967)

ARI = 4.71 × (characters / words) + 0.5 × (words / sentences) − 21.43

Also syllable-free. Like Flesch–Kincaid, Fog, SMOG and Coleman–Liau, it returns a US grade level.

Readability index for other languages

All six formulas were calibrated on English. Russian, Ukrainian, Polish and German words are longer on average, so a clear text in those languages gets a lower Flesch score and a higher grade than an English text of similar difficulty — sometimes a Flesch score below zero. Some languages have their own adaptations. The most cited one for Russian is I. V. Oborneva's version of Flesch:

FRE (Russian) = 206.835 − 1.3 × (words / sentences) − 60.1 × (syllables / word)

For Polish, the Jasnopis project from SWPS University offers a readability tool designed for Polish. For Ukrainian we know of no equally established adaptation, so we do not quote coefficients. Outside English, use any formula as a relative measure: compare two versions of the same text or your own articles with each other.

How to calculate a readability score: a worked example

Take three sentences: "Readability shows how easy a text is to read. It is based on sentence length and word length. Short sentences are easier."

1. Count sentences: 3.
2. Count words: 9 + 9 + 4 = 22.
3. Count syllables: read-a-bil-i-ty = 5, ea-sy = 2, sen-tence = 2, sen-ten-ces = 3, eas-i-er = 3, the rest one each. Total 32.
4. Work out the averages: ASL = 22 / 3 ≈ 7.33 words per sentence, ASW = 32 / 22 ≈ 1.45 syllables per word.
5. Plug them in. Flesch Reading Ease: 206.835 − 1.015 × 7.33 − 84.6 × 1.45 ≈ 76.3 ("fairly easy"). Flesch–Kincaid: 0.39 × 7.33 + 11.8 × 1.45 − 15.59 ≈ 4.4, roughly a fourth-grade text.

Notice how much the syllable term weighs: one extra syllable per ten words lowers Flesch Reading Ease by about 8.5 points. An automated checker estimates syllables with rules, so its count can differ from yours by a syllable or two on words like "sentences" or "easier". On three sentences any score is unstable; for a meaningful result use at least 100 words.

How to interpret a readability index

The grade-level indices (Flesch–Kincaid, Fog, SMOG, Coleman–Liau, ARI) estimate years of US schooling: 8 is a 13–14-year-old, 12 a high-school graduate, 16 and above college level. They usually land within two or three grades of each other. If one formula disagrees sharply, look at what it weighs: long names and jargon inflate Fog and SMOG, many very short sentences pull Flesch–Kincaid down.

• Compare rather than judge. A score is most useful as the difference before and after an edit.
• Benchmark against your own best pages and against the pages ranking for the same query, not against a universal target.
• Check the inputs. If the average sentence runs past 25 words, fix sentences before vocabulary.

What to Do with a Poor Result

1. Break long sentences. The quickest way to improve any index is to put a period instead of a comma.
2. Remove nominalizations. “Verification is being carried out” → “we verify”.
3. Replace terms with understandable ones where the audience is not professional.
4. Add structure: subheadings, lists, tables. Formulas do not see this, but readers do.
5. Read aloud. The place where your breath catches is an overloaded sentence.

What the Formulas Do Not See

Indices count words and syllables but do not understand meaning. A text made up of short sentences filled with terms without explanations will receive an excellent score and remain unclear. Conversely, a complex sentence with a clear example reads easily. Therefore, after edits, it is useful to give the text to someone who is not familiar with the topic — their questions will tell you more than any formula.

Which indices our readability checker calculates

The readability checker takes text or a page URL and returns six formulas: Flesch Reading Ease, Flesch–Kincaid Grade Level, Gunning Fog, SMOG, Coleman–Liau and ARI. For Russian text it adds Oborneva's Flesch. Under the table it shows the base of the calculation — words, sentences and syllables per word — so you can see where a number comes from. A separate block covers text statistics and style metrics: bureaucratic phrasing, filler connectors, repetition, typography and sentence-length variation.

What the checker does not do

• Syllables are estimated: vowel groups with rules for a silent final e and the endings -es/-ed in English, vowel letters in Cyrillic, vowel groups in Polish. Names and loanwords can be off by a syllable.
• Sentence breaks come from punctuation (. ! ? …): headings and list items without a full stop merge into the next sentence, and abbreviations add extra breaks.
• No Dale–Chall score: that formula needs a list of 3,000 familiar words.
• No sense of meaning. Logic, flow and factual accuracy are invisible to formulas — see text coherence, and for fitting an article to a query, article optimization.

Connection to Promotion

An unreadable page loses visitors before they reach the offer — and links do not compensate for this. If a page is on the brink of the top, working with the text and snippet often yields a quicker boost than links: see meta tag verification.