Gunning Fog, SMOG, Coleman–Liau & ARI Calculator

How it works

Fog = 0.4 × [words ÷ sentences + 100 × complex words ÷ words] · SMOG = 1.043 × √(polysyllables × 30 ÷ sentences) + 3.1291 · Flesch Reading Ease = 206.835 − 1.015 × words/sentence − 84.6 × syllables/word · Flesch–Kincaid = 0.39 × words/sentence + 11.8 × syllables/word − 15.59 · Coleman–Liau = 0.0588 L − 0.296 S − 15.8 (L letters and S sentences per 100 words) · ARI = 4.71 × characters/word + 0.5 × words/sentence − 21.43 · Linsear Write r = (easy words + 3 × hard words) ÷ sentences, grade = r ÷ 2 if r > 20, else (r − 2) ÷ 2 · FORCAST = 20 − (one-syllable words per 150 words) ÷ 10

Each readability index estimates the school grade needed to read a passage from surface features, but they weight those features differently. Gunning Fog and SMOG count “hard” words of three or more syllables, which makes them sensitive to vocabulary; SMOG is the usual choice for health information, and Gunning’s rules leave out names, hyphenated compounds and words that reach three syllables only through -es, -ed or -ing. Flesch Reading Ease and Flesch–Kincaid use average sentence length and syllables per word. Coleman–Liau and the Automated Readability Index count letters instead of syllables, so they were easy to compute by machine and tend to punish long but familiar words. Linsear Write and FORCAST are shown for reference: FORCAST ignores sentences, which suits forms and lists. The consensus is the average of Fog, SMOG, Flesch–Kincaid, Coleman–Liau and ARI; a wide spread usually means unusual text. Sentences end at a full stop, question mark or exclamation mark (not after common abbreviations such as Dr. or e.g.), and optionally at a line break, so headings and list items count as sentences. Syllables come from a rule-based counter with a list of irregular words, checked against the CMU Pronouncing Dictionary.

Worked example

For the sample passage (54 words in 3 sentences, 93 syllables, 13 words of three or more syllables, 10 of them complex by Gunning’s rules) the Fog index is 0.4 × (18 + 18.5) = 14.6, SMOG 15.0 (scaled up from only three sentences), Flesch–Kincaid 11.8, Coleman–Liau 13.7 and ARI 12.5, so the consensus is 13.5, college-entry reading. Flesch Reading Ease is 42.9, “difficult”. To reach grade 8 on Flesch–Kincaid with the same words, the average sentence would have to drop from 18 words to about 8, so the long words need to go too.

Sources: McLaughlin (1969), SMOG Grading — a new readability formula, Journal of Reading · Kincaid et al. (1975), Derivation of new readability formulas for Navy enlisted personnel (Flesch–Kincaid, ARI) · CMU Pronouncing Dictionary (syllable check) · Readability Formulas — Linsear Write procedure

Frequently asked questions