Understanding readability scores
Word length, sentence length, one number.
What Flesch and Gunning Fog actually measure, the grade-level intuition they share, and where the numbers are misleading.
Flesch Reading Ease.
Rudolf Flesch's 1948 formula: 206.835 − 1.015 × (words/sentences) − 84.6 × (syllables/words). Higher score = easier. 90-100 is 5th-grade reading; 60-70 is plain English (US Plain Language Act target); 30-50 is academic; below 30 is law-school textbook. The whole formula is two terms: long sentences hurt, long words hurt more.
FRE = 206.835 − 1.015·(W/S) − 84.6·(Syl/W)
Flesch-Kincaid Grade Level.
Same inputs (words per sentence, syllables per word) rearranged to output a US-school-grade number directly. 0.39 × (words/sentences) + 11.8 × (syllables/words) − 15.59. A score of 8 means "average eighth-grader can read it"; 12 means high-school senior. Used by the US Department of Defence (TRADOC requires technical manuals at grade ≤ 12) and many government plain-language guidelines.
Gunning Fog Index.
Robert Gunning's 1952 formula: 0.4 × ((words/sentences) + 100 × (complex_words/words)). Complex words are three+ syllables (excluding proper nouns, compounds, and verb inflections like "indicated" = three syllables). Output is a grade level. Fog tends to score higher than Flesch-Kincaid on the same text because it aggressively counts long words.
A worked score.
A passage: 100 words, 5 sentences, 130 syllables, 8 complex words. Words/ sentences = 20. Syllables/words = 1.30. Complex/words = 0.08. Flesch = 206.835 − 1.015×20 − 84.6×1.30 = 206.835 − 20.3 − 109.98 ≈ 76.6 (plain English). FK Grade = 0.39×20 + 11.8×1.30 − 15.59 ≈ 7.6 (eighth grade). Fog = 0.4×(20 + 8) = 11.2 (eleventh grade). Three formulas; three different answers.
Three scores on one passage
20 words/sentence, 1.30 syllables/word, 8 % complex
Each formula weights the same inputs differently.
FRE 76.6 ; FK 7.6 ; Fog 11.2
= Read consistently across formulas, never single-number
Why the formulas miss things.
They measure surface complexity (length), not actual complexity (concept difficulty). "The cat sat on the mat" scores grade 1 — easy. "The eigenvector spans the kernel" scores grade 6 — also easy by the formula, but incomprehensible to most adults. Readability scores are useful for "is this accidentally hard?" not for "is this conceptually accessible?". Treat them as a smell test, not a quality measure.
What actually helps a reader.
The actions a readability tool implies — shorter sentences, simpler words, fewer subordinate clauses — do help, even if the score is imperfect. Average sentence length under 20 words. Avoid stacked subordinate clauses. Pick concrete nouns over abstract ones. Active voice over passive. These hold across every formula and every audience. The score is the proxy; the practice is the point.