📝 Gunning Fog Index

Description

< What is it? >

• Meaning: the Gunning Fog Index is a readability score that estimates the years of formal education needed to understand an English text on the first reading. It uses sentence length and the percentage of complex words.
• Interpretation: lower scores generally indicate easier reading. A score of 12 roughly corresponds to a US 12th-grade reading level.

Key points

< Calculate the score >

• Formula: divide words by sentences to find average sentence length, then add the percentage of complex words and multiply by 0.4.

  $$\text{Fog Index}=0.4\times\left( \frac{\text{Number of words}}{\text{Number of sentences}} +100\times\frac{\text{Complex words}}{\text{Number of words}} \right)$$

• Complex words: generally, words with three or more syllables. Manual counting rules exclude proper nouns, hyphenated words, and two-syllable verbs made three-syllable by -es or -ed endings. See Salish Kootenai College's calculation guide. Automated implementations can differ in how they count sentences, syllables, and exclusions, so use a consistent method when comparing texts.

• Example: a passage contains 100 words, 5 sentences, and 10 complex words after applying the counting rules.

  $$0.4\times(100/5+100\times10/100) =0.4\times(20+10)=12$$

  The passage has an estimated reading level of US grade 12.

< Interpret the result >

• Approximate reading levels: the score estimates reading difficulty; it does not measure an individual reader's ability.

  Score	Approximate reading level
  6	Sixth grade
  8	Eighth grade
  12	End of high school
  16	College graduate

• Limitations: the index measures surface-level difficulty, not factual accuracy, logical clarity, or familiarity with the subject. Technical terms can raise the score even when an explanation is clear. The English formula should not be applied directly to Chinese or other languages without a validated adaptation.

< Use it in RAG and LLM evaluation >

• Readability metric: use the score alongside separate checks for correctness, relevance, and faithfulness. A low Fog score does not establish that an answer is correct or supported by retrieved evidence.
• Audience matters: choose a suitable reading level for the intended audience rather than minimizing the score at the expense of necessary detail. Very short answers provide little text for a stable estimate; the manual calculation guide recommends a sample of at least 100 words.

Related ideas

• Agentic RAG Evaluation covers evaluating answer quality and the retrieval workflow.
• Evaluation Metrics groups metrics used to assess models and applications.

Reference

• Gunning Fog Index calculation guide (Salish Kootenai College)
• Gunning's Fog Index (Guilford College Writing Manual)