Readability Score

A readability test is any form of evaluation of how easy a text is to read: book, article, message, or document.

In practice, it is generally a numerical score used to estimate either reading ease or the education level required to understand the text.

Depending on the formula used, several statistical variables can characterize the text:

$ C $ the number of characters (often excluding spaces)

$ S $ the number of syllables

$ W $ the number of words

$ W_{S3+} $ the number of words with 3 syllables or more (polysyllabic words)

$ W_{C6+} $ the number of words with 6 or more characters (long words)

$ X $ the number of sentences

Not all formulas use all these variables: some avoid syllable counting, which is considered ambiguous depending on the language and pronunciation.

Each readability index relies on different assumptions: some emphasize syllables, others characters or long words.

As a result, the same text can produce different scores depending on the formula used. These differences are not errors but reflect complementary approaches.

The Flesch Reading Ease Score (FRES) is defined by the formula: $$ FRES = 206.835 - 1.015 \frac{W}{X} - 84.6 \frac{S}{W} $$

This score typically ranges from 0 to 100. The higher the score, the easier the text is to read. Indicative interpretation:

The Flesch-Kincaid Grade Level (FKGL) is defined by: $$ FKGL = 0.39 \frac{W}{X} + 11.8 \frac{S}{W} - 15.59 $$

The result corresponds to a US school grade level, i.e. the number of years of education required to understand the text.

The Automated Readability Index (ARI) is defined by: $$ ARI = 4.71 \frac{C}{W} + 0.5 \frac{W}{X} - 21.43 $$

Unlike other indices, ARI uses the number of characters rather than syllables.

The resulting score corresponds to an estimated education level required to understand the text. The higher the value, the more complex the text (see FKGL table above).

The SMOG grade (Simple Measure of Gobbledygook) is defined by: $$ SMOG = 1.043 \sqrt{ \frac{30 \times W_{S3+}}{X} } + 3.1291 $$

where $ W_{S3+} $ is the number of polysyllabic words (3 syllables or more).

The score corresponds to an estimated education level. This formula is considered more reliable for short texts and is often used in public health contexts (see FKGL above).

The Coleman–Liau index is defined by: $$ CLI = 5.88 \frac{C}{W} - 2.96 \frac{X}{W} - 15.8 $$

This index relies only on the number of characters and sentences, making it suitable for automated computation.

The score corresponds to an estimated education level required to understand the text (see FKGL above).

The Gunning Fog index is defined by: $$ GFI = 0.4 \left( \frac{W}{X} + 100 \frac{W_{S3+}}{W} \right) $$

where $ W_{S3+} $ is the number of complex words (3 syllables or more).

The score corresponds to the number of years of education required to understand the text (see FKGL above).

The LIX index (Läsbarhetsindex) is defined by: $$ LIX = \frac{W}{X} + 100 \frac{W_{C6+}}{W} $$

where $ W_{C6+} $ is the number of words longer than 6 characters.

This index does not require syllable counting, making it robust and suitable for several European languages.

Indicative interpretation: < 30: very easy, 30–40: easy, 40–50: standard, 50–60: difficult

The Linsear Write score is based on weighting short and long words in a text sample.

Classical method: count easy words (1–2 syllables), count difficult words (3 syllables or more, counted double), apply the formula on 100 words, then adjust.

Generalized simplified formula: $$ LW = \frac{W_{S2-} + 3 \times W_{S3+}}{X} $$

The resulting score corresponds to an estimated education level (see FKGL above).

This formula can be easily applied to a full text instead of limiting to 100 words, which is useful for automation.