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说明

The Flesch–Kincaid readability tests are readability tests designed to indicate how difficult a passage in English is to understand. There are two tests, the Flesch Reading Ease, and the Flesch–Kincaid Grade Level. Although they use the same core measures (word length and sentence length), they have different weighting factors. The results of the two tests correlate approximately inversely: a text with a comparatively high score on the Reading Ease test should have a lower score on the Grade-Level test.

Flesch reading ease

In the Flesch reading-ease test, higher scores indicate material that is easier to read; lower numbers mark passages that are more difficult to read. The formula for the Flesch reading-ease score (FRES) test is

0.39\left({\frac {\mbox{total words}}{\mbox{total sentences}}}\right)+11.8\left({\frac {\mbox{total syllables}}{\mbox{total words}}}\right)-15.59

206.835-1.015 * (total words / total sentences) - 84.6 * (total syllables / total words). Scores can be interpreted as shown below.

Score	School level	Notes
100.00-90.00	5th grade	Very easy to read. Easily understood by an average 11-year-old student.
90.0–80.0	6th grade	Easy to read. Conversational English for consumers.
80.0–70.0	7th grade	Fairly easy to read.
70.0–60.0	8th & 9th grade	Plain English. Easily understood by 13- to 15-year-old students.
60.0–50.0	10th to 12th grade	Fairly difficult to read.
50.0–30.0	College	Difficult to read.
30.0–0.0	College graduate	Very difficult to read. Best understood by university graduates.

Flesch–Kincaid grade level

These readability tests are used extensively in the field of education. The "Flesch–Kincaid Grade Level Formula" instead presents a score as a U.S. grade level, making it easier for teachers, parents, librarians, and others to judge the readability level of various books and texts. It can also mean the number of years of education generally required to understand this text, relevant when the formula results in a number greater than 10. The grade level is calculated with the following formula:

0.39\left({\frac {\mbox{total words}}{\mbox{total sentences}}}\right)+11.8\left({\frac {\mbox{total syllables}}{\mbox{total words}}}\right)-15.59

The result is a number that corresponds with a U.S. grade level. The sentence, "The Australian platypus is seemingly a hybrid of a mammal and reptilian creature" is an 11.3 as it has 24 syllables and 13 words. The different weighting factors for words per sentence and syllables per word in each scoring system mean that the two schemes are not directly comparable and cannot be converted. The grade level formula emphasises sentence length over word length. By creating one-word strings with hundreds of random characters, grade levels may be attained that are hundreds of times larger than high school completion in the United States. Due to the formula's construction, the score does not have an upper bound.

The lowest grade level score in theory is −3.40, but there are few real passages in which every sentence consists of a single one-syllable word. Green Eggs and Ham by Dr. Seuss comes close, averaging 5.7 words per sentence and 1.02 syllables per word, with a grade level of −1.3. (Most of the 50 used words are monosyllabic; "anywhere", which occurs eight times, is the only exception.)

Coleman–Liau index
The Coleman–Liau index is a readability test designed by Meri Coleman and T. L. Liau to gauge the understandability of a text. Like the Flesch–Kincaid Grade Level, Gunning fog index, SMOG index, and Automated Readability Index, its output approximates the U.S. grade level thought necessary to comprehend the text.
The Coleman–Liau index is calculated with the following formula:

$CLI=0.0588{L}-0.296{S}-15.8\,\!$

L is the average number of letters per 100 words and S is the average number of sentences per 100 words.

Automated readability index
The automated readability index (ARI) is a readability test for English texts, designed to gauge the understandability of a text. Like the Flesch–Kincaid grade level, Gunning fog index, SMOG index, Fry readability formula, and Coleman–Liau index, it produces an approximate representation of the US grade level needed to comprehend the text. The formula for calculating the automated readability index is given below:

$4.71\left({\frac {\mbox{characters}}{\mbox{words}}}\right)+0.5\left({\frac {\mbox{words}}{\mbox{sentences}}}\right)-21.43$

Dale–Chall readability formula

The Dale–Chall readability formula is a readability test that provides a numeric gauge of the comprehension difficulty that readers come upon when reading a text. It uses a list of 3000 words that groups of fourth-grade American students could reliably understand, considering any word not on that list to be difficult. The formula for calculating the raw score of the Dale–Chall readability score is given below:

0.1579\left({\frac {\mbox{difficult words}}{\mbox{words}}}\times 100\right)+0.0496\left({\frac {\mbox{words}}{\mbox{sentences}}}\right)

If the percentage of difficult words is above 5%, then add 3.6365 to the raw score to get the adjusted score, otherwise the adjusted score is equal to the raw score.

Score	Notes
4.9 or lower	easily understood by an average 4th-grade student or lower
5.0–5.9	easily understood by an average 5th or 6th-grade student
6.0–6.9	easily understood by an average 7th or 8th-grade student
7.0–7.9	easily understood by an average 9th or 10th-grade student
8.0–8.9	easily understood by an average 11th or 12th-grade student
9.0–9.9	easily understood by an average 13th to 15th-grade (college) student

Gunning fog index

迷雾指数（The Gunning FOG Index），是由美国教授 Robert Gunning 于1952年提出的指数。该指数可从词数、难度、完整思维的数量和平均句长等方面考察一篇文章的阅读难度。迷雾指数=0.4[(单词总数/句子总数)+（长单词*数量/单词总数）。
该指数常用来测算要轻松读懂某篇文章，需要读者（原指以英语为母语者，中文中不具备长单词，英文中长单词主要是指多音节词）具备多少年的正规教育。一篇文章的指数值是多少，就表示需要几年级的程度才能看得懂。一篇文章的FOG指数值越低，读者就越容易读懂。有人计算过，英国最畅销的日报该指数平均为10，而较严肃的日报该指数则为13—14。职业科学家的科研论文的FOG指数通常在18—22之间，某些科研论文的FOG指数甚至可达40。在2007年，曾有人比较过微软和苹果两家公司掌门人的演说的FOG指数，结果表明，盖茨演说的FOG指数为9.37，这意味着要听懂这场演讲，最少需接受9.37年的教育；与之相比，乔布斯演说的FOG指数仅为6.9。
In linguistics, the Gunning fog index is a readability test for English writing. The index estimates the years of formal education a person needs to understand the text on the first reading. For instance, a fog index of 12 requires the reading level of a U.S. high school senior (around 18 years old). The test was developed by Robert Gunning, an American businessman, in 1952. The fog index is commonly used to confirm that text can be read easily by the intended audience. Texts for a wide audience generally need a fog index less than 12. Texts requiring near-universal understanding generally need an index less than 8.

Fog Index	Reading level by grade
17	College graduate
16	College senior
15	College junior
14	College sophomore
13	College freshman
12	High school senior
11	High school junior
10	High school sophomore
9	High school freshman
8	Eighth grade
7	Seventh grade
6	Sixth grade

SMOG Index
The SMOG grade is a measure of readability that estimates the years of education needed to understand a piece of writing. SMOG is an acronym for Simple Measure of Gobbledygook.
SMOG is widely used, particularly for checking health messages. The SMOG grade yields a 0.985 correlation with a standard error of 1.5159 grades with the grades of readers who had 100% comprehension of test materials.
The formula for calculating the SMOG grade was developed by G. Harry McLaughlin as a more accurate and more easily calculated substitute for the Gunning fog index and published in 1969. To make calculating a text's readability as simple as possible an approximate formula was also given — count the words of three or more syllables in three 10-sentence samples, estimate the count's square root (from the nearest perfect square), and add 3.
A 2010 study published in the Journal of the Royal College of Physicians of Edinburgh stated that “SMOG should be the preferred measure of readability when evaluating consumer-oriented healthcare material.” The study found that “The Flesch-Kincaid formula significantly underestimated reading difficulty compared with the gold standard SMOG formula.”

${\mbox{grade}}=1.0430{\sqrt {{\mbox{number of polysyllables}}\times {30 \over {\mbox{number of sentences}}}}}+3.1291$

* polysyllables: words of 3 or more syllables

Automated readability index

The automated readability index (ARI) is a readability test for English texts, designed to gauge the understandability of a text. Like the Flesch–Kincaid grade level, Gunning fog index, SMOG index, Fry readability formula, and Coleman–Liau index, it produces an approximate representation of the US grade level needed to comprehend the text. The formula for calculating the automated readability index is given below:

4.71\left({\frac {\mbox{characters}}{\mbox{words}}}\right)+0.5\left({\frac {\mbox{words}}{\mbox{sentences}}}\right)-21.43

where characters is the number of letters and numbers, words is the number of spaces, and sentences is the number of sentences, which were counted manually by the typist when the above formula was developed. Non-integer scores are always rounded up to the nearest whole number, so a score of 10.1 or 10.6 would be converted to 11. As a rough guide, US grade level 1 corresponds to ages 6–8. Reading level grade 8 corresponds to the typical reading level of a 14-year-old US child. Grade 12, the highest US secondary-school grade before college, corresponds to the reading level of a 17-year-old. Unlike the other indices, the ARI, along with the Coleman–Liau, relies on a factor of characters per word, instead of the usual syllables per word. Although opinion varies on its accuracy as compared to the syllables/word and complex words indices, characters/word is often faster to calculate, as the number of characters is more readily and accurately counted by computer programs than syllables. In fact, this index was designed for real-time monitoring of readability on electric typewriters.

Score	Age	Grade Level
1	5-6	Kindergarten
2	6-7	First Grade
3	7-8	Second Grade
4	8-9	Third Grade
5	9-10	Fourth Grade
6	10-11	Fifth Grade
7	11-12	Sixth Grade
8	12-13	Seventh Grade
9	13-14	Eighth Grade
10	14-15	Ninth Grade
11	15-16	Tenth Grade
12	16-17	Eleventh grade
13	17-18	Twelfth grade
14	18-22	College

Flesch reading ease

Flesch–Kincaid grade level

Coleman–Liau index

Automated readability index

Dale–Chall readability formula

Gunning fog index

SMOG Index

Automated readability index