Lexical Diversity Calculator

What does lexical diversity measure?

Lexical diversity is how varied the vocabulary of a text is: whether the writer keeps reusing the same words or draws on a wide range. It is used in second-language research as a sign of proficiency, in writing assessment, in clinical linguistics and in authorship studies. This calculator gives four measures, from the simplest and most length-sensitive to the most robust.

The four formulas

Here N is the number of tokens (running words) and V the number of types (different word forms).

• Type-token ratio: TTR = V / N. Easy to understand, but strongly affected by length. See type-token ratio.
• Root TTR (Guiraud's index): R = V / √N. Guiraud (1954) divided by the square root to soften the length effect. It helps, but scores still drift with length.
• MATTR: slide a 50-word window through the text one word at a time, compute TTR in each window, and average them: MATTR = mean(V_window / 50). Because every window has the same size, length no longer biases the score (Covington & McFall, 2010).
• MTLD: read the text word by word, tracking the running TTR. Each time it falls to 0.72, count one factor and reset. A leftover segment adds a partial factor of (1 − TTR) / (1 − 0.72). Then MTLD = N / factors. The calculation runs forward and backward and the two results are averaged (McCarthy & Jarvis, 2010).

Why does TTR depend on text length?

Every text reuses a small set of function words such as the, of and and. In the first 20 words almost everything is new, so TTR is close to 1. By word 500, most new tokens are repeats of words already used, so V grows far more slowly than N. This follows from Zipf's law. The chart in the tool shows the effect on your own text: the line drops steeply at first and then flattens. A short, dull text can therefore score a higher TTR than a long, rich one. MATTR and MTLD were designed to remove that bias.

How to interpret your scores

For all four, higher means more varied vocabulary. The most reliable use is relative: compare your essay this month with last month's, or a learner's writing with a native-speaker text on the same topic. Absolute benchmarks vary with genre, topic and how words are tokenized, so be careful when comparing numbers from different tools.

Limitations

• Word forms, not words. go, goes and went count as three types. Lemmatized counts would be lower.
• Variety is not quality. Good technical and legal writing repeats key terms on purpose. Diversity also says nothing about whether words are rare or advanced; for that, look at lexical density and word frequency.
• Short texts are unstable. Below about 100 words, every measure jumps around.

Related reading

• Productive vocabulary: the words you actually use
• How to improve vocabulary for writing
• Word frequency counter to see which words you repeat
• Readability checker for sentence and word length

How to use this tool

1. Paste an English text into the box. At least 100 words is recommended; a sample is loaded to start.
2. Read the four scores: TTR, root TTR, MATTR and MTLD.
3. Check the chart to see how TTR changes as the text grows.
4. Compare texts of similar length, preferably using MATTR or MTLD.