Word Frequency Rank Calculator

Work out word frequency rank instantly with clear inputs, formula shown and shareable results.

About Word Frequency Rank Calculator

Zipf's law says frequency is inversely proportional to rank, so the hundredth most common word appears about a hundredth as often as the first. With the top word at 6% of a million word corpus, rank 100 appears roughly 600 times - a relative frequency of 0.06%. The Zipf scale expresses this logarithmically for lexical research.

Formulas

Zipf's law

frequency is proportional to 1 / rank

Zipf value

Zipf = log10(occurrences per billion words), here scaled from the corpus

Worked example

With the default values below, Word Frequency Rank Calculator returns Expected Occurrences In The Corpus of 600. Change any input above and every figure here is recalculated in your browser.

Inputs used

Word frequency rankminimum 1: 100
Corpus sizeminimum 1 words: 1,000,000 words
Frequency of the most common wordaccepts 0–100 %: 6 %

Results

Expected Occurrences In The Corpus: 600
Relative Frequency: 0.0600%
Zipf Value: 5.778
Approximate Cumulative Text Coverage: 27.69%

Step by step

1Values used
2Zipf's law
3Zipf value
4Expected Occurrences In The Corpus= 600
5Relative Frequency= 0.0600
6Zipf Value= 5.778
7Approximate Cumulative Text Coverage= 27.69

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or fees or charges into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does Zipf's law hold at all?

It emerges from any process balancing communication effort against expressiveness, and appears in city sizes and income distributions too.

How many words cover most text?

The top 1000 word families cover about 75% of general English text and the top 3000 about 85%, which is why frequency-ordered vocabulary study is efficient.