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Vocabulary Size Estimate Calculator

Work out vocabulary size estimate instantly with clear inputs, formula shown and shareable results.

About Vocabulary Size Estimate Calculator

Vocabulary size is estimated by testing a random sample from a frequency band and scaling up. Knowing 68 of 100 words sampled from a 20,000 word band implies about 13,600 words, with a 95% interval from 11,770 to 15,430. Educated native English speakers typically know 15,000-20,000 word families.

Formulas

Vocabulary estimate

estimate = (known / sampled) x band size

Confidence interval

estimate plus or minus 1.96 x sqrt(p(1-p)/n) x band size

Worked example

With the default values below, Vocabulary Size Estimate Calculator returns Estimated Vocabulary Size of 13,600. Change any input above and every figure here is recalculated in your browser.

Inputs used

Words known in the sampleminimum 0
68
Words tested in the sampleminimum 1
100
Words in the frequency band sampledminimum 1
20,000

Results

Estimated Vocabulary Size
13,600 words
Proportion Of The Sample Known
68.00%
Lower Bound Of The 95% Interval
11,771
Upper Bound Of The 95% Interval
15,429

Step by step

  1. 1Values used
  2. 2Vocabulary estimate
  3. 3Confidence interval
  4. 4Estimated Vocabulary Size= 13,600 words
  5. 5Proportion Of The Sample Known= 68.00
  6. 6Lower Bound Of The 95% Interval= 11,771
  7. 7Upper Bound Of The 95% Interval= 15,429

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 2 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 is the interval so wide?

Because a 100 word sample estimating 20,000 carries substantial sampling error. Doubling the sample narrows the interval by about 30%.

What counts as knowing a word?

Usually recognising the meaning of the word family, not productive use. Receptive vocabulary is typically twice the productive size.

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