This article discusses issues in measuring lexical diversity, before outlining an approach based on mathematical modelling that produces a measure, D, designed to address these problems. The procedure for obtaining values for D directly from transcripts using software (vocd) is introduced, and then applied to thirty-two children from the Bristol Study of Language Development (Wells 1985) at ten different ages. A significant developmental trend is shown for D and an indication is given of the average scores and ranges to be expected between the ages of 18 and 42 months and at 5 years for these L1 English speakers. The meaning attributable to further ranges of values for D is illustrated by analysing the lexical diversity of academic writing, and its wider application is demonstrated with examples from specific language impairment, morphological development, and foreign/second language learning.