For the last twenty years, many researchers interested in language acquisition have quantified the receptive and productive vocabulary of infants using CDIs – checklists of words filled in by the caregiver. While it is generally accepted that the caregiver can reliably say whether the infant knows and/or produces a given word, we lack an estimate for words that are not listed on CDI. In this study, we provide a mathematical model providing a link between CDI reports and a more plausible estimate of vocabulary size. The model is constrained by statistical data collected from a population of infants and is validated on a longitudinal study comparing diary report with CDI measures.