This paper investigates the theoretical basis for estimating vocal-tract length (VTL) from the formant frequencies of vowel sounds. A statistical inference model was developed to characterize the relationship between vowel type and VTL, on the one hand, and formant frequency and vocal cavity size, on the other. The model was applied to two well known developmental studies of formant frequency. The results show that VTL is the major source of variability after vowel type and that the contribution due to other factors like developmental changes in oral-pharyngeal ratio is small relative to the residual measurement noise. The results suggest that speakers adjust the shape of the vocal tract as they grow to maintain a specific pattern of formant frequencies for individual vowels. This formant-pattern hypothesis motivates development of a statistical-inference model for estimating VTL from formant-frequency data. The technique is illustrated using a third developmental study of formant frequencies. The VTLs of the speakers are estimated and used to provide a more accurate description of the complicated relationship between VTL and glottal pulse rate as children mature into adults.