Abstract Analytical solutions to the minimum uncertainty in the linear traverse technique are presented. These solutions are based on the concept of a perfect operator conducting multiple linear traverses using highly accurate instruments on a well-prepared concrete specimen. The air void parameters calculated from each of the traverses will not be the same and will be distributed around an average value. The uncertainty in the knowledge of the true values of the parameters can be characterized by the dispersion of the multiple values of the parameters obtained. The minimum uncertainty is quantified here as twice the standard deviation (95% confidence interval) of the air void parameter values. The analytical solutions were verified by means of computer simulations of a linear traverse being performed on hardened air-entrained cement paste. Results indicate agreement between the analytical solutions and the computer simulations. The minimum uncertainty in measurements of air content, specific surface, and spacing factor are dependent primarily upon the number of chords in a traverse and secondarily upon the coefficient of variation of the chord lengths. The equations derived herein are applied to the results of a linear traverse conducted on an actual specimen of air-entrained concrete.