A method to determine the uncertainty in reading the location of a concave meniscus in conical graduated volumetric instruments (CGVI) is presented. To estimate the meniscus uncertainty contribution in a volumetric instrument, the cross-section area of the meniscus location is required. Although data for the internal diameter of several volumetric instruments are available in international standards, all of them have cylindrical bodies. Hence, just one internal diameter value is reported for all the readings that can be made on the same apparatus. This work addresses the determination of meniscus reading uncertainty in CGVI through some internal diameters measurements made with an optical comparator. The measurements were used to generate cubic splines to interpolate all the other internal diameters required. With the internal diameter data, proposed formulae allow the computation of the meniscus reading contribution, which had a two percent error at most.