A new stereological relationship is derived for the estimation of average size (average width) of a collection of convex particles in a 3D microstructure. The average size is estimated from measurements performed on projected images of the microstructure generated by total vertical projections. The stereological relationship is as follows: D = IC/(2N0beta). D is the average width, ;IC is the average absolute number of intersections between the specifically oriented and regularly spaced cycloid shape test lines and particle boundaries observed in the total vertical projections, N0 is the total number of particles observed in the total vertical projection and the parameter beta is a characteristic of the measurement grid; it has units of reciprocal of length. The result is applicable to any arbitrary collection of convex particles; the particle orientations need not be isotropic. Only 'intersection counts' are required; it is not necessary to measure sizes of the particles in the projected images.