The angular void fraction distribution in randomly packed fixed beds of uniformly sized spheres in cylindrical containers is analyzed by a nondestructive method where the center coordinates of specially prepared spheres are experimentally obtained using X-ray radiography and the angular void fraction distribution is determined geometrically from these center coordinates. The geometrical solution for the local angular void fraction is determined by dividing the packed bed of uniform spheres into a large number of identical wedge-shaped segments. The local angular void fraction in each wedge-shaped segment is expressed in terms of the solid segments coming from each sphere. The angular void fraction distribution is obtained from the local angular void fractions and their angular positions in the cylindrical container. The angular void fraction distribution is presented for four different diameter aspect ratios, D/d, ranging from 2.02 to 7.99. The height aspect ratio, H/d, of each cylindrical container is approximately 7.84. The data show that there is a linear relationship between the mean angular void fraction and the mean overall void fraction. For diameter aspect ratios greater than 6.0 the two mean void fractions are essentially the same. An empirical correlation is presented which accurately predicts the mean angular void fraction as a function of the mean overall void fraction for packed beds with diameter aspect ratios ranging from 2.02 to 7.99.