Coarse soils are substances made of grains of different shape, size and orientation. In this paper, new massive-measurable grain indexes are defined to develop a simple and systematic theory for the ideal packing of grains. First, a linear relationship between an assemblage of monodisperse spheres and an assemblage of polydisperse grains is deduced. Then, a general formula for the porosity of linearly ordered packings of spheres in contact is settled down by the appropriated choosing of eight neighboring spheres located at the vertices of the unit parallelepiped. The porosity of axisymmetric packings of grains, related to sand piles and axisymmetric compression tests, is proposed to be determined averaging the respective linear parameters. Since they can be tested experimentally, porosities of the densest state and the loosest state of a granular soil can be used to verify the accuracy of the present theory. Diagrams for these extreme quantities show a good agreement between the theoretical lines and the experimental data, no matter the dependency on the protocols and mineral composition. © 2013 AIP Publishing LLC.