A fluid of hard spherocylinders serves as a simple model system for Liquid Crystals. Within classical density functional theory, the free energy of anisotropic hard bodies can be written in terms of weighted densities solely depending on geometry and position of a single oriented particle. We improve upon this Fundamental Measure Theory by providing the exact low-density limit and proposing more suitable expressions for the dense system. To compare the presented approaches, we discuss the phase diagram of hard spherocylinders as well as interfacial and elastic properties. The analytic results for some simple hard-body systems constrain the general form of the functional. This work provides a sophisticated density functional, which allows to deduce macroscopic phenomena from the geometry of the fluid‘s particles. It is straightforward to describe mixtures and confined fluids or to extend the theory to soft interaction potentials.