Random walks and their variants are important for describing a wide range of biological phenomena including animal movements, plant dispersal and cellular locomotion. Over a century ago Lord Rayleigh reported an analytical solution for the radial probability density of the simplest random walk. However, to date this result has not been successfully generalized to include the more biologically realistic correlated random walks, persistent random walks, or the more recently characterized superset of directed walks. Of great practical interest is the expected radial displacement following a finite number of steps. We present a closed form, asymptotically exact solution for all simple directed walks described so far. As an approximation, this outperforms all published results over a wide range of angular error magnitudes. This allows the ecologist to differentiate between navigation using internal versus external directional cues based on the observed trajectories, and demonstrates the potential of directed walk theory for providing insights into animal navigation.